motion of our star the sun

8/4/2019 Motion of Our Star the Sun

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Motion of Our Star the Sun

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practices.

Now that you have your bearings, let's take a look at the position and motion of the closest

star to us, the Sun. Every day the Sun rises in an easterly direction, reaches maximum height

when it crosses the meridian at local noon, and sets in a westerly direction and it takes the

Sun on average 24 hours to go from noon position to noon position the next day. The ``noon

position'' is when the Sun is on the meridian on a given day. Our clocks are based on this

solar day. The exact position on the horizon of the rising and setting Sun varies throughout

the year (remember though, the celestial equator always intercepts the horizon at exactly East

and exactly West). Also, the time of the sunrise and sunset changes throughout the year, very

dramatically so if you live near the poles, so the solar day is measured from ``noon to noon''.

The Sun appears to drift eastward with respect to the stars (or lag behind the stars) over a

year's time. It makes one full circuit of 360 degrees in 365.24 days (very close to 1 degree or

twice its diameter per day). This drift eastward is now known to be caused by the motion of

the Earth around the Sun in its orbit.

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The apparent yearly path of the Sun through the stars is called the ecliptic. This circular path

is tilted 23.5 degrees with respect to the celestial equator because the Earth's rotation axis is

tilted by 23.5 degrees with respect to its orbital plane. Be sure to keep distinct in your mindthe difference between the slow drift of the Sun along the ecliptic during the year and the fast

motion of the rising and setting Sun during a day.



The ecliptic and celestial equator intersect at two points: the vernal (spring) equinox and

autumnal (fall) equinox. The Sun crosses the celestial equator moving northward at the

vernal equinox around March 21 and crosses the celestial equator moving southward at the

autumnal equinox around September 22. When the Sun is on the celestial equator at theequinoxes, everybody on the Earth experiences 12 hours of daylight and 12 hours of night for

those two days (hence, the name ``equinox'' for ``equal night''). The day of the vernal equinox

marks the beginning of the three-month season of spring on our calendar and the day of the

autumn equinox marks the beginning of the season of autumn (fall) on our calendar. On those

two days of the year, the Sun will rise in the exact east direction, follow an arc right along the

celestial equator and set in the exact west direction.



When the Sun is above the celestial equator during the seasons of spring and summer, you

will have more than 12 hours of daylight. The Sun will rise in the northeast, follow a long,

high arc north of the celestial equator, and set in the northwest. Where exactly it rises or sets

and how long the Sun is above the horizon depends on the day of the year and the latitude of

the observer. When the Sun is below the celestial equator during the seasons of autumn and

winter, you will have less than 12 hours of daylight. The Sun will rise in the southeast, followa short, low arc south of the celestial equator, and set in the southwest. The exact path it

follows depends on the date and the observer's latitude.

Make sure you understand this. No matter where you are on the Earth, you will see 1/2 of the

celestial equator's arc. Since the sky appears to rotate around you in 24 hours, anything on the

celestial equator takes 12 hours to go from exact east to exact west. Every celestial object's

diurnal (daily) motion is parallel to the celestial equator. So for northern observers, anything

south of the celestial equator takes less than 12 hours between rise and set, because most of

its rotation arc around you is hidden below the horizon. Anything north of the celestial

equator takes more than 12 hours between rising and setting because most of its rotation arc

is above the horizon. For observers in the southern hemisphere, the situation is reversed.However, remember, that everybody anywhere on the Earth sees 1/2 of the celestial equator

so at the equinox, when the Sun is on the equator, you see 1/2 of its rotation arc around you,

and therefore you have 12 hours of daylight and 12 hours of nightime everyplace on the

Earth.

Select here for animations of the Sun's motion at two different locations on the Earth

The geographic poles and equator are special cases. At the geographic poles the celestial

equator is right along the horizon and the full circle of the celestial equator is visible. Since a

celestial object's diurnal path is parallel to the celestial equator, stars do not rise or set at the

geographic poles. On the equinoxes the Sun moves along the horizon. At the North Pole theSun ``rises'' on March 21st and ``sets'' on September 22. The situation is reversed for the

http://www.astronomynotes.com/nakedeye/animations/sunmotion.htm





South Pole. On the equator observers see one half of every object's full 24-hour path around

them, so the Sun and every other star is above the horizon for exactly 12 hours for every day

of the year.

Since the ecliptic is tilted 23.5 degrees

with respect to the celestial equator, theSun's maximum angular distance from the

celestial equator is 23.5 degrees. This

happens at the solstices. For observers in

the northern hemisphere, the farthest

northern point above the celestial equator

is the summer solstice, and the farthest

southern point is the winter solstice. The

word ``solstice'' means ``sun standing still''

because the Sun stops moving northward

or southward at those points on the ecliptic. The Sun reaches winter solstice around

December 21 and you see the least part of its diurnal path all year---this is the day of the leastamount of daylight and marks the beginning of the season of winter for the northern

hemisphere. On that day the Sun rises at its furthest south position in the southeast, follows

its lowest arc south of the celestial equator, and sets at its furthest south position in the

southwest. The Sun reaches the summer solstice around June 21 and you see the greatest part

of its diurnal path above the horizon all year---this is the day of the most amount of daylight

and marks the beginning of the season of summer for the northern hemisphere. On that day

the Sun rises at its furthest north position in the northeast, follows its highest arc north of the

celestial equator, and sets at its furthest north position in the northwest.

The seasons are opposite for the southern hemisphere (eg., it is summer in the southern

hemisphere when it is winter in the northern hemisphere). The Sun does not get high up

above the horizon on the winter solstice. The Sun's rays hit the ground at a shallow angle at

mid-day so the shadows are long. On the summer solstice the mid-day shadows are much

shorter because the Sun is much higher above the horizon.

To check your understanding of the concepts in this section (and improve it!), go through the

Motions of the Sun module of the University of Nebraska-Lincoln's Astronomy Education

program (link will appear in a new window). One section of the module will also cover solar

and sidereal time that Astronomy Notes covers in a later section.

http://astro.unl.edu/naap/motion3/motion3.html















Celestial Sphere: The Apparent Motions of the Sun, Moon, Planets, and

Stars

World of Earth Science | 2003 | 700+ words | Copyright

Celestial sphere: The apparent motions of the Sun, Moon, planets, and

stars

The celestial sphere is an imaginary projection of the Sun , Moon , planets, stars, and all

astronomical bodies upon an imaginary sphere surrounding Earth. The celestial sphere is a

useful mapping and tracking remnant of the geocentric theory of the ancient Greek

astronomers.

Although originally developed as part of the ancient Greek concept of an Earth-centered

universe (i.e., a geocentric model of the Universe), the hypothetical celestial sphere providesan important tool to astronomers for fixing the location and plotting movements of celestial

objects. The celestial sphere describes an extension of the lines of latitude and longitude ,

and the plotting of all visible celestial objects on a hypothetical sphere surrounding the earth.

The ancient Greek astronomers actually envisioned concentric crystalline spheres, centered

around Earth, upon which the Sun, Moon, planets, and stars moved. Although heliocentric

(Sun-centered) models of the universe were also proposed by the Greeks, they were

disregarded as "counter-intuitive" to the apparent motions of celestial bodies across the sky.

Early in the sixteenth century, Polish astronomer Nicolaus Copernicus (1473–1543)

reasserted the heliocentric theory abandoned by the Ancient Greeks. Although sparking arevolution in astronomy , Copernicus' system was deeply flawed by the fact that the Sun is

certainly not the center of the universe, and Copernicus insisted that planetary orbits were

circular. Even so, the heliocentric model developed by Copernicus fit the observed data better

than the ancient Greek concept. For example, the periodic "backward" motion (retrograde

motion) in the sky of the planets Mars, Jupiter, and Saturn, and the lack of such motion for

Mercury and Venus was more readily explained by the fact that the former planets' orbits

were outside of Earth's. Thus, the earth "overtook" them as it circled the Sun. Planetary

positions could also be predicted much more accurately using the Copernican model.

Danish astronomer Tycho Brahe's (1546–

1601) precise observations of movements across the"celestial sphere" allowed German astronomer and mathematician Johannes Kepler (1571–

1630) to formulate his laws of planetary motion that correctly described the elliptical orbits of

the planets.

The modern celestial sphere is an extension of the latitude and longitude coordinate system

used to fix terrestrial location. The concepts of latitude and longitude create a grid system for

the unique expression of any location on Earth's surface. Latitudes—also known as

parallels—mark and measure distance north or south from the equator. Earth's equator is

designated 0° latitude. The north and south geographic poles respectively measure 90° north

(N) and 90° south (S) from the equator. The angle of latitude is determined as the angle

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between a transverse plane cutting through Earth's equator and the right angle (90°) of the

polar axis . Longitudes—also known as meridians—are great circles that run north andsouth, and converge at the north and south geographic poles.

On the celestial sphere, projections of lines of latitude and longitude are transformed intodeclination and right ascension. A direct extension of Earth's equator at 0° latitude is the

celestial equator at 0° declination. Instead of longitude, right ascension is measured in hours.

Corresponding to Earth's rotation , right ascension is measured from zero hours to 24 hours

around the celestial sphere. Accordingly, one hour represents 15 angular degrees of travel

around the 360° celestial sphere.

Declination is further divided into arcminutes and arcseconds. In 1° of declination, there are

60 arcminutes (60') and in one arcminute there are 60 arcseconds (60"). Right ascension

hours are further subdivided into minutes and seconds of time.

On Earth's surface, the designation of 0° longitude is arbitrary, an international convention

long held since the days of British sea superiority. It establishes the 0° line of longitude—also

known as the Prime Meridian—as the great circle that passes through the Royal National

Observatory in Greenwich, England (United Kingdom). On the celestial sphere, zero hrs (0 h)

right ascension is also arbitrarily defined by international convention as the line of right

ascension where the ecliptic—the apparent movement of the Sun across the celestial sphere

established by the plane of the earth's orbit around the Sun—intersects the celestial equator atthe vernal equinox.

For any latitude on Earth's surface, the extended declination line crosses the observer's zenith.

The zenith is the highest point on the celestial sphere directly above the observer. By

international agreement and customary usage, declinations north of the celestial equator are

designated as positive declinations (+) and declinations south of the celestial equator are

designated as negative declinations (−) south.

Just as every point on Earth can be expressed with a unique set of latitude and longitude

coordinates, every object on the celestial sphere can be specified by declination and right

ascension coordinates.

The polar axis is an imaginary line that extends through the north and south geographic poles.

The earth rotates on its axis as it revolves around the Sun. Earth's axis is tilted approximately

23.5 degrees to the plane of the ecliptic (the plane of planetary orbits about the Sun or the

apparent path of the Sun across the imaginary celestial sphere). The tilt of the polar axis is

principally responsible for variations in solar illumination that result in the cyclic

progressions of the seasons . The polar axis also establishes the principal axis about which

the celestial sphere rotates. The projection of Earth's geographic poles upon the celestial

sphere creates a north celestial pole and a south celestial pole. In the Northern Hemisphere,

the star Polaris is currently within approximately one degree (1°) of the north celestial pole

and thus, from the Northern Hemisphere, all stars and other celestial objects appear to rotate

about Polaris and, depending on the latitude of observation, stars located near Polaris

(circumpolar stars) may never "set."



For any observer, the angle between the north celestial pole and the terrestrial horizon equals

and varies directly with latitude north of the equator. For example, at 30° N latitude an

observer views Polaris at +30° declination, at the terrestrial North Pole (90° N), Polaris would

be directly overhead (at the zenith) at +90° declination.

The celestial meridian is an imaginary arc from the north point on the terrestrial horizon

through the north celestial pole and zenith that terminates on the south point of the terrestrial

horizon.

Regardless of location on Earth, an observer's celestial equator passes through the east and

west points of the terrestrial horizon. In the Northern Hemisphere, the celestial equator is

displaced southward from the zenith (the point directly over the observer's head) by the

number of degrees equal to the observer's latitude.

Rotation about the polar axis results in a diurnal cycle of night and day, and causes the

apparent motion of the Sun across the imaginary celestial sphere. The earth rotates about thepolar axis at approximately 15 angular degrees per hour and makes a complete rotation in

23.9 hours. This corresponds to the apparent rotation of the celestial sphere. Because the

earth rotates eastward (from west to east), objects on the celestial sphere usually move along

paths from east to west (i.e., the Sun "rises" in the east and "sets" in the west). One complete

rotation of the celestial sphere comprises a diurnal cycle.

As the earth rotates on its polar axis, it makes a slightly elliptical orbital revolution about the

Sun in 365.26 days. Earth's revolution about the Sun also corresponds to the cyclic and

seasonal changes of observable stars and constellations on the celestial sphere. Although stars

grouped in traditional constellations have no proximate spatial relationship to one another

(i.e., they may be billions of light years apart) that do have an apparent relationship as a two-

dimensional pattern of stars on the celestial sphere. Accordingly, in the modern sense,

constellations establish regional location of stars on the celestial sphere.

A tropical year (i.e., a year of cyclic seasonal change), equals approximately 365.24 mean

solar days. During this time, the Sun appears to travel completely around the celestial sphere

on the ecliptic and return to the vernal equinox. In contrast, one orbital revolution of Earth

about the Sun returns the Sun to the same backdrop of stars—and is measured as a sidereal

year. On the celestial sphere, a sidereal day is defined as the time it takes for the vernal

equinox—starting from an observer's celestial median—to rotate around with the celestial

sphere and recross that same celestial median. The sidereal day is due to Earth's rotational

period. Because of precession, a sidereal year is approximately 20 minutes and 24 seconds

longer than a tropical year. Although the sidereal year more accurately measures the time it

takes Earth to completely orbit the Sun, the use of the sidereal year would eventually cause

large errors in calendars with regard to seasonal changes. For this reason the tropical year is

the basis for modern Western calendar systems.

Seasons are tied to the apparent movements of the Sun and stars across the celestial sphere. In

the Northern Hemisphere, summer begins at the summer solstice (approximately June 21)

when the Sun is reaches its apparent maximum declination. Winter begins at the winter

solstice (approximately December 21) when the Sun's highest point during the day is itsminimum maximum daily declination. The changes result from a changing orientation of



Earth's polar axis to the Sun that result in a change in the Sun's apparent declination. The

vernal and autumnal equinox are denoted as the points where the celestial equator intersects

the ecliptic.

The location of sunrise on the eastern horizon, and sunset on the western horizon also varies

between a northern most maximum at the summer solstice to a southernmost maximum at thewinter solstice. Only at the vernal and autumnal equinox does the Sun rise at a point due east

or set at a point due west on the terrestrial horizon.

