Astro 120
Problem Set Number 1

Due in recitation Friday, September 9 or Monday, September 12

  1. (10 points) On the following map, derived from the celestial sphere, add or label the following:
    1. The axes.
    2. The celestial equator.
    3. The north and south celestial poles.
    4. The vernal and autumnal equinoxes.
    5. The stars Rigel, Sirius, Arcturus, and Antares (note that you'll need to look up their coordinates in Appendix F your textbook).
    6. The path of the Sun over the course of a year (be sure to indicate the direction of motion).
    7. The position of the Sun on the day you complete this problem set.
    8. Show, roughly, the part of the sky that is dark (i.e. visible at about 10PM or so) on that same day.

  2. (10 points) Describe the approximate direction, in horizon coordinates (i.e. altitude and azimuth), of the sunrise from the following locations on the given dates. Tell a bit about why this event 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 December 21.
      Rises South of due East (Azimuth about 125 degrees) and takes a few minutes to rise (a bit more than 2 minutes) and rises at an angle of 48 degrees to the horizon.
    2. Sunrise viewed from the Earth's equator on September 21.
      Also rises due East (azimuth 90 degrees), and rises faster than in Ames (2 minutes) as it goes straight "up"...
    3. Sunrise from the North Pole on June 21.
      The Sun is up 24 hours/day on June 21 as viewed from anywhere north of the Arctic Circle, so at the pole it doesn't rise - it is above the horizon all day.
    4. Sunrise from the South Pole on September 21.
      Well... the Sun's motion away from the horizion is caused by the changing angle with the Earth; so it takes about 2 days to rise (23.5 degrees covered in 3 months from equinox to solstice, so 2 days to cover the 1/2 degree).
    Why might people at the South Pole be very happy about sunrise on September 21? And why might astronomers at the North Pole also be happy on that same day?
    After 6 months below the horizon, that first view of the sun must be almost miraculous!  Similarly, astronomers at the North Pole say goodbye to the sun and can look forward to several months of nightime observing with no breaks (except for clouds, snowstorms, and rampaging polar bear attacks).

  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.
    The most vulnerable player on the field is the batter - s/he faces the pitcher and must hit (or run away from) the pitch coming at him/her at high speeds.  The batter must not have the sun in his/her eyes, and if the field points to the northeast, the sun will always be behind the hitter.  The right fielder must simply cope.

  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
      48 degrees (90 - latitude); 48+23.5=71.5 degrees; 48 degrees; 48-23.5=24.5 degrees
    2. Cape Town, South Africa (lat 34 deg S, long 18 deg E) on March 21, June 21, September 21, December 21
      55 degrees (90-35); 31.5 degrees (55-23.5); 55 degrees, 55+23.5=78.5 degrees
    3. Tromso, Norway (lat 72 deg N, long 21 deg E) on March 21, June 21, September 21, December 21
      18 degrees (90 - 72); 18+23.5=41.5 degrees; 18 degrees; 18-23.5=-5.5 degrees (below the horizon!)

  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?
    The siderial month is the time it takes the moon to orbit the Earth relative to the stars.  Once it does so, however, the Sun has moved farther East and so some more time is needed for the moon to catch up to the Sun - the synodic month.  As it takes 27.3 days for a siderial month, in that time the sun has moved about 26 degrees farther East.  At the rate the  moon moves (13 degrees per day) it takes the moon 2 more days to catch up the lost ground.