name: 2 earth and sky - west valley college

2Name:

Lab Day and Time:

Earth and SkyFinding your way

Lab Partner 1: Lab Partner 2: Lab Partner 3:

Introduction:

If you are a traveler to a new place you will generally seek a map to help you explore your surroundings. Looking for a map to purchase, you might find maps in a variety of shapes, sizes and level of detail. It is no different if you explore the night sky and there many maps used by astronomers to help in their exploration of the heavens.

In this lab, we will familiarize ourselves with both two-dimensional and three-dimensional maps of the night sky. Some two-dimensional maps are printed in books or magazines and so are made for specific dates and times. Others, known as planispheres or star/sky wheels, are adjustable for date and time.

The night sky does look different from different places on the Earth. For example, the sky seen from Australia is quite different from the sky as seen from England. Both printed charts and sky wheels are designed to be used from specific places on Earth. You would have to obtain a different planisphere for use in England versus Australia just as you would need different maps to explore London versus Sydney. As we will see next week, the three-dimensional map we will use is adjustable for any location on Earth and is more flexible in this regard than the planisphere.

Looking down on any rotating planetary body from space, we would see that it has a spherical shape. To facilitate the study of the surface, an imaginary grid work of lines is drawn on the sphere, to aid in locating surface features. We will explore the system of lines that is used for this purpose by a study of those used on Earth.

In our last lab, we were introduced to the idea of the Celestial Sphere, an imaginary sphere that encircles the Earth on which the stars are located. It should not surprise you, therefore, that astronomers have drawn of grid work of lines on the Celestial Sphere to aid in locating features in the sky. We will also look at this system of lines and the similarities and differences from the system used for planetary bodies.

Objectives: Become familiar with the information available to you on a planisphere. Learn how to set a planisphere for date and time. Learn how to use a planisphere to locate constellations in the sky. Learn the system used by mapmakers to find locations on a globe of the Earth. Learn the system used by astronomers to find the locations of objects in the night sky.

Earth and Sky 1:1 Astronomy 20 – Family of the SunRev: 0.1

EXERCISES

Exercise A. The Planisphere (Star Wheel)

A planisphere is a two-dimensional map of the sky which, unlike printed charts, is adjustable for date and time. Planispheres may be adjusted to take into account the Earth's rotation and revolution around the sun which cause the positions of objects in the sky, relative to the horizon, to change constantly.

Take a moment to look at the way the planisphere is labeled. Identify all of the following on the planisphere:

✔ Traditional Constellations are connected by solid line segments and labeled in all capital letters (e.g. LYRA).

✔ Bright Stars are labeled with their proper names. The first letter is capitalized followed by the others in lower case (e.g. Vega).

✔ Asterisms are labeled in parentheses.✔ Polaris, the North Star, is marked by the rivet around which the chart rotates.✔ Note the position of the band of the Milky Way across the sky.✔ The Celestial Equator is labeled as a solid curved line crossing the chart from east to

west.✔ Right Ascension is marked out, in hours, on the celestial equator.✔ Declination is marked out, in degrees, on the spoked lines radiating out from the rivet.✔ The Ecliptic, the apparent path of the sun amongst the stars, is shown as a dashed line

(wide dashes) which pass through the constellations of zodiac. The position of the sun for a given date is marked on the line.

✔ A few deep-space objects are indicated by their catalog number, e.g. M31. A pair of binoculars or telescope would enable you to see these objects when the sky is sufficiently dark.

Setting the Planisphere: Note that the wheel is labeled with the dates of the year and the frame with the hours of the night. To set the planisphere, simply match the time of night to the date of interest. [Note that during daylight savings time the planisphere must be set an hour earlier than the clock time.]

Date: _______________________ Time: ______________________

If you orient it so that the word “North” is toward the North, you will note that East and West are reversed. This is because you do not hold the planisphere exactly as you would hold a street map. A planisphere is meant to be held above your head since you are looking up at the sky not down at the ground. Now, hold the planisphere above your head, making sure the word North is still oriented to North, you'll note that East and West are now correct.