During the year, the moon and planets appear to move in a restricted region of the celestial

sphere termed the zodiac. The zodiac is a region extending outward approximately 8° from

each side of the ecliptic (the apparent path of the Sun on the celestial sphere). The modern

celestial sphere is divided into twelve traditional zodiacal constellation patterns

(corresponding to the pseudoscientific astrological zodiacal signs) through which the Sun

appears to travel by successive eastwards displacements throughout the year.

During revolution about the Sun, the earth's polar axis exhibits parallelism to Polaris (also

known as the North Star). Although observing parallelism, the orientation of Earth's polar

axis exhibits precession—a circular wobbling exhibited by gyroscopes—that results in a28,000-year-long precessional cycle. Currently, Earth's polar axis points roughly in the

direction of Polaris (the North Star). As a result of precession, over the next 11,000 years,

Earth's axis will precess or wobble so that it assumes an orientation toward the star Vega.

Precession causes an objects celestial coordinates to change. As a result, celestial coordinates

are usually accompanied by a date for which the coordinates are valid.

Corresponding to Earth's rotation, the celestial sphere rotates through 1° in about four

minutes. Because of this, sunrise, sunset, moonrise, and moonset all take approximately two

minutes because both the Sun and Moon have the same apparent size on the celestial sphere

(about 0.5°). The Sun is, of course, much larger, but the Moon is much closer. If measured at

the same time of day, the Sun appears to be displaced eastward on the star field of the

celestial sphere by approximately 1° per day. Because of this apparent displacement, the stars

appear to "rise" approximately four minutes earlier each evening and set four minutes later

each morning. Alternatively, the Sun appears to "rise" four minutes earlier each day and "set"

four minutes earlier each day. A change of approximately four minutes a day corresponds to a

24-hour cycle of "rising" and "setting" times that comprise an annual cycle.

In contrast, if measured at the same time each day, the Moon appears to be displaced

approximately 13° eastward on the celestial sphere per day and therefore "rises" and "sets"

almost one hour earlier each day.

Because the earth is revolving about the Sun, the displacement of the earth along it's orbital

path causes the time it takes to complete a cycle of lunar phases—a synodic month—and

return the Sun, Earth, and Moon to the same starting alignment to be slightly longer than the

sidereal month. The synodic month is approximately 29.5 days.

Earth rotates about its axis at approximately 15 angular degrees per hour. Rotation dictates

the length of the diurnal cycle (i.e., the day/night cycle), and creates "time zones" with



differing local noons. Local noon occurs when the Sun is at the highest point during its daily

skyward arch from east to west (i.e., when the Sun is at its zenith on the celestial meridian).

With regard to the solar meridian, the Sun's location (and reference to local noon) is

described in terms of being ante meridian (am)—east of the celestial meridian—or post

meridian (pm) located west of the celestial meridian.



The stars and their apparent motion.

1) There are about 6,000 stars visible to the naked eye, and about a billion visible using thelargest telescopes. We see the stars only at night, or, rarely, during a solar eclipse but, of

course, they are always up there. It's sometimes useful to distinguish when a star is visible

(only at night) from when it is up (above the horizon), which may be day or night or both.

There are stars in all parts of the sky, and they all move, and they all move together. They

form fixed patterns (constellations), whose form is practically unchanged over centuries. To

us on earth, their motion is as if there were holes punched into a very large (imaginary)

sphere surrounding the earth. The arrangement of holes would be identical to the patterns of

the constellations, and there would be lights behind the holes. If the sphere made a completerotation every 23 hours and 56 minutes, the lights would move exactly as we see the stars

move. Every star would appear to return to the same place in the sky, as seen from the earth's

surface, after 23 hours and 56 minutes, as they actually do. These days we find it easier to

think of the earth as spinning instead of the stars going around, but the idea of this "celestial

sphere" is still useful.

Some stars rise and set. Others are up all the time. These latter are called ``circumpolar''.

Those which rise and set, rise at the same place on the horizon night after night, year after

year. (Where they set doesn't change either). Those which rise in the NE set in the NW.(Think about that statement and try to visualize its meaning.) Those which rise (exactly) in

the east, set (exactly) in the west. Those that rise in the SE set in the SW. (Think about this

one, too.) They all appear to travel in circles, and, depending on where they are in the sky and

where we are on the earth's surface, we see all or part or none of their circles. We see all of

the circles of the circumpolar stars. We see half of the circles of those stars on the equator of

the celestial sphere, less than half for those which lie south of the celestial equator, and more

than half for those which lie north of the equator. For example, looking north, as the stars

come up and go down, they follow the paths shown:

(Just a bit of their paths is obscured by the earth. A star which doesn't set at all is

circumpolar.) But looking south, the paths are:



and we see only the very top of the stars' "circles". The amount of circle cut off determines

the fraction of time the star is not up. Stars near the southern horizon are never up for more

than a few minutes at a time, stars on the equator are up for twelve hours, down for twelve,

and stars in the northern sky are up for more than twelve.

2) The sun's path through the stars: The stars go around once every 23 hours 56 minutes, and

the sun every 24 hours, so the stars are catching and overtaking the sun, and the sun appears

to migrate eastward (to the left , as we look at the sky from the northern hemisphere) through

the stars. After one year, the sun returns to the same place among the stars, and then travels

through them again, repeating year after year and following the same path year after year.

The path the sun takes is called the "ecliptic". This apparant motion of the sun through the

stars happens because the earth moves around the sun. After one year when the earth has

returned to the same place, the sun once again is in front of the same stars.

The planets.

1) Five planets are visible to the naked eye: Mercury, Venus, Mars, Jupiter and Saturn.

Looking just once at the sky, it is hard to tell a planet from a star. The planets rise and set

with the stars. But observed carefully, over several days or weeks, the planets change their

places relative to the stars. The stars are sometimes called "fixed" (i.e.,not moving) stars, to

distinguish them from the "not fixed" (moving) planets. The planets don't wander justanywhere in the sky; they stick pretty close (within 10 degrees or so) to the ecliptic. The part

of the sky around the ecliptic is called the Zodiac. The constellations of the zodiac (the

"what's your sign?" constellations Gemini, Cancer, Leo, Scorpio, etc.) are strung out along

the ecliptic. Each occupies a sector 30 degrees wide. At any specific time, each planet is "in"

one and only one of the zodiacal signs. Unlike the sun and the moon, the planets don't just

move west to east, relative to the stars, a certain fixed number of degrees every day. Rather,

they move sometimes west to east, sometimes east to west, in a complex way. Until the 18th

century, the explanation and prediction of the motions of the planets, together with eclipse

predicting, was probably the main business of astronomers.

2) Two of the more easily observed regularities of planetary motion are:

(a) A planet is "in conjunction" with the sun when it lies in the same line of vision as the sun,

as seen from earth. (i.e., it's directly in front of, or directly behind, the sun.) The time between

two consecutive conjunctions is called a synodic period. For example, the synodic period for

Jupiter is 398 days, and for Venus is 586 days. (In physics, motion which repeats itself is

called ``periodic'' and the length of time it takes to return to its starting point is called its

``period''. Astronomy uses the same word.)



(b) Mercury and Venus are never very far from the sun in the sky. They either set soon after

the sun, or rise just before it. These are called "evening stars" (if they set soon after the sun)

or "morning stars" (if they rise just before the sun). These two planets are never visible in the

night sky for more than a few hours at a time. The other planets may be up at any time.

The Comets

A comet is an object that looks rather large (not simply a dot, like the stars), and kind of

cloudy and blurred. It moves daily with the stars, but changes its position among them fairly

rapidly (as compared, say, to planets). It grows in brightness over a period of weeks or

months, reaches a peak, then subsides and disappears. It may reappear after several or many

years, or it may never reappear. The brightest comets can be seen in the day time.



Lecture 2: The Motion of the Stars and the Sun

The fault, dear Brutus, is not in our stars,

But in ourselves, that we are underlings.

-- WIlliam Shakespeare, Julius Caesar

2.1 The Stars

(Discovering the Universe, 5th ed., §1-0, §1-1)

The human eye can see about 6000 stars without aid.

The picture below covers a field of view of about 70° x 46°, roughly 5% of the

entire sky.

The stars are grouped into constellations.



Most of these are the same ones described by the ancient Greeks and

Babylonians, although the southern hemisphere has many that were "created" by

European explorers a few centuries ago.

The ancients thought of the constellations as representing mythical figures such

as Orion the Hunter and Taurus the Bull.

Nowadays we often think of constellations as "stick figures", consisting of lines

connecting the major stars.



These figures leave out many stars and other objects, including those that require

telescopes to be seen.

So, astronomers now think of a constellation as one of 88 regions that divide up

the sky and completely cover it.

Any object can now be said to lie in one constellation or another.

Many stars have names from Arabic or Greek, e.g. Betelgeuse means "armpit" in

Arabic.

The stars are also given names such as "Alpha Orionis", using letters from the

Greek alphabet followed by the constellation name.

After that, numbers are typically used, e.g. "37 Orionis".

This ordering is typically (but not always) according to brightness.

Extra: an extensive listing of common Star Names and their meanings.

Extra: purchased star names are not recognized by any scientific organization.

See the Naming Stars statement by the International Astronomical Union for

more information on how astronomical names are actually selected.

2.2 The Celestial Sphere

(Discovering the Universe, 5th ed., §1-3)

http://www.ras.ucalgary.ca/~gibson/starnames/



http://www.iau.org/IAU/FAQ/starnames.html



http://www.iau.org/

http://www.iau.org/

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http://www.iau.org/





An important characteristic of the stars is that they have relatively fixed positions

with respect to each other, i.e. the constellations do not change with time.

o The stars do actually move, but this motion is only noticeable to the

unaided eye after a long time, tens of thousands of years or more.

o Nearby stars also exhibit parallax, but this is only visible in a telescope.

Although the stars have many different distances from the Earth, this is not

distinguishable with the naked eye (again, it requires a telescope).

It is therefore useful to think

of the stars as being

"painted" on the interior

surface of a large sphere

centered on the Earth, called

the celestial sphere.

As you are no doubt aware,

the Earth rotates once a day.

We cannot detect this

motion, however, so it

appears to us as if the stars

(and Sun and Moon and

planets) are rotating around

us: they rise in the east and set in the west, once a day.

This is called diurnal motion.

We can imagine diurnal motion as being due to the "rotation" of the celestial

sphere around the Earth.



Picture Information

This motion

can be seen in

the time-lapse

photograph at

the right,

centered on

the north pole

of the

celestial

sphere.

2.3 Latitude and Longitude


It is useful to be able to precisely specify positions on the celestial sphere.

So, a set of coordinates is used that is similar to latitude and longitude on the

Earth.

The system of latitude and longitude was first suggested by Hipparchus, a Greek

astronomer in the 2nd C. B.C.

Recall that the Earth's rotation axis

is a line that passes through the

geographic poles (the North andSouth Poles), and the center of the

Earth.

The Earth rotates around this axis,

leaving the poles fixed.

The equator is a circle on the

Earth's surface that is

perpendicular to the axis and

equidistant from the poles.

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http://www.britannica.com/eb/article?eu=41409&tocid=0







It is a great circle because it is centered on the Earth's center, making it as large

as possible.

The northern hemisphere is the half of the Earth north of the equator, and the

southern hemisphere is the half south of the equator

Any circle parallel to the equator is called a circle of latitude.

The angle (with vertex at the center of the Earth) between a given circle of

latitude and the equator describes that circle and any point on it.

So, the North Pole is at 90° north latitude, the equator itself is 0° latitude, and

Johannesburg, South Africa is roughly 30° south latitude.

Any semicircle passing through the poles is called a meridian of longitude.

One of these is designated as the prime meridian, namely the one passing

through the Royal Observatory in Greenwich, England (just outside London).

The angle (with vertex at the center of the Earth) between a given meridian and

the prime meridian describes that meridian and any point on it.

So, Johannesburg is at 30° east longitude.

Note that 180° west longitude is the same meridian as 180° east longitude.

2.4 Celestial Coordinates


We describe the celestial sphere using a

similar geographical notation:

o The North Celestial Pole is the point

on the celestial sphere directly abovethe Earth's North Pole.

Similarly, the South Celestial Pole is

directly above the Earth's South Pole.

o The star Polaris, in the constellation

Ursa Minor, is located very close to

the North Celestial Pole.

Polaris is therefore also called the North Star.

Question: can you identify Polaris in the photo of the polar sky above?

http://www.opencourse.info/astronomy/introduction/02.motion_stars_sun/index.html#diurnal%20motion






o The celestial equator is directly above the Earth's equator.

Positions on the celestial sphere can also be measured relative to these markings,

although different names are used besides latitude and longitude.

Declination corresponds to latitude,

and is measured in the same way, but

relative to the celestial equator (0°

dec).

The north celestial pole is at 90° north

declination (+90° dec). The south

celestial pole is at 90° south declination

(-90° dec).

Circles of constant declination are all

parallel to the celestial equator.

For any position on the surface of the

Earth, the point on the celestial sphere

that is directly overhead is called the

zenith.

Since the Earth and the celestial sphere are

concentric, simple geometry shows that

the zenith will always have a declination

equal to the latitude of the observer (such

as for Atlanta in the picture).



A star's position along a circle of

constant declination is described

by a second number called right

ascension.

Right ascension corresponds tolongitude, but different units are

used.

Instead of 360°, a circle is broken

into 24 hours of right ascension.

So, 360° = 24 h R.A., 15° = 1 h R.A.,

and 1° = 4 min R.A.

Note that hours of right ascension is a unit of angle, not time, although there is

an obvious connection due to the daily rotation of the celestial sphere.

Right ascension is measured from the celestial meridian, chosen to be 0 h R.A.

(which is also the same as 24 h R.A.)

The celestial meridian is a semicircle connecting the celestial poles and passing

through a particular point on the celestial equator called the vernal equinox

(defined below).

Question: to what position on Earth is the vernal equinox analogous?

Right ascension increases from west to east (note that we are looking at the

exterior of the celestial sphere in the above picture).

With the two numbers of

declination and right

ascension, the position of

any object in the sky can be

precisely described.

Question: what is the

approximate position of the

galaxy shown?

2.5 The Motion of the Sun

http://www.opencourse.info/astronomy/introduction/02.motion_stars_sun/#vernal%20equinox







Although the stars

are fixed relative to

each other, the Sun

moves relative tothe stars.

Once a year, the

Sun traces out a

circle on the

celestial sphere

called the ecliptic.

