## Astro 120 Problem Set Number 1

### Due in recitation Friday, September 12 or Monday, September 15

1. (10 points) On the following sketch of the celestial sphere, add or label the following:
1. The axes.
2. The celestial equator.
3. The north and south celestial poles.
4. The ecliptic.
5. The vernal and autumnal equinoxes.
6. The stars Vega, Sirius, Betelgeuse, and Alpha Centauri (note that you'll need to look up their coordinates in your textbook).
7. The path of the Sun over the course of a year (be sure to indicate the direction of motion).
8. The position of the Sun on the day you complete this problem set.
9. The part of the sky that is dark on that same day.

2. (10 points) Describe the approximate direction, in horizon coordinates, of the sunrise from the following locations on the given dates. Tell a bit about why this sunrise might be unusual (if at all). Also estimate how long it takes for the Sun to clear the horizon (the Sun has an angular diameter of about 0.5 degrees).
1. Sunrise from here in Ames on September 21.
2. Sunrise viewed from the Earth's equator on September 21.
3. Sunrise from the North Pole on March 21.
4. Sunrise from the South Pole on September 21.
Why might people at the North Pole be very happy about sunrise on March 21? And why might astronomers at the South Pole also be happy on that same day?

3. (4 points) It is an unwritten rule in baseball that the orientation of the diamond points northeast - that is, the line starting at home plate, running in the direction of second base, usually points to an azimuth of about 45 degrees. Speculate on why that might be, given the usual position of the batter and fielders and the direction of their gazes. Remember that baseball traditions mostly originated before stadium lights were invented; i.e. think of day games.

4. (10 points) What is the altitude of the noon Sun on the following dates at these locations?
1. Ames, IA (lat 42 deg N, long 93 deg W) on March 21, June 21, September 21, December 21
2. Tromso, Norway (lat 72 deg N, long 21 deg E) on March 21, June 21, September 21, December 21
3. Key West, FL (lat 23.5 deg N, long 80 deg W) on March 21, June 21, September 21, December 21

5. (6 points) Explain why the sidereal month is shorter than the synodic month. You will need to explain the meaning of the two months in your answer. Why is the difference between the two types of months 2 days, and not, say, 4 or 6?