Using the Celestial Sphere to

Understanding Astronomical Coordinate Systems

A exercise to do with your Learning Technologies celestial sphere

by Harold Williams of Montgomery College







Now rectify the globe---this means set the latitude for where we are on the earth at Montgomery College (approximately 39 north). Use the protractor attached to the white Styrofoam block that the dowel is sticking in to do this correctly. Think about how you would do this for the north pole, the south pole, and the equator. But do it for this latitude.

Horizon Coordinate System

1. Locate the zenith on the celestial sphere.

2. Locate the nadir on the celestial sphere.

3. Rotate the celestial sphere, notice that the stars on the zenith and nadir change as the celestial sphere rotates.

4. How long does it take for the celestial sphere to turn once around relative to the stars? __________ This is a sidereal day. It is not quite 24 hours. What is it exactly? ___________ What causes it to be different from 24 hours? Explain in a sentence or two or a labeled sketch.
 
 
 

What kind of day does your watch or a good clock keep anyway? ______________

5. Using your celestial sphere rectified for our latitude notice the azimuth circle labeled N, E, S, and W on the brown paper. This is the horizon. The azimuth coordinate is measured along the horizon. Label the azimuth circle on the horizon. Label N, North, 0. Label E, East, 90. Label S, South, 180. Label W, West, 270. Now additionally label N as 360.

6. The coordinate altitude in the astronomical coordinate system called the Horizon system is measured from the horizon up or down. The altitude of the horizon is zero. When the altitude is above the horizon it is denoted as a positive angle. When the altitude is below the horizon it is denoted as a negative angle. What is the altitude of the zenith in degrees? _________ What is the altitude of the nadir in degrees? _________ What is the altitude half way up in the sky in degrees? What is the altitude of the north pole from Takoma Park? _________What has the altitude of the north pole got to do with the latitude of any place in the northern hemisphere? __________ What has the altitude of the south pole got to do with the latitude of any place in the southern hemisphere? __________ What is the altitude of the north pole on the equator of the earth? ___________ What is the altitude of the south pole on the equator? _____________

7. What is the altitude of the sun at sun rise? ___________What is the altitude of the sun at sun set? ________

8. The great arc which runs from the north point on the horizon to the zenith and from the zenith to the south point on the horizon is called the Meridian. How many degrees are their in this meridian? __________ When an object in the sky---like the sun, moon, or stars---crosses the meridian it is said to transit the meridian. Objects which are near enough to the poles never raise or set, they are said to be circumpolar. Since we live in the northern hemisphere with a latitude of almost 39 degrees, then celestial objects within about 39 degrees of the north pole never raise or set they are always above our horizon. These circumpolar objects cross the meridian twice. Once when they are lowest in the sky and once when they are highest in the sky. Notice this on your celestial sphere with the pointer stars in the big dipper, ursa major, Dube and Merack. Likewise their are circumpolar celestial objects that are 39 from south pole which never raise or set they are always below our horizon, so we can never see these circumpolar objects. Centauri, the brightest star in the constellation of Centarus and the closest star to the earth other than the sun---about 4 light years away (the distance that light can travel in 4 years)---is such a circumpolar star near enough to the south pole as to be always below our horizon and therefore always invisible to us in the Washington metro area. Which direction would you have to go to be able to see Centauri?
 
 

Most celestial objects are not circumpolar from the Washington metro area. Where on the earth are all of the stars circumpolar? _________ Notice in the Washington metro area the sun which moves along the ecliptic, the moon, and all the planets which move near the ecliptic are never circumpolar. Since the sun moves along the ecliptic, because the earth goes around the sun as we modern people understand, where on the earth---in what region of the earth---is the sun sometime during the year circumpolar.________________

9. The sun is never over head in the Washington metro area. Rotate the celestial sphere around while it is rectified for our latitude and notice that the ecliptic is never overhead. What day does the sun transit the meridian at its lowest? ___________ What is the altitude of the sun when it transits at is lowest? ___________ No wonder this is such a depressing day. On this day when it transits at its lowest what direction does it raise from? On this day when it transits at its lowest what direction does it set from? ____________ What day does the sun transit the meridian at the highest? ____________ What is the altitude of the sun when it transits at it highest? _________ It is little wonder that this day is seldom depressing.