The ecliptic is tilted

at an angle of 23.5°

with respect to the celestial equator.

(The Moon and planets also move near the ecliptic.)

The Sun crosses the celestial equator at exactly two points, called equinoxes,

from the Latin for "equal nights" (for reasons we'll see later).

The equinox where the Sun ascends from the southern to the northern

hemisphere is called the spring or vernal equinox because the Sun is there on

March 21.

The vernal equinox is chosen to be 0 h R.A.

The Sun again crosses the celestial equator halfway around, at 12 h R.A.

This position is called the autumnal equinox because the Sun is there on

September 23.

The positions where the Sun reaches its highest and lowest points are called

solstices, from the Latin for "the Sun stops" as it changes direction.

The Sun is highest in the sky (in the northern hemisphere) when it is at 6 h R.A.

This position is called the summer solstice because the Sun is there on June 21.

The Sun then has a declination of +23.5°.

The Sun is lowest in the sky (in the northern hemisphere) when it is at 18 h R.A.

This position is called the winter solstice because the Sun is there on December



21.

The Sun then has a declination of -23.5°.

2.6 The Local Horizon


To an observer on the Earth, only one half of the celestial sphere can be observed

at a time.

As a result, in

Atlanta the sky

appears roughly as

shown at the right.

The local horizon,

often just called

the horizon, is the

circle that divides

the Earth and the sky from each other.

The compass directions north, south, east, and west are marked along the

horizon.

North will be underneath the north celestial pole.

When we face north, east is on our right and west is on our left.

Another coordinate system that is commonly used to locate objects in the sky is

the altazimuth system, which is based on the local horizon.

The altitude of an object is the angle between it and the horizon.

The horizon has an altitude of 0° and the zenith has an altitude of 90°.

The azimuth of an object is the angle between it and north, measured clockwise

along the horizon.

North has an azimuth of 0°, east has an azimuth of 90°, south has an azimuth of

180°, and west has an azimuth of 270°.

The local meridian, often just called the meridian, is a semicircle that passes

through the celestial poles and the zenith.

Question: the local meridian is a projection onto the celestial sphere of what



previously described item on the Earth?

Note that the horizon, zenith, and meridian are fixed relative to the observer;

hence the stars and sun will move past them with time.

Question: what happens to these items when the observer moves to a different

location on the Earth?

Simple geometry shows that the

angle between the zenith and the

celestial equator (i.e. the zenith's

declination) must also be the angle

between the north celestial pole and

the north horizon.

Since the zenith's declination is

equal to one's latitude, Columbus was always able to determine his latitude when

he crossed the Atlantic Ocean by measuring the altitude of Polaris.

During the summer, the Sun is located

near the summer solstice, north of the

celestial equator.

In Atlanta, it therefore appears high in

the sky at transit, 33.7° - 23.5° = 10.2°

away from the zenith.

During the winter the Sun is near the winter solstice, south of the celestial

equator.

In Atlanta, it therefore appears low in the sky at transit, 33.7° + 23.5° = 57.2°

away from the zenith.

At a latitude of 23.5° N, the tropic of Cancer, the Sun just reaches the zenith on

the summer solstice.

At 23.5° S, the tropic of Capricorn, it just reaches the zenith on the winter

solstice.

http://www.opencourse.info/astronomy/introduction/02.motion_stars_sun/#zenith



http://www.opencourse.info/astronomy/introduction/02.motion_stars_sun/#North%20Star%20Polaris







Between these latitudes (the tropics), the Sun crosses the zenith twice during the

year.

Tropic is from the Greek for "turning", again describing the Sun's motion at the

solstice.

Cancer and Capricorn are the constellations where the Sun is located at the

solstices (or rather where it was located in 500 B.C...).

The closer the Sun is to the zenith, the more

concentrated its light is on the Earth's surface, so the

more energy it transfers.

This is why summer is warmer and winter is colder,

and why the tropics are warm year round.

2.7 Day and Night


We define the synodic day as the time for the Sun to transit twice.

The synodic day is defined to be exactly 24 hours long, i.e. it is the "day" you are

familiar with.

When the Sun is at transit we say it is 12 noon.



Since this can only happen at one longitude at a time, it used to be that every

town had its own "time zone".

This was a nightmare for the railroads to keep track of, so in the 19th century

they convinced Congress to implement time zones, breaking up the country intofour broad areas that shared the same clock time.

This meant that, for most places, noon no longer occurred when the Sun was at

transit, but it simplified scheduling, especially when broadcast radio and TV came

along.

Atlanta is on the western edge of the Eastern Time Zone, so the Sun doesn't

transit until 12:40 P.M. EST (1:40 P.M. EDT).

As the Sun rises and approaches the meridian, it is "before the meridian" or antemeridian (A.M.).

As the Sun sets toward the horizon, it is "after the meridian" or post meridian

(P.M.).

Because the Sun is so bright, we can only see the stars at night.

These are the stars on the opposite side of the celestial sphere from the location

of the Sun.

But which stars we see depends on the time of the year, because the Sun moves

along the ecliptic!

The Sun moves about one degree, or 4 minutes of RA, along the ecliptic every day

(360°/365 d).

This solar motion means that a particular star will rise (or transit, or set) about 4

min earlier on each subsequent night.

The sidereal day is defined as the time for a star to cross the meridian twice.

The sidereal day is equal to 23 h 56 min 14 s.



Astronomy

This page examines the astronomical background to the various cycles relevant to

Yeats‟s A Vision, particularly the precession of the equinoxes and some of theMoon‟s cycles.

The Great Year and the Precession of the Equinoxes

The Lunar Cycle

Draconic, Saronic and Metonic Cycles

The Great Year and the Precession of the Equinoxes

The whole concept of the „Great Year‟ is based

upon a genuine astronomical phenomenon. The

Earth‟s axis is not fixed and includes a slight

„wobble‟, properly called „nutation‟, usually

compared to that of a spinning-top when it is

slowing down. This means that the poles describe

circles, and that the North Pole does not always

point to the same star or even any star. Currently

Polaris, the Pole Star, appears to be very close tothe „Celestial North Pole‟, but some four thousand

years ago Thuban in Draco was nearer, and in

another twelve thousand years Vega in Lyra will

be nearer.

http://www.yeatsvision.com/Astronomy.html#Prec


http://www.yeatsvision.com/Astronomy.html#Lunar


http://www.yeatsvision.com/Astronomy.html#Saros







The path of the Northern Celestial Pole The path of the Southern Celestial Pole

elestial Poles are projections of the Earth’s poles into the sky. The star closest to the poles varies with the Earth’s nutation: Polaris is currently

orthern Pole Star and there is no star close to the Southern Pole. The circles described by the Earth’s and the Celestial poles are centred on the

ic poles, the Northern one situated in Draco and the Southern one in Doradus.

her site gives a clear astronomical explanation and Keith Powell's site has Java Applet of an Astrolabe which can be used to show the effects of

ssion (by advancing the centuries, the shifting of the stars with relation to the pole, shown by the cross hairs, is perceptible, as is the moveme

Zodiacal stars, for example Regulus or Aldebaran, with respect to the tropical Zodiac, shown by the red circle).

Accompanying this polar symptom of the phenomenon, is the equatorial symptom,

the „Precession of the Equinoxes‟, reputedly first noted by Hipparchus (ca.190

BCE-125 BCE). The equinoxes are determined by the apparent passage of the Sun

over the equator (corresponding with the moment in the Earth‟s orbit when its axis

is a tangent to the ellipse of the orbit) and this happens when the Earth-Sun system

is at the same point in its cycle. The Sun therefore appears to be at the sameposition relative to the starry background each year. However, this shifts very

gradually, by 50.26" a year, or roughly 1° every seventy years. Since the Sun and

Full Moon appear to be about half a degree across their diameter, this shift is just

perceptible within a life-time (½°=30'=1800"). Hipparchus used his own

observations and those of the previous 150 years to calculate the length of the

tropical or solar year at 365.242 days (modern calculations give a mean length

365.242199; these are the figures given by the Encyclopaedia Britannica, others

vary, and because the Earth‟s speed varies, different figures arise for different

reference points).

http://www.nordita.dk/~steen/fysik51/ast/astt8_files/AT40103.htm



http://www.autodidacts.f2s.com/astro/info/prec.html




http://www.yeatsvision.com/Astronomy.html#tropic


http://www.britannica.com/clockworks/article2.html



http://www.geocities.com/calendopaedia/tropyear.htm










The

point

taken

for

measurem

ent of

the

prece

ssion

is

usuall

y the

Vernal Equinox, which in our calendar takes place in March, and which is called

the First Point of Aries, since the Equinox occurred when the Sun was in Aries

when the terms were defined. This point is not arbitrary, representing one of two points where the ecliptic, the Sun‟s apparent path or the plane of the Earth‟s path

round the Sun, crosses the Earth‟s equator. The First Point of Aries marks the

apparent passage of the Sun northwards over the equator and its counterpart, the

First Point of Libra, marks its passage southwards. What is arbitrary is that this

point is taken astronomically as 0 in terms of Right Ascension. The First Point of

Aries is not, however, fixed: in the 2000 years leading up to the start of the

Christian era, the apparent position of the Sun at the moment of the Vernal Equinox

was in the constellation of Aries; it lay on the boundary between Aries and Pisces at

the beginning of the Christian era, and has since then been shifting through Pisces

and is approaching Aquarius (see Great Year).

Yeats himself gives quite a full treatment of the phenomenon of precession in thecontext of the „Great Year‟, and uses the „slippage‟ of the Vernal Equinox

backward through the constellations as the great chronocrator of the gyres‟ cycles

( AV B 252-5; AV A 149-58). As Yeats identifies, the astronomical measurement of

the time taken for a complete circle of the equinox‟s progress against the stars and

the changing of pole-stars is just under 26,000 years (25,786).

The historical equinoctial point, with particular reference to the Temple of Amon-Ra; from E. M.

Plunket, Ancient Calendars and Constellations, one of the books that Yeats consulted for A Vision.

http://liftoff.msfc.nasa.gov/academy/universe/RADEC.HTML



http://www.yeatsvision.com/GreatYear.html



http://www.yeatsvision.com/Biblio.html#Plunket










To the astronomer, for whom the constellations and Zodiac are conveniences and

purely geocentric illusions, this cycle is merely one of many, and, though it must be

taken into account, it has no particular significance. To the astrologer, for whom the

constellations, particularly those of the Zodiac, have meaning and influence, the

phenomenon takes on other dimensions. One of these is that the passage of the Sunbackwards through the twelve signs of the Zodiac, is a kind of year, and since each

sign measures a month of the Sun's annual motion, the Sun‟s precessional passage

through one sign is a kind of month too, albeit some 2,150 years long. Since each

sign is supposed to colour the way in which the Sun operates during the year, it

follows that the Sun‟s precessional passage through a sign will also be coloured by

that sign. See the Astrological Great Year.

A further consequence for astrology is that there are now two Zodiacs in use, that

based on the stars and that based on Earth‟s seasons. The first, called the sidereal

Zodiac (Latin: sidera, stars), is used in India for example, and corresponds largely

with the constellations, though the divisions are regularised to 30° each; the secondZodiac is called tropical (Greek: tropoi, the turning-points of the Sun), the most

widely used one in the West, and the signs of the Zodiac are defined by the position

of the Sun at the equinoxes and solstices, which are the starts of the four cardinal

signs: Aries, Cancer, Libra and Capricorn. The difference between these two

Zodiacs is the effect of the precession (though the exact boundaries and date of

coincidence are disputed), so that tropical Aries now starts at the same point as

sidereal Pisces, and at midsummer, when the Sun is entering tropical Cancer, it is at

the beginning of the constellation of Gemini. See the Astrological Zodiac.

The Phases of the Moon and Eclipses, Andreas Cellarius, Atlas Coelestis (Amsterdam, 1660).

http://www.yeatsvision.com/Astrology.html#GreatYear



http://www.yeatsvision.com/Astrology.html#Zodiac







The Lunar Cycle

The Moon measures two separate kinds of month in its orbit around the Earth. The

independent sidereal month marks the return of the Moon to the same point in the

sky reckoned by its position against the background of the stars (or, confusingly

perhaps, with respect to the equinoctial points of the tropical system). The synodic

month marks the return of the Moon to the same phase in the lunation cycle,

usually New Moon to New Moon (Greek: synodos, meeting, conjunction). The

apparent motion of the Moon taken on its own against the stars is relatively simple;

in contrast the phases trace the relationship between moving bodies, the Moon and

Sun, as seen from a Earth, so that when the same phase or relative position recurstheir „absolute‟ sidereal positions are completely different, and the cycle is greater

than a circle.

TheMoo

n

appe

ars to

move

about

13°

per

day,

thoug

h thedista

nce

varies from less than 12° to more than 15°, so that, if a reference point is taken with

respect to the stars, the Moon returns to the same point in a mean time of 27.32

days. Based on this sidereal cycle, divisions of the circle into 27 or 28 have been

used in various forms of astrology in China, India and Arabia. These are the lunar

equivalent of the signs of the Zodiac and are generally known in European tradition

through the Arabian system of the manâzil al-qumar , the resting-places of the

Moon, usually translated via Latin as „Mansions‟ or „Stations‟. (For more details,

see the Mansions of the Moon.)

The Sun appears to move about 1° per day, in the

same direction as the Moon, and in the opposite

direction to its movement across the sky during the

day. If one takes the star which is hidden by the

New Moon as a reference point, when the Moon

reaches the same star after 27.32 days, the Sun has moved some 27 degrees further

on. After slightly more than two days the Moon makes up the difference, so that the

synodic cycle is an average of 29.53059 days long (Hipparchus reached a figure of

29.53058). Most astrological uses of this cycle tend, therefore, to take the period as

29 or 30 days, usually 29. Examples include, for instance, Thomas Goode‟s popular

booklet The Gipsy Fortune Teller , which gives “Judgements for the 29 Days of the

The Moon's Phase is

lunar phases

http://www.yeatsvision.com/Mansions.html



http://www.calculatorcat.com/moon_phases/moon_phases.phtml






Moon” by W. Parker, Professor of Astrology, and Albert Raphael, writing in 1901,

used 29 days as well in his “Prognostication from the Moon‟s Age”. More

symbolically, Eliphas Lévi‟s The Magical Ritual of the Sanctum Regnum

Interpreted by the Tarot Trumps (translated by William Wynn Westcott) gives 29

“days of the Moon” corresponding to the twenty-two Tarot Trumps and the sevenplanets of the ancients.

