Motions of the Earth and Moon

Motions of the Moon• The moon revolves around Earth once in 27.32 days. This is called its

sidereal period of revolution because it is measured relative to the starsstars.

• The moon rotates once in 27.32 days. This is its sidereal period ofsidereal period ofrotationrotation. Because of this, we always see the same side of the moon from Earth.

h d i i bi h f h ill i d• As the moon moves eastward in its orbit, the part of the illuminated half that we see changes. The fraction of the illuminated half that is visible from Earth is called the phase, usually expressed as a percentage.

Sunlight

eastward

N

Why do we always see the same side of the moon?

The moon’s rotation period is equal to its period of revolutionperiod of revolution.

Earth

Phases of the MoonFi tA l t l

Waxing crescent

First quarter

Waxing gibbous

A complete cycle of phases is called a lunation.

Newfull New

eastward

The time to The synodic period of the mooncomplete a cycle of

phases is called the synodic periodof the moon. It is

period of the moon is 29.53 days. That is, about 1 week from new to first quarter one week

Waning gibbous

Thirdquarter

Waning crescent

the moon’s period of revolution with respect to the sun.

quarter, one week from first quarter to full, etc..

How is the time of day for an observer related to the location of that observer on earth?

Sunset

NMidnightNorth Pole

NoonMidnight Sunlight

S iSunrise

Note: eastward is the direction in which earth rotates. In the diagram, a line is drawn tangent to the observer’s location, with the direction of rotation labeled E and the opposite direction

Lunar Phases and Time of Day

Sunset

pplabeled W. These two points identify the eastern and western horizons.

WEW

E

NoonMidnight North PoleSunlight

EW

E

W

Sunrise

SSHere, the sun is at the vernal equinox, so the date is near March 20

Lunar Phases and the Seasons

date is near March 20.

VEAE

What is the phase of the moon if the date is March 20, and the moon is

WS

and the moon is at the summer solstice?

An internet tutorial and practice quiz on the phases of the moon is located at http://www.calvin.edu/~lmolnar/moon/index.html.

Lunar and Solar Eclipses

angular diameter linear diameter206265 distance

=′′

The maximum distance between Earth and the Sun is about 152,000,000 km, and the diameter of the sun’s photosphere (the region of the Sun that is normally visible) is 1,390,000 km. Calculate the angular diameter of the Sun at this distance.

206265 distance

, , C g S

Calculate θ.8d 1.52 10 km= × 6D 1.39 10 km= ×

5 D2.06265 10d

⎛ ⎞θ = × ⎜ ⎟⎝ ⎠

65

8

1.39 102.06265 101.52 10

×θ = × ×

×

1θ = 0.524º

When the Moon is closest to Earth, its angular diameter is 0.549º. If it then comes

31.886 10 arcsecθ = ×3 11.886 10

3600θ = × × °

between us and the Sun, it blocks (eclipses) the photosphere. This phenomenon is called a total solar eclipse.

The Sun’s angular diameter can be as large as 0.542º and the Moon’s as small as 0.491º. g gWhen the Moon comes between Earth and the Sun under these conditions, a ring of the photosphere is visible. This is called an annular eclipse.

The Structure of a ShadowThe Structure of a Shadow

Sun

The green sphere in the diagram represents either Earth or the Moon No sunlight reaches the region

A cross section of the shadow at the dotted line would look like the figure below.Earth or the Moon. No sunlight reaches the region

labeled U. This is the darkest part (called the umbra) of the shadow of the green sphere; it is the region in which the Sun is totally eclipsed. P labels h f h h d h h i

the figure below.

umbra

the penumbra of the shadow, where the Sun is partially eclipsed. From region A, an observer would see an annular eclipse.

penumbra

Earth-Sun-Moon Configurations for Lunar and Solar Eclipses

• For a lunar eclipse to occur, the Moon must pass through Earth’s shadow. This can only happen at a full Moon.

• For a solar eclipse to occur, the Moon’s shadow must fall on Earth. This can only happen when the Moon is new.y pp

• Why isn’t there a lunar eclipse at every full Moon and a solar eclipse at every new Moon?

NewMoon

Full Moon

Sunlight

Earth

g

The Moon’s orbit does not lie in the ecliptic. Thereis an angle of about 5º between the plane of Earth’sorbit and the plane of the Moon’s orbit. Because of

Ecliptic

pthis, the shadows usually miss as shown at the right.

Line of Nodes

Under ideal lunar eclipse conditions, the length of Earth’s umbra is 1.4 million km and the distance from Earth to the moon is 363 thousand km. The diameter of Earth’s umbra at that distance is 9500 km, and the diameter of its penumbra is 16,000 km. Since the diameter of the Moon is only 3476 km, it is possible for the entire Moon to pass through Earth’s umbra. The Moon is then seen totally eclipsed by anyone on Earth who can see the Moon Three kinds of lunar eclipse are possible: total partial and penumbralthe Moon. Three kinds of lunar eclipse are possible: total, partial, and penumbral.