On this day when it transits at its highest what direction does it raise from? ____________On this day when it transits at its highest what direction does it set from? ____________ On what two days does the sun raise exactly from the east and set exactly from the west? _________ By the way that means on all of the other day that the sun is either north or south of east and west when it raises or sets. Are you surprised? ______ Most people who have never been nature priests or astronomers are surprised. This coordinate system is based upon the physical fact that we live on the earth and gravity pulls us to the earth establishing and up and a down locally. How high up in angle is called altitude and how far over along the horizon is called azimuth!

Celestial Equatorial coordinate System

This coordinate system is fixed in the celestial sphere so you can take your celestial sphere and hold it in your hand it need not be rectified with the north pole 39 above the north point on the horizon. The 24 dots along the celestial equator should already be numbered 0 through 24 starting with 0 which is also 24 on the vernal equinox point in Pisces. This point should already be labeled VE for Vernal Equinox. The coordinate measured along the celestial equator and numbered 0 through 24 is the right ascension and it is measured in arc hours.

1. What is the right ascension of the vernal equinox?

2. What is the right ascension of the summer solstice?

3. What is the right ascension of the autumnal equinox?

4. What is the right ascension of the winter solstice?

Declination is the other coordinate in the celestial equatorial coordinate system and it is measured perpendicular to the celestial equator. The declination coordinate is measured in degrees. The declination of the celestial equator is 0. Declinations between the celestial equator and the north pole are positive. Declinations between the celestial equator and the south pole are negative. The declination of the north pole is 90. The declination of the south pole is -90.

5. What is the declination of the vernal equinox?

6. What is the declination of the summer solstice?

7. What is the declination of the autumnal equinox?

8. What is the declination of the winter solstice?

9. What is the approximate right ascension and declination of the following

bright stars in Orion?   For a star Map of Orion click here.
Star Name right ascension declination
Betelgeuse
Beltrix
Rigel
Salf
Mintaka
Alnitak
Alnilam

This coordinate system is based upon the physical fact that the earth rotates about its north south axis once a day.

Ecliptic Coordinate System

The ecliptic coordinate system is also fixed in the celestial sphere so your sphere need not be rectified. The ecliptic coordinates are called ecliptic longitude and ecliptic latitude. The ecliptic longitude is measure in degrees along the ecliptic. The ecliptic longitude varies from 0 to 360 degrees with 0 and 360 being the same point since the ecliptic is a great circle in the celestial sphere. The zero of ecliptic longitude is the vernal equinox. The ecliptic latitude is measured in degrees perpendicular to the ecliptic. The ecliptic latitude of the ecliptic is zero. The ecliptic latitude between the ecliptic and the north ecliptic pole is positive. The ecliptic latitude between the ecliptic and the south ecliptic pole is negative. As you can probably guess by now the ecliptic latitude of the north ecliptic pole is 90 and the ecliptic latitude of the south ecliptic pole is -90.

What is the ecliptic longitude and latitude of the following points on the

celestial sphere?
Ecliptic longitude Ecliptic latitude
Vernal equinox
Summer solstice
Autumnal equinox
Winter solstice

All of the planets except Pluto travel around the sun in a plane which is only 5 from the earth's orbital plane. The earth's moon orbital plane is also only 5 from the earth's orbital plane. The earth's orbital plane about the sun and the ecliptic are really the same thing. Pluto, in fact, orbits about the sun in a plane that is only 17 from the ecliptic. This coordinate system is based upon the physical fact that the earth revolves about the sun in a year.

Galactic Coordinate System

The galactic coordinate system is also fixed in the celestial sphere so your sphere need not be rectified. The galactic coordinates are called galactic longitude and galactic latitude. The galactic longitude is measure in degrees along the galactic equator which is the midplane of our Milky Way Galaxy. The galactic longitude varies from 0 to 360 degrees with 0 and 360 being the same point since the galactic equator is a great circle in the celestial sphere. The zero of galactic longitude is the direction from our solar system to the center of the Milky Way Galaxy---this is in the constellation Cygnus. The galactic latitude is measured in degrees perpendicular to the galactic equator. The galactic latitude of the galactic equator is zero. The galactic latitude between the galactic equator and the north galactic pole is positive. The galactic latitude between the galactic equator and the south galactic pole is negative. What is the galactic latitude of the following?
Galactic Latitude
Galactic north pole
Galactic south pole

This coordinate system is mainly used to show celestial objects as either being inside of our Milky Way Galaxy or outside of it. This coordinate system is based upon the physical fact that we live in a flattened disk of stars that the solar system revolves about in approximately 250 million years.