Although it has no

direct relevance

here, the Moon‟s

rotation period is

exactly the same as

its sidereal cycle,

and it is because of

this that one side of

its surface isalways hidden

from Earth. In fact,

only 41% is visible

during any one

lunar cycle, but„wobbles‟, called

librations, mean

that 59% of the

surface is visible

over time.

Although there are

twenty-nine or

thirty (solar) days

of the Moon, there

is no fixed number

for the phases of

the Moon. There is

a continuous

change and cycle,

and the most

general division of

that cycle is into

eight: new,

crescent, half,

gibbous, full,

waning gibbous,

waning half, decrescent. Andreas Cellarius, however, in his Atlas Coelestis of 1660,

gives 36 separate phases (see above). Obviously a natural division between the

phases is the Moon‟s appearance on subsequent days, though it appears for different

lengths of time and at different times of day or night, so that 24 hours is not always

the most natural interval.

Athanasius Kircher, Ars Magna Lucis et Umbrae (Rome: Scheus, 1646):

‘The Selenic Shadowdial or the Process of the Lunation’. The spirals show the length of the Moon’s appearance in the sky, with its

rising and setting. The scheme gives the Moon twenty-eight phases and

the engraver, Pierre Miotte, has reversed the appearance of the waxing

and waning moons for the northern hemisphere.








http://www.yeatsvision.com/Biblio.html#WWW






A more logical reference point, perhaps, is the lunar equivalent of noon, its

„southing‟ or culmination, even though the Moon is not always visible because of

the Sun‟s brightness. Because of its movement, the Moon souths 53 minutes later

each day on average, so that „noon‟ to „noon‟ is on average 24.83 hours, which

divided into the length of the synodic month (708.7 hours), gives 28.5, which is notso far from Yeats‟s number.

The reason for choosing the Moon‟s southing rather than moonrise or moonset, is

that like sunrise and sunset these vary with the Moon‟s position in the Zodiac,

although, over the course of the month, they average the same length of „lunar day‟.

But averages are not real except in equatorial latitudes. In more extreme latitudes

the difference depends on the Moon‟s longitude, its apparent position in the Zodiac,

in exactly the same way that the Sun‟s path varies with the time of the year (and

even with respect to the Sun, there are further complications produced by the

Earth‟s tilt and elliptical orbit, see Analemma.com, so that the earliest sunrise is not

on the longest day etc., explained on Analemma‟s page about "Other Phenomena").The constellation of Gemini is always above the horizon for some 17 hours in

Dublin (53°20'N), so that when the Sun‟s position is aligned with Gemini, during

June, the day lasts for 17 hours (and Gemini itself is invisible); the constellation of

Sagittarius, in contrast, is only ever above the horizon in Dublin for some 7 hours,

so that when the Sun is aligned with Sagittarius, in December, the day lasts for 7

hours. The same is true of the Moon, but its cycle is that of the sidereal month

rather than the year. The new Moon is, of course, exactly the same as the Sun, but

the full Moon is its complementary opposite. The full Moon of midwinter

(December in northern latitudes), when the Moon is opposite to the Sun, will

therefore be above the horizon for as long as the Sun at midsummer; and the full

Moon of midsummer will be above the horizon for as long as the Sun at midwinter.The points of relative equality, therefore, are the full Moons in March and

September, the months of the equinoxes, when the Sun and Moon are in the

constellations of Pisces and Virgo.

http://www.analemma.com/Pages/framesPage.html










The Moon’s position around the Zodiac, as the Moon’s ‘seasons’:

Ver , Spring, from Aries to Gemini (A to B); Aestas, Summer, from

Cancer to Virgo (B to C); Autumnus, Autumn or Fall, from Libra to

Sagittarius (C to D); Hyems, Winter, from Capricorn to Pisces (D

to A). The diagram includes the inevitable ‘mistake’ of making

the phases coincide with the Zodiac, though it counts thirty days

for the cycle.

From Athanasius Kircher’s Ars Magna Lucis et Umbrae (1646).

The Full Moon in

March, however, rises

more slowly than the

Full Moon in

September, for those inthe northern

hemisphere. This is

linked to the length of

time which it takes

various points of the

ecliptic, and therefore

also the constellations or

signs of the Zodiac, to

rise. Although they are

all thirty degrees long,

the signs of the Zodiac(either tropical or

sidereal) rise over the

horizon at different

speeds, with the range

of difference becoming

progressively more

extreme as one moves

away from the equator,

and more extreme at the

„equinoctial‟ points than

the „solstitial‟. Takingthe tropical signs used

by western astrology, in

the northern hemisphere

the signs of Pisces and

Aries rise in

considerably less time

than Virgo and Libra (in

the sidereal Zodiac these

are shifted to Aquarius

and Pisces, Leo and

Virgo). In Dublin, forinstance, Aries rises in

less than 50 minutes,

while Libra rises in

some 2 hours and 55

minutes. The so-called

signs of „long

ascension‟ in the

tropical Zodiac are

Cancer, Leo, Virgo,

Libra, Scorpio and

Sagittarius, while those



of „short ascension‟ are

Capricorn, Aquarius,

Pisces, Aries, Taurus

and Gemini. In the

southern hemisphere,the situation is reversed.

As a consequence of

this phenomenon, the

Full Moon in March,

which will be in the

tropical sign of Virgo, if

it comes before the

equinox, or Libra, if it

comes after, and will

rise slowly over the

eastern horizon.

Draconic, Saronic and Metonic Cycles

The Moon‟s behaviour is extremely complex, but other elements in the Moon‟s behaviour

which are relevant here are the Draconic, Saronic and Metonic cycles, which are largely

concerned with longer periods.

The Draconic cycle is linked with the paths of the Moon and Sun, and the two points where

the Moon‟s path crosses the apparent path of the Sun, the ecliptic, which are c alled the

Moon‟s Nodes (the Moon‟s orbit is tilted at an average of 5° with respect to the ecliptic). The

point where the Moon goes from south of the ecliptic to north of the ecliptic is called the

Ascending or North Node and the opposite point the Descending or South Node, these are

traditionally the Dragon‟s Head and the Dragon‟s Tail, respectively, and from this Dragon

comes the adjective „draconic‟. The ecliptic owes its name to the fact that an eclipse of the

Sun or Moon can only happen when the Moon is at these points, where the two bodies

coincide, since otherwise, although the Sun and Moon are in conjunction at the New Moon oropposition at the Full Moon, the Moon‟s path is above or below that of the Sun, so that the

bodies or the Earth‟s shadow do not coincide. The lunar Nodes are usually imaginary points

formed by the planes of the two orbits (except for the moment when the Moon is actually atone of them), and appear to go backwards through the Zodiac, so that a Draconic month

(27.21 days) is slightly shorter than the Moon‟s Sidereal Month (27.32 days), and the Nodes

complete a cycle around the Zodiac in 6793.4 days (18.6 years), the Draconic cycle. (For

further information, see an article by Dwight Ennis, an astrologer, on the astronomy of the

Lunar Nodes.) In Indian astrology, Jyotish, the Dragon‟s Head (Rahu) and Tail (Ketu) are

accorded almost equal status with the planets.

http://www.astrologyclub.org/articles/nodes/nodes.htm





The Dragon of the Lunar Nodes and the Eclipse Points, from Kircher's Ars Magna Lucis et Umbrae

When the Draconic months are taken together with the months of the New Moons (the

Synodic months, 29.53 days), and the months of the Moon‟s farthest distance from the Earth

or perigee (the Anomalistic months, 27.55 days), they all reach a whole number of cycles (or

almost) in 6585.32 days, just over 18 years, which is called the Saronic cycle (see NASA‟s

site for more). Within the Saronic cycle sequences of eclipses repeat themselves, since the

Sun, Moon and Earth return to almost the same relative positions. In consecutive cycles the

later eclipse occurs at roughly the same latitude and for the same duration but about 8 hourslater and 115° of longitude further west. The word is a Greek form of a Babylonian word

shâr or shâru which may mean „universe‟ or the number 3,600. Each saros contains about 43

solar and 28 lunar eclipses, and the slight element of difference in the bodies‟ positions

accumulates so that an eclipse cycle ends after a number of saroses, 71 saroses for solar and

48 for lunar eclipses (see also WordIQ‟s site on the Eclipse Cycle.

Within the Metonic cycle of 19 years the lunar calendar of synodic months reaches a form of

accord with the solar calendar, so that the phases of the Moon occur on the same days of the

solar year, though there is a slight difference and therefore a gradual accumulation of „error‟.

Devised by Meton of Athens ca. 432 BCE, the cycle‟s application is mainly in calendar -

making and is numerical rather than truly astronomical, representing the point where the two

cycles both complete a whole number of cycles, or almost: modern observation shows that 19

solar years are 6939.6 days and 235 lunations are 6939.69 days. The cycle, for instance,

determines the Jewish calendar, where seven intercalary months (First Adar) are added

during each period of nineteen years in order to keep the lunar calendar in line with the

seasons (19 x 12 = 228 and 228 + 7 = 235). It enters the Christian calendar in the date of

Easter, and the so-called „golden number‟ of the year: if the new Moon falls on 1st January,

the year‟s number is 1, and so on.

It is as though innumerable dials, some that recorded minutes alone, some seconds alone,

http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros.html




http://www.wordiq.com/definition/Eclipse_cycle








some hours alone, some months alone, some years alone, were all to complete their circles

when Big Ben struck twelve upon the last night of the century. My instructors offer for a

symbol the lesser unities that combine into a work of art and leave no remainder, but we

may substitue if we will the lesser movements which combine into the circle that in Hegel’s

Logic unites not summer solstice to summer solstice but absolute to absolute. “The Months

and Years are also numbered, but they are not perfect numbers but parts of other numbers.

The time of the development of the universe is perfect, for it is a part of nothing, it is a whole

and for that reason resembles eternity. It is before all else an integrity, but only eternity

confers upon existence that complete integrity which remains in itself; that of time develops,

development is indeed a temporal image of that which remains in itself.” ( AV B 248-49)

Astrology

http://www.yeatsvision.com/Astrology.html





Motion of the Sun

What's covered here:

How does the Sun appear to move over the course of a year?

What defines the seasons?

What causes the seasons?

What is really going on - does the Earth move or does the Sun move?

What is the zodiac, and does it help you predict the future? (NO!!!!)

What are the phases of the Moon?

What causes tides?

What are eclipses?

Once people figured out how the stars moved - or thought they did - they could turn their attention

to the next object - the Sun. Unfortunately, its motion isn't easy to understand. The Sun's path varies

over the course of the year. Sometimes it rises in the northeast, and sometimes it rises in the

southeast. Only on two days does it rise directly in the East and set directly in the West. These

special dates are known as the Equinoxes. To give you their full names, they are the Vernal Equinox,

which is around March 21, and the Autumnal Equinox, which is around September 21. You may

recognize these dates as the beginnings of the seasons of Spring and Autumn. These dates - the

Equinoxes - have nothing to do with the weather; they have to do with the location of the Sun

relative to the Celestial Equator.

Now for the rest of the year, the Sun's path and its rising and setting locations vary. As seen

from Iowa, during the winter the Sun rises in the southeast and sets in the southwest. In the

summer it rises in the northeast and sets in the northwest. There are two days when the rising

and setting locations are at their most extreme (furthest north or furthest south). These days

are also the dates that the Sun travels a path that is also an extreme - very long and high

above the horizon or very short and low to the horizon. These are the days known as the

Winter Solstice, which occurs around December 21 (shortest day), while the other is called,

oddly enough, the Summer Solstice, and it occurs around June 21. Of course, you know

these days as the beginning of Winter and Summer. Like the dates of Equinoxes, they have

really nothing to do with the weather, but with the position of the Sun relative to the CelestialEquator.

One thing you have to remember about the Sun is that it makes it very difficult to see

anything else in the sky when it is out - even though the stars and planets are out there, the

brightness of the Sun is so overwhelming that you don't have much of a chance of see them

until the Sun sets. Which stars would be visible? Which constellations would be visible if we

could turn off the Sun? That depends upon what time of the year you look. If you were to turn

the Sun down so that you could see the stars at the same time that you could see the Sun, you

would notice that the Sun appears to move slowly toward the East from one day to the next -

it moves about 1º each day. In about a month it has moved 30º to the East relative to the stars;

in four months, it will be about 120º east of where it started; and after one year, it will havegone about 360º. That means it is back where it started from, since there are 360º in a circle!



This also explains why we see different constellations in different seasons. As the Sun moves

slowly in front of various constellations, those constellations are no longer visible since they

are too close to the Sun, but constellations far from them are visible, since they will be visible

when the Sun has set or before it rises. Since the Sun appears to move relative to these stars,

it will gradually cover up other stars, and other stars that were previously not visible will

again be viewable as the Sun gets further away from them.

Actually, the folks in the old days could figure out where the Sun would be relative to the

stars by looking at the stars which were visible when the Sun set. They knew which

constellations the Sun covered up and when they were covered up (which time of the year

they were or were not visible). If you were to map out the path of the Sun relative to the stars,

you would see it as a curved line on the Celestial Sphere. Take a look at Figure 1 to see the

path relative to the Celestial Equator. This image is of a flattened out Celestial Sphere, and

the dates mark the locations of the Sun relative to the stars over the course of the year.

Figure 1. The path of the Sun, the ecliptic, shown relative to the background stars and the

Celestial Equator (dec=0). The location of the Sun on the equinoxes and solstices isindicated. Some declination values are also indicated.

As is apparent, the path of the Sun is curved relative to the Celestial Equator. There are times

during the year when it is north of the Celestial Equator and other times when it is south of it.

The declination of the Sun varies throughout the year. (Of course, its R. A. changes as well,

becoming slowly larger each day as the Sun moves eastward relative to the stars, but we'll

pay more attention to the declination). On the days of the Equinoxes, the Sun is right on the

Celestial Equator, so it has a declination of 0º, and on the Solstices, it has the most extreme

value for its declination, 23.5º N on the date of the Summer Solstice and 23.5º S on the

Winter Solstice. The Solstice dates mark when the Sun is at its greatest distance from the

Celestial Equator.

The path the Sun appears to make amongst the stars is known as the ecliptic. Just like the

Celestial Equator, it would make a large circle on the

Celestial Sphere. In fact the ecliptic is a big circle that

is tilted 23.5º relative to the circle made by the

Celestial equator. This is shown in Figure 2.

Figure 2. The location of the Ecliptic on the Celestial

Sphere.