On the planisphere, East and West are closer to North than to South. This is because the flattened view needs to be distorted in order for the wheel to work properly. The Southern sky is particularly stretched and so some planispheres will put the Southern sky on the back side to minimize the distortion.

When viewing the Northern sky, it is best to hold the planisphere in front of you with the northern horizon on the planisphere parallel to the true northern horizon. Hold it similarly for the other directions (east is in front of you when facing east, etc.). When viewing the center (zenith) of the sky, it is best to hold the planisphere directly over your head.


Star Brightness: The stars on the planisphere are marked by dots of all different sizes. The size of the star on the wheel has nothing to do with the size of the star in space. The larger the dot is on the wheel, the brighter the star is in the sky. The brightness of stars is denoted by a magnitude scale. Now look at the upper left corner of the planisphere and you'll see the apparent magnitude scale that is used on this star wheel where the brightness of stars is indicated with a number. The brighter the star, the smaller the magnitude (number) label than dimmer stars (i.e. a 1st magnitude star is brighter than a 3rd magnitude star).

Your instructor will set the planetarium for the time listed above. Last time, you were asked to find another bright star that is not in a constellation that you know. Find that star again. Make a rough sketch of the constellation below. (Use the planisphere to help you.)

What is the name of the star?

What is the name of the constellation?

Your instructor will now set the planetarium for a different time. Using today’s date, figure the time that the planetarium is set for. [Suggestion: Look at the Little Dipper and rotate the Star Wheel to match.]

Date: _______________________ Time: ______________________

Star Wheel practice problems

1. If it is Fall Semester, at what time today will Aldebaran in Taurus rise? If it is Spring Semester, at what time today will Denebola in Leo rise?

2. At what compass position will it be when it rises?

3. What constellation will be closest to the zenith at 9 p.m. tonight?


4. Constellations that never go below the horizon are known as ‘circumpolar' constellations. Use your star wheel to identify three such constellations and record them in the spaces below. (Note: Which, if any, constellations are circumpolar depends on where on Earth you are observing from. When not otherwise specified, we'll assume we are observing from Saratoga.)

5. A nearby spiral galaxy, known as the Great Galaxy in Andromeda is catalogued as M31, is in the constellation of Andromeda and is also known as the Andromeda galaxy or, simply, Andromeda. Andromeda is much, much, farther away than any of the stars that make up the constellation called Andromeda; all of those stars are inside our Milky Way Galaxy. This galaxy is the furthest object you can see with the naked eye (that is, without a telescope), but only from dark sites. In what compass direction should you look for it in early September at 9 p.m.?

Exercise B. Latitude and Longitude

Latitude and longitude provide us with a way to give an "address" of any point on earth. Each degree of latitude or longitude can be divided into 60 minutes and each minute into 60 seconds. For example, 34 degrees, 23 minutes, and 23 seconds is written as 34° 23’ 23”. The round earth has no starting or stopping points or edges. Cartographers must designate where our numbering begins. The earth rotates on an axis, running through the poles, and the North Star (Polaris) makes a good reference point directly over the North Pole. A horizontal line around the middle of the earth equally distant from the two poles is easily located and is called the equator. The angular distance from equator to pole is 90° north or south. Most maps have horizontal lines of latitude (parallels) drawn in every 10° to 20°. Latitude is the angular distance north or south of the equator, measured as an angle in degrees from the center of Earth.

Parallels of Latitude:

All latitude lines are parallel to the equator. Their distance from the equator is measured in degrees of arc because of the circular nature of earth’s surface. Sixty degrees north latitude is a 60° angle from the equator to the center of earth to the 60° parallel.

Great Circles:

Note that as you move from the equator to higher latitudes (north or south), the diameter of the circles gets smaller. The north pole, at 90°, is such a small circle that you can put you foot on it. A great circle is one that completely encircles the full circumference of earth at its largest diameter. There is only one great circle of latitude, the equator. As you will see below, all meridians of lines of longitude are great circles.

Figure 1: Parallels of Latitude.


