APAS 1010

PROBLEM SET #1

Ursa Major, Ursa Minor, and Polaris

   In Greek myth the great bear was originally the gorgeous Callisto of Arcadia, daughter of King Lycaon. She was transformed into the bear to hide her from the jealous Juno. Her young son, Arcas, while out hunting, did not recognize his mother and was about to slay her, and the gods placed them both in the heavens as the Big and Little Bear. Because of the enmity of Juno, the bears are not allowed to go to rest beneath the rim of the earth like the other constellations, but must circle the Pole eternally. They have long tails because Jupiter flung them by their tails. Callisto has appeared in the heavens also as one of the moons of Jupiter. Not the most beautiful of moons, Callisto is the most pock marked of them all.

   But, back to the tip the tail of Little Bear. The altitude of the north pole point above the northern horizon is always equal to the latitude of the observer. Thus at the equator, the altitude of the north pole is zero, and at the north pole of the earth the altitude of 90 degrees. In Boulder the altitude of the north pole is 40 degrees.In the skies of Boulder, a star that is less than 40 degrees from the pole never sets and is known as a circumpolar star, and its constellation is a circumpolar constellation.

   Our latitude on the earth is the number of degrees we are north or south of the earth's equator. The declination of a star on the celestial sphere is its angle above or below the celestial equator. The celestial equator is always directly above the earth's equator.

   The declination of the north pole point is 90 degrees and the declination of the celestial equator is 0 degrees. In Boulder the range of declinations of stars that are circumpolar is 50-90 degrees.

QUESTIONS:

  1. What is the range of declinations of circumpolar stars at the north pole of the earth?
  2. What is the range of declinations of circumpolar stars at the equator of the earth?
  3. What is the altitude of the north pole at Aswan (23.5 degrees) and Cairo (30 degrees)?
  4. What are the ranges of declinations of circumpolar stars at Athens and Cairo?
  5. The outmost pointer star of the Big Dipper has a declination of 56 degreees. At what latitude is it no longer circumpolar ?

DEFINITIONS:

Celestial equator: outward projection of earth's equator. Thus at earth's equator the celestial equator passes through the zenith and at the earth's pole the celestial equator lies along the horizon.
Celestial pole: point on celestial sphere intersected by the earth's axis of rotation.
Declination: angular distance on the celestial sphere above or below the celestial equator.
Right Ascension: distance measured (in hours of time) eastward along the celestial equator starting at the location of the sun at vernal equinox.
Equinox: Dates when the sun crosses the celestial equator, when the sun has a declination of 0 degrees.
Vernal equinox: The day at which the sun crosses the celestial equator moving from south to north; approximately on March 21.
Solstices: Two days when the "sun stands still" on approximately June 21 (summer solstice) and December 21 (winter solstice). At summer solstice the sun has a declination of +23.5 degrees, and at winter solstice it has a declination of -23.5 degrees.
Zenith: Directly overhead; altitude of 90 degrees. Zenith sun refers to the situation of the sun crossing the zenith. The sun never crosses the zenith at Boulder. Only between the Tropic of Cancer (latitude +23.5 degrees) and Tropic of Capricorn (latitude -23.5 degrees) does the sun cross the zenith.
At solar noon the altitude of the sun above the southern horizon is equal to 90 degrees minus latitude plus declination. Thus at equinox the altitude of the sun at noon is 50 degrees above the southern horizon; at summer solstice the altitude of the sun at noon is 73.5 degrees.

QUESTIONS:

6. What is the altitude of the sun at noon in Boulder on December 21?
7. What is the altitude of the sun at noon on the Tropic of Cancer on December 21?
8. What is the altitude of the sun at the North Pole of the earth on Summer Solstice? At Athens and Cairo?
9. On what day does the sun cross the zenith at the earth's equator?
10. What is the altitude of the sun on June 21 as seen from the north pole. Describe the motion of the sun throughout that day.
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