Why is it like this? Why does the Sun travel on its own unusual path? Here is where I get to

shatter all of your delusions - there is no Santa Claus! Oh, wait, that wasn't the delusion I was

supposed to shatter. No, the concept I get to confuse you with is concerning all these motions

I have described so far.

The stars do not move across the sky in approximately 24 hours. The Sun does not move across the sky in approximately 24 hours.

The Sun does not travel amongst the stars and moves slowly eastward each day.

If they aren't moving, what is? WE ARE! Almost all the motions of the sky are due to motions of the

Earth. The main motion is the rotation of the Earth. We spin around once in approximately 24 hours

- that is why we see the stars and Sun appear to move in about 24 hours. What about the Sun

moving eastward relative to the stars over the course of the year? Again, we are doing it - we are

moving around the Sun, and it takes one year for us to get back to where we started. This motion

results in our seeing the Sun in front of stars of different constellations over the course of the year.

Figure 3 illustrates this concept. I'm not saying that nothing in the Universe moves except for theEarth - it's just that the Earth's motion is so large, so close, and so obvious to our senses that it has

the greatest influence on how we see the sky. As you'll see, practically everything in the Universe

moves.

Figure 3. The apparent

motion of the Sun amongst

the stars is due to the

motion of the Earth around

the Sun and our changing

viewpoint. The stars that

we would see behind the

Sun in January would be

different from the stars we

would see behind the Sun in February, March, and every other month, since we are changing the

location from which we view the Sun.

If our motion about the Sun makes it look like the Sun is in front of different stars over the course of

the year, why is the apparent path of the Sun, the ecliptic, tilted relative to the Celestial Equator?

Again, our bad - we're the ones that are tilted. If you hold your head to the side and walk around all

day like that, and if you don't know you have your head tilted, you might think that the entire world

is at an angle.

Since the Earth is tilted, there are times when the tilt has the Sun located north of the

Celestial Equator and other times when the Sun is located south of the Celestial Equator. If

the Earth were not tilted then the Sun would be always located on the Celestial Equator -

which would be pretty boring. The angle of the tilt, 23.5º, is an important number (remember

seeing it in values for the Sun's declination?). Just stay tuned, you'll see it again.

The Earth is tilted over; is that such a big deal? You're darn right it is, because without this

tilt, there would be no seasons. As the Earth goes around the Sun, the tilt of the Earth causesdifferent parts of the Earth to receive different amounts of sunlight. During the months of



May, June and July, the northern hemisphere of the Earth is tilted more toward the Earth than

the southern hemisphere. That gives the northern hemisphere a greater amount of heat and

results in higher temperatures and more sunburns. The opposite is true during November,

December and January, when the Northern hemisphere is tilted away from the Sun. Check

out Figure 4 to see the situation.

Figure 4. The tilt of the Earth and its motion

around the Sun make it appear as if the Sun is

going further to the north (north of the

Celestial Equator) or south (south of the

Celestial Equator) over the course of a year.

Here is an animated image showing how the

surface of the Earth gets different amounts of sunlight depending upon the time of year and

the latitude. Each image is taken about one week apart at the same time of day, and since the

curved surface of the Earth is flattened down in the image the lighting pattern is rather

strangely shaped. You should pay careful attention to the date of each image and how someparts of the Earth are in total darkness some times during the course of the year (the polar

regions). If you want to see how the sunlight falls on the surface of the Earth over the course

of a single day, just click here. In this case, the images are about one hour apart.

On the Summer and the Winter Solstice (around June 21 and December 21 respectively), the

Sun reaches its most northern and southern declinations. People who live at a latitude of 23.5º

north and south of the equator will have the Sun at their zenith at noon only on that day of the

year (June 21 or December 21 depending upon whether they live at 23.5º north or south).

You may have noticed these latitudes marked on maps because of their special relation to the

Sun - these are the Tropics. They are the Tropic of Capricorn, located at 23.5º S, when the

Sun is at the zenith on about December 21, and the Tropic of Cancer, found at a latitude of

23.5º N, where the Sun is found at the zenith on about June 21.

These two lines also limit the locations where the Sun is visible at the zenith. Only between

the latitudes of 23.5º N and 23.5º S would you ever have the Sun directly overhead. Since the

declination system is an extension of the latitude system, the Sun's declination can only have

values within that range as well, between 23.5º N and 23.5º S.

Here is an animation of the Sun relative to the stars. Each image is seven days apart so that

you are seeing how far the Sun moves in a week's time relative to the stars. You'll see that it

moves toward the left (East), and sometimes it goes further to the south and sometimes itgoes further to the north. These are the stars and constellations that the Sun would appear to

be in front of at some time during the year, if we could see the stars located behind the Sun in

the daytime. You may notice that many of the constellation names are familiar to you; gee, I

wonder from where?

We have the Sun appearing to move amongst the stars (but you know that it is really due to

the motion of the Earth around the Sun) along the ecliptic. This path, the ecliptic, goes

through various constellations in the sky. In fact, it goes roughly through 12 rather special

constellations. These constellations are sort of set apart from the rest of the constellations

because of this aspect and we refer to them as the zodiac. This brings up a rather interesting

aspect of astrology - determining what your "sign" is. If you were to look in a newspaper at ahoroscope column, you can determine what your "sign" is by the date of your birth. What

http://www.uni.edu/morgans/astro/course/Notes/section1/geochrone.gif


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http://www.uni.edu/morgans/astro/course/Notes/section1/zodiac_anim.gif







does the date have to do with it? The date is supposed to correspond to the location of the Sun

relative to the stars on the day you were born. Since the Sun appears to move, the stars it is in

front of will change gradually over the course of a year. Whatever constellation (of the

zodiac) the Sun was in front of on the day you were born will tell you what your "sign" is.

This may seem like a straightforward explanation, but it is not very correct.

If you were born today, what would your sign be? This should be the constellation that the

sun is located in today. If the date is August 30, then a person born today would be of the

"sign" Virgo, at least according to what it says in the paper. That means the Sun is in front of

the stars of the constellation of Virgo on August 30. Is it? If you were to go to the star charts

and check, you'd find that the Sun is in the constellation of Leo, not Virgo. In fact, it won't be

in Virgo for some time. By the time it is in Virgo, the astrology columns in the newspaper say

that the Sun is supposed to be in Libra. The Sun is not in the constellation that corresponds to

the dates of the horoscope signs. The Sun is usually located in the previous "sign's"

constellation. All of the signs are off by one. All that time you thought you were a Scorpio,

you were actually born under the sign of Libra - of course, if you believe any of that

astrology crap to begin with, you're in more trouble than I can believe.

Why is the system all screwed up? Is this any way to do business? Of course it is not, and to

be honest, the system was originally set up correctly. When this system was initially set up,

the Sun was in the correct "sign," so that on August 30, the Sun was in the constellation of

Virgo (unlike how it is now). Things have changed since the astrological signs were first set

up by the Babylonians in about 2000 BC. The entire system has been gradually shifting due

to the wobbling of the Earth. The Earth is wobbling? Yes, the Earth sort of acts like a

spinning top - and like a spinning top, it wobbles. We shouldn't say wobbles, since that

doesn't sound too scientific. The term precession is used to describe the wobbling - and it

does sound more scientific. The Earth is slowly precessing, and the pole of the Earth, or the

axis of rotation, will point one way, then another, then back again and so on, just like a

wobbling toy top. This is mainly due to the Moon's gravitational influence.

Originally, on the Vernal Equinox in 2000 BC, the Sun was located in between Aries and

Pisces, so for the next month everyone should be an Aries (March 21 - April 21). Due to the

Earth's precession, the Earth has wobbled so much that the celestial poles and equator are

aligned with different parts of the sky. Things got screwed up, since the location of the

celestial equator defines the location in the sky where the equinoxes occur. Now, on the

Vernal Equinox, the Sun is not at the same location relative to the stars it was in when the

system was set up. It's actually in Pisces and getting closer to Aquarius - which, by the way,

is sort of the basis for that song "Age of Aquarius," but you might be too young to rememberthat golden oldie. The beginnings of the seasons have also slowly changed relative to the

stars, since the equinoxes mark these. It used to be that the first day of spring occurred when

the Sun was in front of the stars of Aries; now it occurs when the Sun is in front of the stars

of Pisces.

I've put together two little movies that show how the changing orientation of the Earth's poles

changes the coordinates. The first movie shows how the location of the celestial pole changes

over time, from about 5000 BC to about 10,000 AD. The celestial pole would be at the center

of the circle for the coordinate grid. This movie only shows part of the entire precession cycle

(about half), but it is still enough to see how the "North Star" changes over time. We're

actually kind of lucky to have the current star at that location now, since for most of the timethere isn't a very bright star near the north Celestial pole. The second movie shows the effect

http://www.uni.edu/morgans/astro/course/Notes/section1/polarprecession.mov



http://www.uni.edu/morgans/astro/course/Notes/section1/equinoxprecession.mov







of the changing alignment on the declination and Right Ascension system. The program is set

up to show where the Sun is on the first day of spring - which is how we set the Right

Ascension value, since that is where it equals 0, and on this date the Sun's declination is also

0. The program causes the grid to tilt a bit, but you'll see that the Sun remains on the 0 RA

and 0 Dec location for each time step, which is 100 years. Our grid of RA and dec must also

change relative to the stars, since we keep changing our alignment to the Sun due toprecession. While it takes a long time to make the shift noticeable, it was known to ancient

astronomers, though of course they didn't know the cause. Nowadays if we want to point our

telescopes with very precise coordinates we have to calculate the effects of precession on the

coordinates - which is pretty small from year to year, but is important if you want very

precise coordinates.

The tilt of the Earth doesn't change much (currently at 23.5º ), but the direction that the pole

points changes. The North pole star (Polaris) will not be there all the time - in a few hundred

years the current north star will be just another star in the northern sky, since it will not be

located at the North Celestial Pole. In the past, other stars would have been called the Pole

star, since they were closer to the North Celestial Pole than Polaris was. During your lifetime, Polaris will be the North Star, since the wobbling is pretty slow. One precession takes

about 26,000 years. Figure 5 shows a simplified view of the precession of the Earth.

Figure 5. The direction that the Earth's pole points

changes slowly so that in the far future it will be pointing to

stars such as Alderamin, Vega, Thuban, and eventually

again Polaris.

Length of a Day - Solar versus Sidereal

How long does it take the Earth to spin around exactly once?

We could figure that out by timing how long it takes something

in the sky to get back to its original position from one day to the next. If we time the motion of the

Sun, we see that it takes almost exactly 24 hours for the Sun to get back to where it started from one

day to the next. I guess that answers it, right? Before we jump the gun, let's time another object - a

bright star, for example. How long does it take a star to get back to the same place in the sky from

one day to the next? Does it take 24 hours for one complete rotation? No it doesn't. It takes 23

hours and 56 minutes. Big deal; that's almost 24 hours; there is only a four minute difference; does it

really matter? You bet your banana skin it matters!The basic upshot is stars rise or set four minutes

earlier each day. If a star rises tonight at 8 P.M., it will rise at 7:56 the next night, then 7:52 the night

after, and then 7:48 the next night. A week after the first rise time, it will rise 4 x 7 = 28 minutesearlier (7:32). In one week, a star will be rising about half an hour earlier - that's a pretty big

difference, so don't ignore those four minutes.

Why is there a four minute difference? Which of these values tells us what the rotation period of the

Earth is? Remember, it is the spinning of the Earth that causes the observed motions of the Sun and

the stars over the course of the day (or night) - but there are two different time spans here - which

one corresponds to the rotation period of the Earth?

Believe it or not, it is the stars, not the Sun, that determine the amount of time for one rotation of

the Earth. While all clocks on the Earth are based on the 24 hour time scale of the Solar Day, it is the



more subtle Sidereal Day (or "star" day) that tells us how fast the Earth is spinning. It takes the Earth

23 hours and 56 minutes to complete one rotation.

Why is there a difference between a Solar day and a Sidereal day? The cause is the motion of

the Earth, in this case our orbital motion around the Sun. To illustrate what's going on, follow

the stick in Figure 6. It starts out one day pointing directly at the Sun (at noon) and at a verydistant star (a star way off to the right).

Figure 6. The time it takes for a position on the Earth to line up with

a distant star (way off to the right) is 23 hours and 56 minutes.

However, the Sun will not be lined up with the position on the Earth,

and an additional four minutes are needed.

After 23 hours and 56 minutes, the Earth will have not only made one complete rotation, but will

have also moved in its orbit. The stick will no longer be pointing toward the Sun, but it will again be

pointing toward the star - this tells us that the Earth has made exactly (no more, no less) onerotation. The time on our watches is 11:56 AM - NOT NOON! - since it is 23 hours and 56 minutes

from the previous day. If you want to see the stick pointing again at the Sun, you must wait four

more minutes for the Earth to spin a little bit further around. When that happens, the time will again

be noon.

You might be a bit amazed at how I was able to easily draw up the motions of the Earth and such so

quickly, but how did I know which way it was going? There is a rule about how things in the solar

system move and you can use it to draw similar diagrams. All major motions in the solar system are

in a COUNTER-CLOCK WISE direction when observed from above the North Pole. This includes the

motions associated with the Earth, the Moon, the orbital motions of the planets, and most of their

rotation motions as well. There are of course some exceptions, but they aren't that common. If you

have to quickly draw any solar system motions, you'll know which way the stuff is moving - again,

there are a few exceptions and I'll tell you what they are if necessary.

The Moon

After figuring out how the stars and the Sun move, it is time to tackle the next object - the Moon.

The motion of the Moon is more complex; it doesn't follow exactly the ecliptic or the celestial

equator, but does make a path around the Earth that is similar to each of those paths. What sets the

Moon apart from the other objects is the fact that its appearance changes - it goes through phases.

The phases of the Moon take 29.5 days to go through an entire cycle.

The phases occur in a very predictable sequence. Here is the order of thephases - New (when you can't see the Moon - it's all dark), Waxing Crescent,

First Quarter (when you see the right half lit), Waxing Gibbous, Full (when

you see the entire lit surface), Waning Gibbous, Third Quarter - also called

Last Quarter (when you see the left side lit up), Waning Crescent, and back to

where we started, New. A picture of the phases is shown in Figure 7. It takes

about one week to go from one major phase to the next - by major phase I mean New, the

Quarters and Full. If the Moon is New today, it will be a First Quarter Moon in about one

week, and a full Moon two weeks from today. The fact that it takes about 29.5 days to go



through the cycle is the reason there are about 30 days in a month, since many ancient

societies used the Moon as a time keeper.

Figure 7. The phases of the Moon as seen from Iowa when the Moon is high in the sky (on

your meridian).

