HOMEWORK SET #1
DUE: 15 SEPTEMBER

• show all steps in the simple required calculations. That way, if you make an arithmetic error on a question, it still may be possible for us to assign partial credit.

• write complete sentences. Be legible! We can't give a grade to something we can't read.

• cleanly labeled diagrams are almost always helpful and sometimes are required for a complete explanation.

• come to the help sessions if you are not absolutely clear on how to do any of the questions.

1. What is the altitude of the North Celestial Pole in Seattle, Washington? How about in La Serena, Chile?

2. As discussed in class, the dates of the solstices and equinoxes correspond to particular points in the Earth's orbit about the Sun. What is the highest point (altitude) that the Sun can rise on March 21, June 21, September 21, and December 21 in Seattle and La Serena?

3. If, for example, the Sun transits (crosses) the local celestial meridian in Seattle at exactly local noon on a certain day, how much time will elapse in Seattle before the Sun next transits in La Serena?

4. Circumpolar stars are defined as stars that never set below the horizon of an observer at a particular latitude. One consequence of this is that astronomers often need to travel on taxpayers' expense to places like Chile to make their observations. What is the range of declinations for the group of stars that are always visible (they never set above the horizon) in Seattle and La Serena? How about the range in declination that are never visible (they never rise about the horizon) in these two cities?

5. What is the average angular size of the Sun as seen from the Earth? (Please use the small-angle formula and show all steps). Use the same method to calculate the angular size of the Moon and Mercury as seen from the Earth. What do you conclude?

6. At approximately what time of the year is the full Moon highest in the skies of Austin, Texas? What is the highest point or altitude (approximately) to which it can rise in our skies?

7. We know that the Earth's rotation axis is tilted by 23.5 degrees with respect to the axis of its orbit, so that the Earth's equator does not line up with the plane of its orbit. We also understand that this causes the seasons on the Earth. So! With the aid of cleanly labeled pictures of the Earth in its orbit, speculate what would be nature of the seasons on an earth that was "standing straight up" such that the tilt between rotational and orbital axes was 0 degrees. How about if the earth was "lying on its side" such that the rotation axis was lying in the plane of the orbit. In this, keep the rotational pole pointing to the "North Star" at all times of the year. No calculations required here! Just look at your sensible pictures and make sensible conclusions.

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