Penumbral: Moon passes through

eastward

Penumbral: Moon passes through the penumbra.

Total: all of the Moon passes through the umbra.

Partial: only part of the Moon passes through the umbra

Lunar Eclipse

During the penumbral phase of a total lunar eclipse or during a penumbral eclipse, the full Moon is slightly fainter than usual. During the total phase, it is not completely dark because some sunlight is refracted (i e bent))toward the Moon by earth’s atmosphere Asbecause some sunlight is refracted (i.e., bent))toward the Moon by earth s atmosphere. As it passes through Earth’s atmosphere, the sunlight is also scattered. More blue light is scattered than red, so the Moon looks orange during totality as shown in these photographs.

Under ideal lunar eclipse conditions, the diameter of the Moon’s umbra is about 270 km, and the diameter of its penumbra is about 6000 km. Since Earth’s radius is about 6380 km the only people who can see a total solar eclipse are those who happen to be6380 km, the only people who can see a total solar eclipse are those who happen to be along the narrow path followed by the umbra; this path is called the path of totality.

For an observer at Earth’s equator, the umbra

Umbra of

q ,moves at about 1730 km/h due to the combination of the orbital motion of the Moon and the rotation of Earth. The time for the mbra to pass o er s ch an obser er isMoon’s

shadowthe umbra to pass over such an observer is therefore no more than about 7.5 minutes. Total eclipses at higher latitudes are even shorter.

EarthOn the other hand, it can take as much as 1 hour and 45 minutes for the Moon t t E th’ bto traverse Earth’s umbra.

There are three kinds of solar eclipse: total (photosphere completely blocked by the Moon partial (photosphere partially blocked by the Moon) and annular (MoonMoon, partial (photosphere partially blocked by the Moon), and annular (Moon blocks the central part of the photosphere, but leaves a thin ring of photosphere visible.

Solar Eclipse from SatelliteBBecause Earth rotates and the Moon

This is a satellite view of the

f moves in its orbit, the shadow moves at

passage of the Moon’s shadow over the surface moves at

more than 1000 mph. Since the

of Earth during a total solar eclipse diameter of

the umbra is no more than about

eclipse. While the umbra passes over than about

168 miles, a total solar eclipse can

a region, the people in that region see a total last no more

than 7.5 minutes.

see a total solar eclipse.

Total Solar Eclipse as Seen from the Ground

Notice that just, before the beginning and beginning and just before the end of totality,there is a b i ht fl hbright flash near the edge of the sun. This phenomenon is

The white halo seen during totality is thep

called the diamond ring effect. It is the result of

totality is the part of the Sun’s atmosphere called the

result of sunlight passing through a valley on the Moon

corona.

while the rest of the sun is eclipsed.

Chromosphere and Prominences

When the photosphere is eclipsed, the outer regions of the Sun’s atmosphere can be Th i k i hi h h d h f l h d k i ll dseen. The pink region, which has an average depth of several thousand km, is called

the chromosphere. The corona is the tenuous, but very hot, region that shows up as a white irregular halo around the Sun during totality. The clouds of hot gas that rise above the chomosphere into the corona are called prominences.p p

Predicting Eclipses

The moon’s orbit is tilted 5o 8' 43" to the plane of the ecliptic. It crosses the ecliptic twice a month These crossing points are called the nodes of its orbittwice a month. These crossing points are called the nodes of its orbit.

Conditions for an eclipse to occur:1. The moon must be full (lunar eclipse) or new (solar eclipse).2. The sun must be near a node of the moon’s orbit.

Eclipse season: a time interval during which the sun is close enough to a node for an eclipse to occur – about 32 days for solar eclipses, 22 days for lunar eclipses.an eclipse to occur about 32 days for solar eclipses, 22 days for lunar eclipses.

Line of nodes: a line that passes through the two nodes of the moon’s orbit.

Eclipse year: the amount of time for the sun to return to a node = 346.62 days

The eclipse seasons begin 19 days earlier each year.

111 saros cycle = 18 years 11 days = 6585.321 days 223 lunar synodic periods3

=

6585.321 223.00=6585.321 19.00=3.00

29.5319.00

346.62

If the line of nodes points toward the sun on a given date, and the moon is new, a solar eclipse will occur 6585 321 days later an eclipse of the same type will occur but it willeclipse will occur. 6585.321 days later, an eclipse of the same type will occur – but it will be seen 0.321 × 360 = 120o farther west.

Annular eclipse on 2/15/199. When will the same eclipse occur again?

When will it occur again and be visible from the same location?

Total Solar Eclipses Visible from the USA

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