What causes the phases? To figure that out, you need to look at the interaction of the light

source (Sun) and the alignment of the Moon with the Earth. The Moon will have a certain

phase depending upon two things -

1. The location of the Moon in its orbit about the Earth2. The location of the Sun relative to the Earth and the Moon at that time

Don't forget about these two things.

The Quarter Moons occur when the Sun and the Moon are 90º degrees apart in the sky asviewed from the Earth. The New and Full phases occur during times when the Earth, Moon

and Sun are in a straight line. Figure 8 is a composite of the various phases and the location

of the Moon in the sky. Remember, it takes about a week for the Moon to go from one major

phase to the next, so that the view you see during one evening isn't too much different from

the view you see the next night. You may have seen the Moon when it is close to the Full

phase and it may appear to you to be Full for several days, while technically it is only Full at

the time it is in a line with the Earth and the Sun. Also, the way that the Moon is illuminated

gives us the view we see - when most of the lit surface is turned away from the Earth, we see

only a small crescent; when most of the surface is turned toward the Earth, we see the

gibbous phase Moon.

Here is a little java program showing just one phase at a time. You can see how the Moon

looks to you in the sky

depending upon where it is

located in its orbit about

the Earth.

Figure 8. The phases of

the Moon shown at their

locations relative to the

position of the Earth and

the Sun (off to the right).

The phase of the Moon is

determined by its location

relative to the Earth and

Sun. The right side of the

Moon is the only part that is illuminated, since the

http://www.uni.edu/morgans/astro/course/java/MoonPhases/moonphases.html





Sun is off to the right. The phase that we see depends upon how much of that side of the Moon

is visible from the Earth, which depends upon where the Moon is in its orbit about the Earth.

At what time of day does the Moon rise and set? When does it cross your meridian (this is

another way of asking "When is it highest in the sky?")? Well, that will depend on the phase.

The phase will determine the location of the Moon relative to the Sun. Your location relativeto the Sun will determine what time of day it is. Remember, we base our time system upon

the location of the Sun - so if the Sun is on your meridian (high in the sky), then it is Noon at

the part of the Earth you are located at. A person at a location on the opposite side of the

Earth from you would be looking at their watch and noting that it is midnight. Of course,

daylight savings time, and the rather irregular way that time zones are set up, may actually

mean that it is not exactly noon or midnight, but we'll make it simple and assume that it is.

Take a look at the set up shown in Figure 9. If you were at the point labeled "noon," the Sun

would be high in the sky, but the Moon would be on the horizon - it would be rising. If you

were located at the location labeled 6 PM, the Moon would be high in the sky, and the Sun

would be on the horizon; in this case, this is also referred to as the time of sunset. A person atthe midnight position would see the Moon on the horizon, setting. Remember, as viewed

from above the North pole, all motions are counter-clockwise. The Earth will be spinning

around while the Moon remains in about the same position (the first quarter phase location).

All day, anyone seeing the Moon would see a First Quarter moon. To see the Moon you must

be located on the side of the Earth that is toward the Moon, so the person located at the 6 AM

spot wouldn't see the First Quarter Moon, and neither would anyone located at a position

corresponding to 1 AM, 2 AM, 3 AM... all the way until Noon. It would take a day or two for

there to be a noticeable change in the Moon's rising and setting times.

Follow this link to see a little java program showing how the different phases of the Moon

would appear to an observer, when they would be seeing them and what the Moon would be

doing. You can also change the

location of the observer to get

different times of day.

Figure 9. The location of the

First Quarter Moon allows you

to determine when it rises

(noon), sets (midnight) and

when it is high overhead (6

P.M.).

In diagrams like Figure 9, you

would first have to put the Moon

in the appropriate location

relative to the Sun and the Earth

for its current phase, then what you see depends upon where on the Earth you are, and your

time depends upon where you are relative to the Sun. A few basic rules to follow for the

Moon-rising-setting problems -

1. New Moon is in line with the Sun, so it does everything exactly when the Sun does its stuff - rises

at 6 AM, sets at 6 PM, and on the meridian at Noon.2. Full Moon does everything at opposite times relative to the Sun - rises at 6 PM, sets at 6 AM, and

http://www.uni.edu/morgans/astro/course/java/MoonPhases/moonlocation.html






is highest (on the meridian) at Midnight.

3. The Quarter phases are located at a 90 degree angle relative to the Sun.

Once you figure these things out, it is pretty easy to figure out what the Moon is doing and when it is

doing it.

Follow this link to see a little java program that quizzes you about the what the Moon is

doing depending upon the set up. You can determine the answer or just keep guessing until

the program tells you the answer. Either way, you'll eventually get the correct answer and a

diagram showing you the set up.

How long does it take the Moon to orbit once around the Earth? It takes about 27.3 days.

Why not 29.5 days (the time for the phase cycle)?

Again, it has to do with the fact that the Earth is moving around the Sun. Take a peak at

Figure 10. It shows the variation from one Full moon to the next. Remember, the Moon has to

be in a straight line with the Earth and Sun for it to be Full. It starts out lined up with the Sun,

but after 27.3 days, the Moon will have made one complete orbit of the Earth (again be

located to the left of the Earth). At this time is it Full? No, because it is not in a perfect line

with the Sun. You have to wait about 2 more days for it to again be aligned with the Sun and

for it to be Full again.

If you spend a couple of days watching the Moon relative to the stars you'd see that it moves

about 12 degrees each night (since it has to go 360 degrees in about 30 days). You may not

notice the motion of the Moon relative to the stars over the course of an evening since it is

sometimes difficult to see the stars close to the Moon, but you can certainly note the fact that

each night it rises about 50 minutes than the previous night, so the Moon's position relative tothe stars has changed.

Figure 10. The Moon makes one complete

orbit of the Earth in 27.3 days, but it will not

be again Full until a total of 29.5 days has

passed.

One orbit of the Moon takes 27.3 Days. This

would be the Moon's Sidereal Period since it

is the time for the Moon to be back in the same

location relative to the stars, and this is alsothe time for one orbit. How long does it take

for one rotation (spin) on its axis? Does the Moon actually spin on its axis? If you said "no,"

then you're wrong. The Moon does spin on its axis, but it does it in 27.3 days. That's the same

amount of time for one orbit - what does that mean? It means that one side of the Moon

always faces the Earth - that the Moon has one side tidally locked with the Earth.

If you still think that the Moon doesn't spin around think about this - if it didn't, we'd see

different sides of the Moon, not just always the same view. This is shown in Figure 11. If the

Moon did not rotate, it would always have one side pointing in the same direction, as is

shown by a line on it. That line would always be pointing in the same direction in space, but

on the Earth we would see different sides of the Moon as it goes around the Earth. That's not

http://www.uni.edu/morgans/astro/course/java/MoonPhases/moonquiz.html






what we see - we can only see one side of the Moon from the Earth, since that one side is

always pointing toward us.

Figure 11. The Moon makes one

complete orbit in the same

amount of time it takes to makeone rotation. If it didn't rotate,

we'd have the situation on the left,

where different sides of the Moon

would be visible from the Earth

as it goes around the Earth. One

side of the Moon is always facing

the Earth, since the orbital period

is the same as the rotation period.

The time for it to complete a cycle of phases is 29.5 days. I don't think we can just call it that,

can we? No, of course not; we'll have to give it a more "scientific name." We refer to thistime as the Synodic Period. This is just the time it takes for the same Earth-Sun-Moon

alignments to occur again, so it is the time for the Moon to go from one Full Moon to the next

Full Moon, or the time it takes to go from one first quarter moon to the next first quarter

moon - either way, it is 29.5 days.

Tides

You may have noticed that I used the phrase "tidally locked" above. What's that all about?

Living in Iowa, you are probably not too familiar with the phenomena of tides, and just to be

clear, I'm not referring to laundry detergent - what I'm talking about is how the Moon and theEarth pull upon one another and how the consequences of those "pulls" are predictable. Tides

usually refer to the water levels of large bodies of water like the oceans which change near

the shore due to the pull of the Moon (and the Sun) on the water. While we haven't gotten to

gravity yet, you can at least appreciate the fact that a large nearby object like the Moon has a

pretty good gravitational influence on the Earth - it is pulling on the Earth all the time, but the

only thing that we see responding to the pull is the water. This gravitational pull causes a

bulge in the water in the oceans. This bulge follows the motion of the Moon.

The bulges actually occur on both sides of the Earth. The side that's closest to the Moon feels

the strongest pull and bulges out, and the side furthest from the Moon feels a lesser pull and

is sort of left behind (since the center of the Earth also feels the pull, more than the water onthe furthest side of the Earth). This is shown in Figure 12.

Figure 12. The Moon's pull on the water and

the Earth produces bulges on the two sides of

the Earth. The degree of the pull is shown by

the arrows, with the side nearer the Moon

having the largest pull, and the side further

having the smallest pull.

Since it takes only 23 hours and 56 minutes



for the Earth to rotate, coastal locations will pass through the high water bulges (have high

tides) two times each day. Remember, the motion of the Moon is much slower, so the Earth

actually rotates through the tides.

The Sun also has an influence on the tides, but since it is further away, it doesn't pull as strongly.

However, when both the Moon and the Sun are pulling along the same axis, the tides are highest.These tides are known as spring tides, and they have nothing to do with Spring, but they occur when

the Moon is either Full or New. When the Moon and Sun are 90 degrees apart from one another

(during the Quarter phases) the tides are flattened out - these are the neap tides. Tides are very

important for coastal regions, since in some places, you can't get a ship out of the harbor if the

water level is too low. A storm that occurs during high tide could cause coastal flooding (this is often

seen during hurricanes). Knowing when the high tides occur is very important for many places for a

variety of reasons.

Tides also have an important side effect on a planet (and its moon). The rotation rate of the Earth is

changing - it is slowing down - since all of this pulling and tugging is going on. Now you know why it

seems like some days last forever (well, not really). The slow down has already happened with the

Moon; that's why only one side of the Moon faces the Earth. In the past the Moon spun around a lot

faster. The Earth's strong pull on it has locked one side of the Moon to always face the Earth.

Another side effect of this slow down of the rotation of the Earth and the Moon is that the Moon has

been getting further and further away from the Earth very slowly. After a few million years the

length of a day on the Earth will be very long and the Moon will be visible from only one side of the

Earth (and be very far away). We have a long way to go before that happens.

Eclipses

Eclipses are events that occur when one object blocks another, usually resulting in something

getting darker or appearing fainter than before. The path of the Sun, the ecliptic, is so named

because that is where eclipses are seen to occur. The Sun, the Earth and the Moon all participate in

two different main eclipse types - Lunar Eclipses and Solar Eclipses.

Lunar eclipses occur only when the Moon is Full and it is located on or very close to the ecliptic. In

this case the shadow of the Earth falls upon the Moon, making it dark. Why don't we have lunar

eclipses during each Full Moon? The orbit of the Moon is slightly tilted with respect to the Earth's

orbit about the Sun, about 5 degrees. For there to be an eclipse the Moon has to be at the point

where the planes of the orbit of the Moon and Earth intersect - the nodes. This also explains why wedon't have eclipses every month - the orbit of the Moon is not aligned exactly with the ecliptic;

sometimes it is above it, sometimes below it. To further complicate things, the orbit of the Moon

"wobbles" with a period of 18.6 years. This aspect means that eclipse paths repeat with a period of

18.6 years. When you view the solar eclipse maps at the end of this set of notes, you will see the

repeating eclipse paths - those

that have the same shape.

Figure 13. The tilt of the

Moon's orbit means that most



of the time it isn't lined up for an eclipse to occur.

Is the Moon entirely dark during a lunar eclipse? No, you can still see it, though it is dimmed

and often colored. Why? The Earth has an atmosphere which tends to bend light around the

Earth, and this falls upon the Moon. The light does get discolored, though; often a red, orange

or brown color is seen. This really scared the heck out of folks in the old days when theydidn't know what was going on, which was most of the time.

Figure 14. A multiple exposure

image of a lunar eclipse. When the

eclipse first starts out the brightness

of the Moon is so great that only

short exposures are used. The

umbra, which is the darkest part of

the shadow, doesn't appear to have

any color in these images. Only at

mid-eclipse is the Moon darkened enough so that the color of the

umbra is visible. Eclipse

photograph copyright 2000 by Fred

Espenak courtesy of

www.MrEclipse.com.

There are two regions of the shadow, the umbra and penumbra. These correspond to the darkest

part of the shadow and the not completely dark part respectively. These are shown in Figure 15. If

you were on the Moon, and looked back toward the Earth (and the Sun), you would see the Sun

blocked out if you were in the umbra, while if you were in the penumbra, some part of the Sun'ssurface would still be visible to you.

Figure 15. The shadows, umbra

and penumbra, cast by the Earth

during a lunar eclipse. The Moon

is experiencing a total lunar

eclipse here since it is in the

umbra - the darkest shadow.

Lunar eclipses can be full - the Moon passes completely through the Earth's umbral shadow,

partial - it passes only through part of the umbral shadow, or penumbral - it only passesthrough the penumbra. The best are of course the full eclipses, which can last for hours as the

Moon traverses the entire length of the umbral shadow, while the least exciting are the

penumbral eclipses, which are really difficult to see since the sunlight that falls on the Moon's

surface is so bright to begin with. Here is a table of lunar eclipses that will be occurring over

the next few years - some of which are visible from Iowa. Here is an animation showing how

the December 2010 lunar eclipse will look from Iowa. The locations of the umbra and

penumbra shadows are indicated. The locations of the Earth's shadows appear to vary slightly

in the animation, since the Earth is moving as well as the Moon.

http://www.mreclipse.com/MrEclipse.html


http://www.uni.edu/morgans/astro/course/Notes/section1/lunareclipses.html



http://www.uni.edu/morgans/astro/course/Notes/section1/2010lunar.mov








Figure 16. The shadows, umbra

and penumbra, cast by the

Earth during a lunar eclipse are

seen as circles here. The

shadows that the Earth casts

look like circles, since it is asphere. The Moon's path is

shown for the three different

types of lunar eclipses. The top

path is for a penumbral eclipse,

where the Moon never passes

into the umbra, but is only in the

penumbral shadow. The central

path shows a total lunar eclipse,

where the Moon passes entirely

through the umbral shadow. The bottom path is for a partial eclipse, where only a part of the

Moon's shadow goes into the umbra. It is possible to have partial penumbral eclipses, but those are so lame they aren't worth mentioning.