In order to tell the which half of the Earth we are looking at , the letters N (north) or S (south) are attached to the number of degrees. Thus, if I move northward from the equator to Portland, Oregon, I arrive at 45°N latitude. Similarly, a trip to the Antarctic Circle will put me at 66° 30’ S latitude.

Determining Latitude

We can determine our latitude in the Northern Hemisphere by measuring the angle from the horizon to the North Star (Polaris). If Polaris is directly overhead (at 90°), our position is the North Pole. If the Polaris is right on the horizon (at 0°), our position is the equator. Look in the night sky tonight and estimate how high of an angle the North Star is above the horizon where we live. To measure accurately we use a sextant (a protractor with a level bubble). You can make your own, crude sextant by using a protractor (with zero hole), string, and small weight (see figure 2b).

Since Polaris is very far above the Earth's axis, all lines of sight (LOS) to Polaris will essentially be parallel. At the equator, the LOS to Polaris coincides with the local horizon, forming parallel lines. The parallels do not intersect and have a 0° angle between them. At the North Pole, Polaris is directly overheard, making a 90° angle with the local horizon. The North Pole is at 90°N latitude.

(b)

(a)

Figure 2: The local horizon angle with Polaris is your latitude in northern Hemisphere (a). Model for a home-made sextant (b). Note that the string hangs near the 60° mark, but the tilt is not 60� . The angle of tilt that you are measuring (the angle of the hanging string from the vertical) is measured from the 90°mark to the 60� mark and is actually a 30� tilt. So your latitude would be 30°N.

Homework

From your home or nearby park, find the Big Dipper asterism in the night sky. Use the ‘pointer stars’ on the Big Dipper’s bowl to locate Polaris, the North Star. Measure the angle to Polaris. Remember that you are measuring from 90°, so you will have to count the number of degrees away from 90°.

Record your sextant observations here:


1: On figure 3 (below), sketch and label the equator.

2: On figure 3, make an angle by drawing a line from point A on the equator to point B. Extend this line from point B to point C in the northern hemisphere. Measure this angle with the protractor. What is the latitude of point C? ______________________

3: Draw a line on figure 3 parallel to the equator that also goes through point C (a parallel of latitude!). All points on this line are 45° N latitude.

4: Using a protractor, measure angle ABD on figure 3. Then draw a line parallel to the equator that also goes through point D. What is the latitude of point D? _________________ Label the line with its proper latitude.

Figure 3. Globe for latitude and longitude work.

Figure 4. Globe for determining latitude.

5: Look at the Earth globes we are using. How many degrees of latitude separate the parallels on the globe? ________________

6: Keep in mind that the lines (circles) of latitude are parallel to the equator and to each other (latitudes are also called parallels). Sketch the 60º N and 80º N parallels on figure 3 by using the protractor to measure these angular distances from the equator.

7: On Figure 4, determine the latitude for each designated point in the table below. Remember to indicate whether the point is north or south latitude.


Point Latitude

Point A

Point B

Point C

Point D

Point E

Point F

8: Use a globe to locate the cities listed below and give their latitude to the nearest degree. Indicate N or S and include the word latitude.

St. Petersburg, Russia

Antananarivo, Madagascar

Quezon City, Philippines

Oaxaca, Mexico

Saratoga, California

9: By using the globe, give the name of a city or feature that is equally as far south of the equator as Saratoga, California is north of the equator. ____________________________________________

10: The farthest one can be from the equator is (45°, 90°, 180°) of latitude.

11: There are five special parallels of latitude marked and named on most globes by dashed lines. Use a globe to locate the following special parallels and indicate the name given to each. The equator has already been labeled.

66°30’00” N

23°30’00” N

0°00’00” EQUATOR

23°30’00” S

66°30’00” S

12: In your own words, describe the relation between latitude and the angle of Polaris above the local horizon?


13: You measure an angle of 21° between the North Star and the local horizon with your sextant. What is your latitude?

