Homework Assignment Number Three

This is your first homework assignment that is primarily mathematical. Please show your work; include sentences explaining what you are doing. You may of course use a calculator for numerical values, but do not expect full credit for a “correct” numerical answer unaccompanied by work or explanation! You will need to determine some numbers below from the Internet or hardcopy; please cite your source. For the purposes of this homework, we will assume that the circumference of the earth through the poles is 24,900 miles.

1. Using a globe or an atlas, determine the location on the earth, which is directly opposite that of Colorado Springs! (We call these antipodal points.)
2. Well, problem #1 was exciting. Now find two antipodal points, both of which are on dry land!
3. I have friends in Orlando, Florida, and friends in London, England. How high in the sky does the sun reach for these friends on the summer solstice? How high in the sky does the sun reach for these friends on the winter solstice?
4. Use an Internet or hardcopy source, find out the latitude for Colorado Springs and Pueblo. Assume that Pueblo is due south of Colorado Springs. Then compute the distance from Colorado Springs to Pueblo! Find a mileage figure from an atlas or elsewhere, and compare your answer to this. Speculate briefly on the difference between your answers, taking into account the various mathematical and practical assumptions you’ve made.
5. Denver and Indianapolis are at almost the same latitude. Find our what these latitudes are. Use this latitude, and their difference in longitude to compute the distance between them, if we traveled along the line of latitude between them. Find out the air flight distance between these two cities, and again speculate briefly on the difference between your answer the air flight distance.
6. The modern estimate for the mean length of the synodic period for the moon is 29.530588 days (see Table 2.4 in Richards). If we were to use 29.5 days as an estimate, how far off would we, if we measure time in hours, minutes and seconds?
7. (Problem 3 continued) How many of our 29.5-day months would pass, before we would be one full day off? How many of our 29.5-day months would pass, before we would be one full month off?
8. The modern estimate for the mean length of one tropical year is 365.242199 days. How many hours, minutes and seconds would we be off if we used an estimate of 365.5 days? How many of our 365.5-day years would pass, before we would be one full week off?