While not as spectacular as solar eclipses, lunar eclipses are still rather neat to see - though

they are best viewed when there are no clouds in the sky. There are usually about 2 lunar

eclipses each year, though they are not always visible from the US. To see the eclipse you

have to see the Moon at the time of the eclipse, so many people can see one. Of course it is

possible to predict the dates and times of eclipses. The next "good" lunar eclipses visible

from the US will occur on the night of December 21, 2010.

Much more spectacular are solar eclipses. These occur only when the Moon is New and

located on the ecliptic (it is on the node). Just by chance the Moon and the Sun have about the

same angular size - they are both about 1/2 degree in size. The size of the shadow - the umbra

- is very small, because the Moon can only just barely cover up the Sun. This is illustrated in

Figure 17.

Figure 17. The shadows cast by the Moon during a Solar eclipse. Only at the point on the

Earth where the umbra reaches the surface would you experience a total solar eclipse.

To experience a total solar eclipse, you must be located in the narrow umbral path of

darkness. This is often referred to as the path of totality. It is so narrow (at most only about

300 km wide), and the motions of the Sun, Moon and Earth are rather fast, that you will onlyexperience at most about seven minutes of totality. During the moments before the total

eclipse, various features can be seen; amongst them is the diamond ring effect, where it

appears as if the last bit of sunshine makes a diamond ring in the sky. Once the main surface

of the Sun is covered up, the outer layers of the Sun, such as the chromosphere and corona,

are visible.



Figure 18. The diamond ring

effect. Only a fraction of the

surface of the Sun is visible

here, but it is enough to cast

a bright light through the

valleys along the edge of the Moon. Eclipse photograph

copyright 2001 by Fred

Espenak courtesy of

www.MrEclipse.com.

You were probably told in

elementary school "Don't

ever look at a solar eclipse -

you'll go blind!" or something

like that. That's not entirely

true, though you have a prettygood opportunity to really screw up your eyes if you are really stupid. As a general rule you

should never stare at the Sun, and most of the time people don't do that. When people hear

that there is going to be an eclipse, they get pretty stupid and think "Gosh, I'll have to use my

binoculars to see the eclipse!" or "I better get my telescope out to see the eclipse!" No, no, no,

no, no! If you look at the sun with binoculars or a telescope at any time, not just when an

eclipse is occurring, you will probably permanently damage your eyes. You should never

look at the Sun with any sort of instrument that magnifies it. Cameras are also a no-no, since

their lenses can magnify the Sun and this is just as bad as using a telescope. Looking at the

Sun with binoculars or a telescope is equivalent to frying ants on the sidewalk with a

magnifying glass, only in this case, the ants are your eyeballs. Don't do it!

Even if you don't use anything to magnify the Sun, and decide to watch it with your

sunglasses, that's pretty stupid as well. Even polarized glasses won't protect you while staring

at the Sun. You've probably glanced at the Sun for short periods of time, and you're left with

an "afterglow" of its image. If you do that too much, that "afterglow" won't go away - ever.

During eclipses people can get proper eye protection to allow them to safely view the Sun.

These filtered glasses are available at low cost and provide a safe method of viewing the Sun.

You may have heard of other things that can be used,

but not all of those things are reliable.

Figure 19. Eclipse glasses, with special filters, are thebest way to view an eclipse safely.

Now after all of this stuff about not staring at the Sun, I

have to tell you that there is a time when it is okay to

look at the Sun with a regular telescope - during

totality, when the Moon completely covers up the Sun.

At no time before total coverage and at no time after is

it safe, only when the surface of the Sun is completely

blocked from view. While the surface of the Sun is blocked, it is possible to see the other

layers of the Sun's atmosphere, the big fluffy corona and the pinkish chromosphere.

Whether you actually see these layers depends upon what the Sun is doing - how "active" itis. People who observe and photograph eclipses are very careful to time their viewing.






Usually they find the exact time for the start and finish of totality and use stop watches or

alarms to prevent themselves from damaging their eyes. Before totality, they have to use

special cameras or telescope filters to view and photograph the Sun safely, but when totality

hits, they take these filters off and start snapping pictures like crazy.

Figure 20. A series of imagesshowing a total solar eclipse.

The images are combined

together to show the eclipse in

different stages, with totality

occurring in the middle image.

Eclipse photograph copyright

2001 by Fred Espenak courtesy

of www.MrEclipse.com.

It is also possible that the

Moon's umbral shadow may noteven reach the Earth. This will

occur when the Moon is slightly

further away and its angular size

is slightly too small to completely cover up the Sun. In this case, only the penumbra of the

eclipse reaches the Earth. This produces an Annular eclipse. A viewer of the eclipse would

see the Sun as a ring about the Moon. Click here to see animation of an annular eclipse. There

are also eclipses that change from one type to another. These are hybrid eclipses which can

start out as an annular eclipse and then become a total eclipse or the other way around. You

have to remember that the circumstances for a total eclipse to occur are very precise, and

often these conditions can't always be met.

An annular eclipse is a type of partial eclipse, where only part of the Sun is covered up.

During a total solar eclipse, you need to be in the path of totality to get the full, dark eclipse.

Otherwise, you will only experience a partial eclipse. Only those people who are in exactly

the right place at exactly the right time will get to see anything exciting (weather permitting),

because of the rather special arrangement for a solar eclipse, especially a total solar eclipse.

For this reason, many people will go to a lot of trouble and money to be at exactly the right

place to see a total solar eclipse.

Eclipses are amongst the most popular astronomical events for non-astronomers to view and

you can spend a lot of money traveling around the world to view various eclipses. There areabout two solar eclipses each year, but they are sometimes only partial or annular eclipses.

Often the path of totality is over oceans, so it isn't always easy to view them. Figure 21 shows

the path of some recent past eclipses and those that are coming up over the next few decades.

As can be expected, many of the eclipse paths are located over oceans since the Earth is

covered with so much water. A table of upcoming solar eclipses can be found here.

Unfortunately, you'll have to wait until 2012 for the next solar eclipse to be visible in Iowa,

and even then it will only be a partial eclipse.

If you want to wait for one to come to you, then you have a bit of a wait. The next total solar

eclipse visible from the US will be Aug. 21, 2017. Don't forget that date! It should be a

seriously fun time! Here is a computer simulation showing how it will look from UNI on thatdate. To see the total eclipse, you'll have to head south.




http://www.uni.edu/morgans/astro/course/Notes/section1/annularanim.gif



http://www.uni.edu/morgans/astro/course/Notes/section1/solareclipses.html



http://www.uni.edu/morgans/astro/course/Notes/section1/2017.mov









Eclipses of any type are fairly rare since they require a specific set of conditions. And there

are quite a few things that factor into eclipses (both solar and lunar eclipses). You have the

variation in the distance of the Moon and the Sun from the Earth, and the changing alignment

of the Moon's orbit relative to the ecliptic. Eclipses listed in the tables noted above are not

very common, with only a handful of eclipses each year. So the next time one is visible from

your location, make sure you take the time to view it - you will have to wait a long time forthe next one!

Figure 21. Paths of total solar eclipses are shown (on left) and annular eclipses (on the right). If you

click on the image you'll see a larger version of the map. For the total eclipse maps, an observer

would have to be located in the dark path to experience a total solar eclipse. To see the Sun

"surround" the Moon during an annular eclipse, and observer would have to be located along the

paths shown in the map on the righ. Eclipse maps courtesy of Fred Espenak - NASA/Goddard Space

Flight Center. For more information on solar and lunar eclipses, see Fred Espenak's Eclipse Home

Page: http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html

http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html



http://www.uni.edu/morgans/astro/course/Notes/section1/aneclipse.gif

http://www.uni.edu/morgans/astro/course/Notes/section1/eclipsemaps.gif

http://www.uni.edu/morgans/astro/course/Notes/section1/aneclipse.gif

http://www.uni.edu/morgans/astro/course/Notes/section1/eclipsemaps.gif




Celestial Sphere: The Apparent Motions of the Sun, Moon, Planets, andStars

World of Earth Science

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Celestial sphere: The apparent motions of the Sun, Moon, planets, and

stars

The celestial sphere is an imaginary projection of the Sun , Moon , planets, stars, and all

astronomical bodies upon an imaginary sphere surrounding Earth. The celestial sphere is auseful mapping and tracking remnant of the geocentric theory of the ancient Greek

astronomers.


universe (i.e., a geocentric model of the Universe), the hypothetical celestial sphere provides

an important tool to astronomers for fixing the location and plotting movements of celestial

objects. The celestial sphere describes an extension of the lines of latitude and longitude ,



around Earth, upon which the Sun, Moon, planets, and stars moved. Although heliocentric(Sun-centered) models of the universe were also proposed by the Greeks, they were


Early in the sixteenth century, Polish astronomer Nicolaus Copernicus (1473 – 1543)

reasserted the heliocentric theory abandoned by the Ancient Greeks. Although sparking a

revolution in astronomy , Copernicus' system was deeply flawed by the fact that the Sun is


circular. Even so, the heliocentric model developed by Copernicus fit the observed data better

than the ancient Greek concept. For example, the periodic "backward" motion (retrograde

motion) in the sky of the planets Mars, Jupiter, and Saturn, and the lack of such motion for

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Mercury and Venus was more readily explained by the fact that the former planets' orbits

were outside of Earth's. Thus, the earth "overtook" them as it circled the

Why is there apparent motion of the stars and sun.?Why is there apparent motion of the stars and sun.

still researching, can't find much and could do with a little help.

thanks in advance.

1 year ago

The earth spins round in 24 hours, that's why the sun, moon and stars all seem to rise in the east and

travel across the sky and set in the west

Sun and Star Motion, Time, Moon Phases, Eclipses

Apparent Motion of the Sun and the Seasons

Earth Science

Mr. Sweeney

LICHS

5.17.06

.. How does the sun appear to move?

Do Now: Describe the apparent motion of the sun over the period of a day

.

Apparent Motion of the Sun

The sun appears to rise in the east and set in the west because Earth rotates from west to east

The sun reaches its maximum altitude (height) in the sky at solar noon

Apparent Motion of the Sun

The altitude of the sun at solar noon depends on the time of year and the latitude of the

observerThe closer the observer is to the equator, the higher the sun is at solar noon



The altitude of the sun is only directly overhead (90°angle) near the equator between the

tropics of Capricorn and Cancer

Therefore, in the northern hemisphere, the sun appears to move across the southern sky

In the southern hemisphere, the sun appears to move across the northern sky

The Seasons

Earth Science

Mr. Sweeney

LICHS

5.18.06

.. Why does the Earth experience seasons?

Do Now: Name the areas on Earth where the sun can be directly overhead (90° angle).

The Seasons

Earths axis of rotation is tilted 23.5°

The direction of Earths tilt changes as it revolves around the sun

This affects the location of the suns direct rays

In the northern hemisphere,

Summer occurs when the Earth is tilted toward the sun and its rays are the most direct

Winter occurs when the Earth is tilted away from the sun and its rays are the least direct

Spring and Fall occur in between summer and winter when the suns rays are directly over theequator

In the southern hemisphere, the seasons occur at opposite times of the year

Ex: It is winter in the S. hemisphere when it is summer in the N. hemisphere

Solstices

In the northern hemisphere the sun is

Highest in the sky on the summer solstice (June 21)

Lowest in the sky on the winter solstice (Dec. 21)

Equinoxes

Over the equator on the vernal (spring, Mar. 21) and autumnal (fall, Sept. 23) equinoxes

Apparent Motion of the Stars

Earth Science

Mr. Sweeney

LICHS

5.19.06

.. How do the stars appear to move?



Do Now: Describe the Earths tilt direction and the angle of the suns rays during summer and

winter in the northern hemisphere.

Apparent Motion of the Stars

The stars also appear to move from east to west because of the Earths rotationPolaris (north star) is located above the north pole

Never appears to move

Nearby stars appear to revolve around Polaris

Altitude of Polaris is equal to the latitude of the observer

Constellations

A constellation is a group of stars that form a pattern

Remain fixed (motionless) relative to our solar system

Used to locate celestial objects

Different constellations are visible at different times of the year

Provides evidence of Earths revolution

Models Explaining Apparent Motion

The geocentric model places Earth at the center of the solar system

The sun, other planets, moon, and stars revolve around Earth at different speeds along

circular orbits

Doesnt explain retrograde motion very well

The heliocentric model places the sun at the center of the solar system

Earth rotates on an axis and revolves around the sun along with the other planets

The moon revolves around the EarthEarths rotation explains apparent motion of the sun, planets, and stars

Originally stated that planets revolved at constant speeds along circular orbits

Later, it was realized that planets revolved at different speeds along elliptical orbits

Earths Rotation and Time

Earth Science

Mr. Sweeney

LICHS

5.22.06

.. How is time measured?

Do Now: Explain the two main differences between the geocentric and heliocentric models of

the solar system.

Earths Rotation and Time

A solar day is the length of time between two consecutive solar noons

The length of a solar day changes because of the change in Earths orbiting velocity

The average length of 24 hours for a solar day is used to keep it simple

The Earth rotates 360° in 24 hours = 15° per hour = 1° per 4 minutes



Each degree of rotation corresponds with a line of longitude (meridian)

Every place along a meridian has the same local time

Time Zones

Time zones are used to standardize time around the worldThere are 24 time zones

15° bands representing 1 hour of time

Run parallel to lines of longitude

All areas of Earth within a time zone maintain the same local time

Ex: Eastern Standard Time, Pacific Standard Time

The time designated for each zone is based on the time at the prime meridian in Greenwich,

England

The prime meridian marks O° longitude

A day begins in the Pacific ocean along the International Date Line (180° longitude)

The Phases of the Moon

Earth Science

Mr. Sweeney

LICHS

5.23.06

.. How does the moons revolution affect its appearance?

Do Now: Explain why time in L.A. is 3 hours earlier than N.Y.

Phases of the Moon

Half of the moons surface receives light from the sun

The amount of the illuminated (light) side that can be seen from Earth changes as the moon

orbits Earth

The changes in the appearance of the illuminated side are called the moons phases

The moon is waxing when the amount of the moons illuminated side appears to be increasing

The moon is waning when the amount of the moons illuminated side appears to be decreasing

The phases of the moon occur in a cycle

A complete lunar cycle starts with a new phase (completely dark)

As the amount of the illuminated side increases, the moon goes through waxing crescent, first

quarter, and waxing gibbous phases

The moon gradually becomes full (completely illuminated)

As the amount of the illuminated side decreases, the moon goes through waning gibbous, last

(3rd) quarter, and waning crescent phases

The cycle ends when the new moon phase occurs again

The moons period of revolution is 27.3 days

However, the period between two consecutive new moons is 29.5 days

The revolution of the Earth around the sun causes the moon to be short of completing the



cycle after 27.3 days

Therefore, the moon has to revolve a little more (2.2 days) to reach new moon phase

The Moon and Tides

Earth ScienceMr. Sweeney

LICHS

5.24.06

.. How does the moon affect the tides?