Meridians of Longitude

Meridians of Longitude:

Think of meridians of longitude as circling the earth from North Pole to South Pole and then back up to North Pole. Each longitude encircles the full circumference of Earth, each at the widest diameter. So, all meridians of longitude are also great circles.

Figure 5. Meridians of Longitude

Whereas as latitude indicates how far north or south you are of the equator, longitude indicates how far you are east or west from a given place. The poles, equator, and parallels of latitude are defined by a planet’s intrinsic property of rotation, but placement of a Prime Meridian from which to measure longitude, is arbitrary. Historically, a number of different cities were used and this led to a diversity of maps that all had different longitudes for the same places. The International Meridian Conference of 1884 (see additional notes at the end of the lab) selected the meridian that passes through the Royal Greenwich Observatory in Greenwich, England to be the Prime Meridian, aka, the Greenwich Meridian.

Thus, the zero degree meridian is called the prime meridian. We have divided the Earth into a western and eastern hemisphere and longitude starts at 0� and increases in both directions (east and west) from the prime meridian until you arrive 180° east or west of the prime meridian where we have located the international dateline. Again, lines about 10° to 20° apart are drawn on the globe or map covering the entire 360°. These are called meridians of longitude, and they converge at the North and South Poles. Longitude is the angular distance measured east and west of the prime meridian.

San Francisco is a little more than 120°W longitude, and Japan is about 130°E longitude. On your globe, find Mexico City at about 99° W longitude and about 20°N Latitude.

Show your instructor. Instructor initials here: _________________

14: On Figure 3 above, locate and label the prime meridian.

15: On Figure 3, label the eastern and western hemispheres.

16: How many degrees of longitude separate each of the meridians on your globe?

17: Keep in mind that meridians are farthest apart at the equator and converge at the poles. Sketch and label several meridians on Figure 3. Note that the meridian that goes from the North Pole through points C, A, and D will be the 90° E longitude meridian. Sketch at least three others in both the western and eastern hemispheres.


18: Use the diagram below, Figure 6, to determine the longitude for each designated point. Note that if a point does not lie on exactly on a labeled meridian, you must interpolate (estimate). Indicate whether the point is east or west of the prime meridian.

Figure 6. Longitude Exercise

Point Latitude

Point A

Point B

Point C

Point D

Point E

Point F


19: Use a globe to locate the cities listed below and give their longitude to the nearest degree. Indicate either E or W longitude.

Perth, Australia

Apia, Samoa

Sitka, Alaska

McMurdo Ice Station, Antarctica

Alexandria, Egypt

Saratoga, California

20: Using a globe, give the name of a city or feature that is at the same latitude as Saratoga, California, but equally distant from the prime meridian in the opposite hemisphere. ________________________

21: The farthest a place can be directly east or west of the prime meridian is (45°, 90°. 180°) of longitude. _____

Exercise C. Declination and Right Ascension

Now, let's look at the celestial globe. You'll see it is made of two concentric spheres. The inner sphere represents the Earth and the outer sphere represents the celestial sphere. You will notice that the Earth sphere is marked with parallels of latitude and meridians of longitude. If you now turn your attention to the celestial sphere, you will see that it also has parallels and meridians marked on it, though we call them by different names than the ones used for Earth: Parallels of Declination (Figure 7) and Meridians of Right Ascension (Figure 8).

The celestial sphere is an ancient model of the universe that astronomers still find useful since the sky does appear to look like a sphere that surrounds the Earth. In the celestial sphere model, it is the rotation of the celestial sphere that 'explains' the motion of the sky as seen from a stationary Earth.

We still speak of the motion of the Sun, Moon and stars across the sky during the day although it is the Earth that is rotating.

If you look at the celestial globe, you'll see that the spin axis of the celestial sphere is an extension of the spin axis of the Earth. Thus, the extension of the Earth's poles and equator onto the Celestial Sphere mark the Celestial Poles and the Celestial equator.

Lines drawn parallel to the celestial equator are know as parallels of declination. Their distance from the equator is measured in degrees of arc because of the circular nature of earth’s surface. Sixty degrees north declination is a 60° angle from the celestial equator to the center of sphere to the 60° parallel.