Do Now: Determine the moons phase in a week given a current phase of waxing gibbous.

The Moon and Tides

The tides are the cyclic rise and fall of ocean waters due to the gravitational pull of the sun

and moon

The moon has a greater affect on the tides than the sun because it is closer to Earth

High Tide

High tide occurs when the ocean water level reaches the highest point on the shore

Occurs twice a day 12 hrs 25 min apart

Occurs on two opposite sides of the EarthThe side nearest the moon

The side farthest from the moon

Low Tide

Low tide occurs when the ocean water level reaches the lowest point on the shore

Occurs twice a day 12 hrs 25 min apart

Occurs on two opposite sides of the Earth

The sides of the Earth that are perpendicular (at 90° angles) to the sides of Earth where high

tide is occurring

Ocean is stretched thin in these areas

Changes in Tides

As the moon revolves around the Earth, high and low tide locations change

The difference in height between high and low tides also changes

Spring Tides

High tides are highest and low tides are lowest (largest difference in tide height) when

The moon is in between the Earth and the sun (new moon phase)

The Earth is in between the sun and moon (full moon phase)



Neap Tides

High tides are lowest and low tides are highest (smallest difference in tide height) when

The moon is at a 90° angle to the Earth and sun (1st and last/3rd quarter phase)

Eclipses

Earth Science

Mr. Sweeney

LICHS

5.25.06

.. How do eclipses occur?

Do Now: Describe the positions of the moon during spring and neap tides.

Eclipses

An eclipse occurs when a celestial object moves into the shadow of another celestial object

Partial eclipse object partly blocked

Total eclipse object completely blocked

Lunar EclipseA lunar eclipse occurs during a full moon phase when the moon moves into the shadow of the

Earth

However, lunar eclipses do not occur every full moon because the moons orbit is tilted 5° to

Earths orbit

Average of 2-3 lunar eclipses a year

Solar Eclipse

A solar eclipse occurs during a new moon phase when the moon casts a shadow on the Earth

Visible only from a small area of Earths surface

Occurs 2-5 times a year worldwide

The Moons Apparent Diameter

The diameter of the moon appears to change as it revolves around Earth

The moon appears bigger when it is closer and smaller when it is farther away

This change in apparent diameter helps prove the elliptical shape of orbit



Celestial Sphere: the Apparent Motions of the Sun, Moon, Planets, and Stars

The celestial sphere is an imaginary projection of the Sun, Moon, planets, stars, and all


useful mapping and tracking remnant of the geocentric theory of the ancient Greek

astronomers.


universe (i.e., a geocentric model of the Universe), the hypothetical celestial sphere provides

an important tool to astronomers for fixing the location and plotting movements of celestial

objects. The celestial sphere describes an extension of the lines of latitude and longitude,



around Earth, upon which the Sun, Moon, planets, and stars moved. Although heliocentric

(Sun-centered) models of the universe were also proposed by the Greeks, they were


Early in the sixteenth century, Polish astronomer Nicolaus Copernicus (1473 – 1543)

reasserted the heliocentric theory abandoned by the Ancient Greeks. Although sparking a

revolution in astronomy, Copernicus' system was deeply flawed by the fact that the Sun is


circular.



Celestial Sphere: The Apparent Motions of the Sun, Moon, Planets, andStars

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The celestial sphere is an imaginary projection of the Sun, Moon, planets, stars, and all


useful mapping and tracking remnant of the geocentric theory of the ancient Greek astronomers.Although originally developed as part of the ancient Greek concept of an Earth-centered universe

(i.e., a geocentric model of the Universe), the hypothetical celestial sphere provides an important

tool to astronomers for fixing the location and plotting movements of celestial objects. The

celestial sphere describes an extension of the lines of latitude and longitude, and the plotting of

all visible celestial objects on a hypothetical sphere surrounding the earth.


around Earth, upon which the Sun, Moon, planets, and stars moved. Although heliocentric (Sun-

centered) models of the universe were also proposed by the Greeks, they were disregarded as

"counter-intuitive" to the apparent motions of celestial bodies across the sky.

Early in the sixteenth century, Polish astronomer Nicolaus Copernicus (1473 –1543) reassertedthe heliocentric theory abandoned by the Ancient Greeks. Although sparking a revolution

inastronomy, Copernicus' system was deeply flawed by the fact that the Sun is certainly not the

center of the universe, and Copernicus insisted that planetary orbits were circular. Even so, the

heliocentric model developed by Copernicus fit the observed data better than the ancient Greek

concept. For example, the periodic "backward" motion (retrograde motion) in the sky of the

planets Mars, Jupiter, and Saturn, and the lack of such motion for Mercury and Venus was more

readily explained by the fact that the former planets' orbits were outside of Earth's. Thus, the

earth "overtook" them as it circled the Sun. Planetary positions could also be predicted much

more accurately using the Copernican model.

Danish astronomer Tycho Brahe's (1546 –1601) precise observations of movements across the"celestial sphere" allowed German astronomer and mathematician Johannes Kepler (1571 –

1630) to formulate his laws of planetary motion that correctly described the elliptical orbits of the

planets.

The modern celestial sphere is an extension of the latitude and longitude coordinate system used

to fix terrestrial location. The concepts of latitude and longitude create a grid system for the

unique expression of any location on Earth's surface. Latitudes—also known as parallels—mark

and measure distance north or south from the equator. Earth's equator is designated 0° latitude.

The north and south geographic poles respectively measure 90° north (N) and 90° south (S) from

the equator. The angle of latitude is determined as the angle between a transverse plane cutting

through Earth's equator and the right angle (90°) of the polar axis. Longitudes—also known as

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meridians—are great circles that run north and south, and converge at the north and south

geographic poles.

On the celestial sphere, projections of lines of latitude and longitude are transformed into

declination and right ascension. A direct extension of Earth's equator at 0° latitude is the celestial

equator at 0° declination. Instead of longitude, right ascension is measured in hours.Corresponding to Earth's rotation, right ascension is measured from zero hours to 24 hours

around the celestial sphere. Accordingly, one hour represents 15 angular degrees of travel

around the 360° celestial sphere.

Declination is further divided into arcminutes and arcseconds. In 1° of declination, there are 60

arcminutes (60') and in one arcminute there are 60 arcseconds (60"). Right ascension hours are

further subdivided into minutes and seconds of time.

On Earth's surface, the designation of 0° longitude is arbitrary, an international convention long

held since the days of British sea superiority. It establishes the 0° line of longitude—also known

as the Prime Meridian—as the great circle that passes through the Royal National Observatory inGreenwich, England (United Kingdom). On the celestial sphere, zero hrs (0 h) right ascension is

also arbitrarily defined by international convention as the line of right ascension where the

ecliptic—the apparent movement of the Sun across the celestial sphere established by the plane

of the earth's orbit around the Sun—intersects the celestial equator at the vernal equinox.

For any latitude on Earth's surface, the extended declination line crosses the observer's zenith.

The zenith is the highest point on the celestial sphere directly above the observer. By

international agreement and customary usage, declinations north of the celestial equator are

designated as positive declinations (+) and declinations south of the celestial equator are

designated as negative declinations (−) south.

Just as every point on Earth can be expressed with a unique set of latitude and longitude

coordinates, every object on the celestial sphere can be specified by declination and right

ascension coordinates.

The polar axis is an imaginary line that extends through the north and south geographic poles.

The earth rotates on its axis as it revolves around the Sun. Earth's axis is tilted approximately

23.5 degrees to the plane of the ecliptic (the plane of planetary orbits about the Sun or the

apparent path of the Sun across the imaginary celestial sphere). The tilt of the polar axis is

principally responsible for variations in solar illumination that result in the cyclic progressions of

the seasons. The polar axis also establishes the principal axis about which the celestial sphere

rotates. The projection of Earth's geographic poles upon the celestial sphere creates a northcelestial pole and a south celestial pole. In the Northern Hemisphere, the star Polaris is currently

within approximately one degree (1°) of the north celestial pole and thus, from the Northern

Hemisphere, all stars and other celestial objects appear to rotate about Polaris and, depending

on the latitude of observation, stars located near Polaris (circumpolar stars) may never "set."

For any observer, the angle between the north celestial pole and the terrestrial horizon equals

and varies directly with latitude north of the equator. For example, at 30° N latitude an observer

views Polaris at +30° declination, at the terrestrial North Pole (90° N), Polaris would be directly

overhead (at the zenith) at +90° declination.

The celestial meridian is an imaginary arc from the north point on the terrestrial horizon through

the north celestial pole and zenith that terminates on the south point of the terrestrial horizon.

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Regardless of location on Earth, an observer's celestial equator passes through the east and

west points of the terrestrial horizon. In the Northern Hemisphere, the celestial equator is

displaced southward from the zenith (the point directly over the observer's head) by the number

of degrees equal to the observer's latitude.

Rotation about the polar axis results in a diurnal cycle of night and day, and causes the apparentmotion of the Sun across the imaginary celestial sphere. The earth rotates about the polar axis at

approximately 15 angular degrees per hour and makes a complete rotation in 23.9 hours. This

corresponds to the apparent rotation of the celestial sphere. Because the earth rotates eastward

(from west to east), objects on the celestial sphere usually move along paths from east to west

(i.e., the Sun "rises" in the east and "sets" in the west). One complete rotation of the celestial

sphere comprises a diurnal cycle.

As the earth rotates on its polar axis, it makes a slightly elliptical orbital revolution about the Sun

in 365.26 days. Earth's revolution about the Sun also corresponds to the cyclic and seasonal

changes of observable stars and constellations on the celestial sphere. Although stars grouped

in traditional constellations have no proximate spatial relationship to one another (i.e., they maybe billions of light years apart) that do have an apparent relationship as a two-dimensional

pattern of stars on the celestial sphere. Accordingly, in the modern sense, constellations

establish regional location of stars on the celestial sphere.

A tropical year (i.e., a year of cyclic seasonal change), equals approximately 365.24 mean solar

days. During this time, the Sun appears to travel completely around the celestial sphere on the

ecliptic and return to the vernal equinox. In contrast, one orbital revolution of Earth about the Sun

returns the Sun to the same backdrop of stars—and is measured as a sidereal year. On the

celestial sphere, a sidereal day is defined as the time it takes for the vernal equinox—starting

from an observer's celestial median—to rotate around with the celestial sphere and recross that

same celestial median. The sidereal day is due to Earth's rotational period. Because of

precession, a sidereal year is approximately 20 minutes and 24 seconds longer than a tropical

year. Although the sidereal year more accurately measures the time it takes Earth to completely

orbit the Sun, the use of the sidereal year would eventually cause large errors in calendars with

regard to seasonal changes. For this reason the tropical year is the basis for modern Western

calendar systems.

Seasons are tied to the apparent movements of the Sun and stars across the celestial sphere. In

the Northern Hemisphere, summer begins at the summer solstice (approximately June 21) when

the Sun is reaches its apparent maximum declination. Winter begins at the winter solstice

(approximately December 21) when the Sun's highest point during the day is its minimummaximum daily declination. The changes result from a changing orientation of Earth's polar axis

to the Sun that result in a change in the Sun's apparent declination. The vernal and autumnal

equinox are denoted as the points where the celestial equator intersects the ecliptic.

The location of sunrise on the eastern horizon, and sunset on the western horizon also varies

between a northern most maximum at the summer solstice to a southernmost maximum at the

winter solstice. Only at the vernal and autumnal equinox does the Sun rise at a point due east or

set at a point due west on the terrestrial horizon.

During the year, the moon and planets appear to move in a restricted region of the celestial

sphere termed the zodiac. The zodiac is a region extending outward approximately 8° from eachside of the ecliptic (the apparent path of the Sun on the celestial sphere). The modern celestial



sphere is divided into twelve traditional zodiacal constellation patterns (corresponding to the

pseudoscientific astrological zodiacal signs) through which the Sun appears to travel by

successive eastwards displacements throughout the year.

During revolution about the Sun, the earth's polar axis exhibits parallelism to Polaris (also known

as the North Star). Although observing parallelism, the orientation of Earth's polar axis exhibitsprecession—a circular wobbling exhibited by gyroscopes—that results in a 28,000-year-long

precessional cycle. Currently, Earth's polar axis points roughly in the direction of Polaris (the

North Star). As a result of precession, over the next 11,000 years, Earth's axis will precess or

wobble so that it assumes an orientation toward the star Vega.

Precession causes an objects celestial coordinates to change. As a result, celestial coordinates

are usually accompanied by a date for which the coordinates are valid.

Corresponding to Earth's rotation, the celestial sphere rotates through 1° in about four minutes.

Because of this, sunrise, sunset, moonrise, and moonset all take approximately two minutes

because both the Sun and Moon have the same apparent size on the celestial sphere (about0.5°). The Sun is, of course, much larger, but the Moon is much closer. If measured at the same

time of day, the Sun appears to be displaced eastward on the star field of the celestial sphere by

approximately 1° per day. Because of this apparent displacement, the stars appear to "rise"

approximately four minutes earlier each evening and set four minutes later each morning.

Alternatively, the Sun appears to "rise" four minutes earlier each day and "set" four minutes

earlier each day. A change of approximately four minutes a day corresponds to a 24-hour cycle

of "rising" and "setting" times that comprise an annual cycle.

In contrast, if measured at the same time each day, the Moon appears to be displaced

approximately 13° eastward on the celestial sphere per day and therefore "rises" and "sets"

almost one hour earlier each day.

Because the earth is revolving about the Sun, the displacement of the earth along it's orbital path

causes the time it takes to complete a cycle of lunar phases—a synodic month—and return the

Sun, Earth, and Moon to the same starting alignment to be slightly longer than the sidereal

month. The synodic month is approximately 29.5 days.

Earth rotates about its axis at approximately 15 angular degrees per hour. Rotation dictates the

length of the diurnal cycle (i.e., the day/night cycle), and creates "time zones" with differing local

noons. Local noon occurs when the Sun is at the highest point during its daily skyward arch from

east to west (i.e., when the Sun is at its zenith on the celestial meridian). With regard to the solar

meridian, the Sun's location (and reference to local noon) is described in terms of being antemeridian (am)—east of the celestial meridian—or post meridian (pm) located west of the celestial

meridian.

motion of our star the sun

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