Figure 7. Parallels of Declination


22: Use the celestial globe to locate the stars listed below (the constellation names follow the star names) and give their declination to the nearest degree. Indicate N or S and include the word declination. On the globe, star names are printed in black and constellation names are printed in blue.

Sirius (CANIS MAJOR) S. Declination

Betelgeuse (ORION) N. Declination

Antares (SCORPIUS)

Dubhe (URSA MAJOR)

Rigil Kentaurus (CENTAURUS)

The lines that run from pole to pole are called meridians and just as with the Earth, one meridian must be designated a celestial prime meridian. We can not use a reference point on the Earth to determine the prime meridian of the skies because as the earth rotates that reference point would move along the celestial sphere. We need a reference that is 'on' the celestial sphere that remains constant as the Earth rotates.

Astronomers use a point of intersection between the Ecliptic and the Celestial Equator to determine which meridian will be the celestial prime meridian. The Sun is located at this intersection on March 21st and you will note the meridian that passes through this intersection point is labeled both 0h and 0� .

Figure 8. Meridians of Right Ascension

There are many ways used to divide a circle into smaller parts. Most of us are familiar with dividing a circle into 360 increments that we call degrees. Since the sky rotates once every day, astronomers have found an alternative way of dividing a circle to be more convenient to use. Astronomers divide the circle that we use to measure the Meridians of Right Ascension into 24 parts that are called hours. Hours are subdivided into 60 parts called minutes. Thus, every hour the sky rotates through 1 hour of this angle we call Right Ascension. If you look at the celestial sphere, you'll see that there are 24 meridians of Right Ascension that are labeled 0h, 1h, 2h... 23h. Although the celestial sphere has markings alongside these meridians in degrees, the convention is to use hours. You will also notice that, unlike Longitude, Right Ascension is measured all the way around the circle going in one direction. Right Ascension starts at 0h

and increases in the easterly direction (since the sky rotates from east to west) until you return to the starting point. We can see the relationship between the two ways of dividing a circle. The sky, actually the earth, rotates 360� in 24 hours. If you look at the angle between the meridians you'll see that, in the time to rotate through one hour of right ascension, the sky (earth) has rotated through degrees.


23: Use the celestial globe to locate the stars listed below (the constellation names follow the star names) and give their Right Ascension to the nearest minute. Indicate N or S and include the abbreviation for Right Ascension: 'R.A.' . On the globe, star names are printed in black and constellation names are printed in blue.

Sirius (CANIS MAJOR) R.A.

Betelgeuse (ORION) R.A.

Antares (SCORPIUS)

Dubhe (URSA MAJOR)

Rigil Kentaurus (CENTAURUS)

24: Given the following coordinates, find the following objects on the celestial sphere and write down the name of the object and the constellation in which it lies.

Right Ascension Declination Name Constellation

22h 58m R.A. 30 S. Declination



18h 37m R.A. 39 N. Declination

00h 43m R.A. 41 N. Declination

Additional notes:

Sir George Biddell Airy, Fellow of the Royal Society, was an English mathematician and astronomer and Astronomer Royal from 1835 to 1881. His achievements include work on planetary orbits, measuring the mean density of the Earth, and establishing Greenwich as the location of the Prime Meridian, aka Greenwich Meridian, in 1851.

By 1884, over two-thirds of all ships and tonnage used it as the reference meridian on their maps. In October of that year, at the behest of U.S. President Chester A. Arthur 41 delegates from 25 nations met in Washington D.C., USA, for the International Meridian Conference to determine the Prime Meridian of the world. This conference selected the Greenwich Meridian as the official Prime Meridian due to its popularity. However, France abstained from the vote and French maps continued to use the Paris Meridian. The Paris Meridian (a meridian which runs through the Paris Observatory in Paris, France) was a long-standing rival to Greenwich as the prime meridian of the world, as was the Antwerp Meridian in Flanders, for several decades.


name: 2 earth and sky - west valley college

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