General Astronomy, 29:61
Fall, 2005
Third Homework Set...September 9, 2005.
Due September 16, 2005

Show calculations and give reasons for your answers. Don't go around confused and despondent; if you do not know how to get started, ask us for help. The purpose of problem sets is to promote thinking and lead to understanding, not produce a confiteor of revealed truth. Note: Data for some of these problems can be found in the appendix of the textbook.

(1) You have a good clock and you set it to read 12:00 at local apparent noon. It turns out on the day you do this, the apparent solar day is 24h 0m 10s. Twenty days later, you measure the position of the Sun at 12:00. Where is it? By this I mean, is it on the meridian, is it to the east of the meridian, west of the meridian, etc? If it is not on the meridian, give a measure of how much it is to the east or west (i.e. how much earlier did it transit, or much longer will you have to wait for it to transit). It will be a help to thinking about this problem if you first remember what kind of time a regular clock keeps.

(2) The latitude of San Diego is $32^{\circ} 43^{'}$. Calculate the maximum flux of solar heating of the ground (units Watts/m$^2$). Note that I am asking for the effective heating of the Earth in Watts per unit of area on the ground, not the solar constant as defined in class. What is the minimum solar heating flux?

(3) You are transported by spaceship to the planet Minerva, which orbits the star Tau Ceti. Minerva has an orbital period about its star of 180.0 Earth days. The sidereal rotational period of Minerva is 1.5 Earth days. (a) What is the mean solar day on Minerva (units of Earth days)? (b) What is the length of the year in mean solar days as observed on Minerva. (c) The Minervans celebrate the start of their year on the day of the summer solstice. They also decide to define each year as having exactly 120 days (again, days as measured on Minerva, not Earth days). How long will it take before their calendar is so badly out of whack that the first day of the year falls on the winter solstice?

(4) The inclination of the Moon's orbit to the plane of the ecliptic is $5^{\circ} 8^{'}$. Approximating the Moon's orbit by a circle (we'll learn better next week), what is the maximum distance that the Moon is above or below the plane of the ecliptic?

(5) It is 2PM on November 1. What is the Local Sidereal Time? Hint # 1: For the precision of this problem, don't worry about distinguishing between the length of the mean solar day and the sidereal day. Hint # 2: Think about your SC1 chart.

(6) Van Allen Hall has a latitude of $41^{\circ}31^{'}$ N, and longitude $91^{\circ}32^{'}$W. The latitude and longitude of a point in Des Moines are $41^{\circ}32^{'}$N and $93^{\circ}39^{'}$ W, respectively. It is local apparent noon here in Iowa City. What is the apparent solar time in Des Moines?

(7) Is it possible to have a full moon twice in a calendar month? Explain your answer.

(8) Where on the Earth is it possible for the ecliptic to lie on the horizon? Give your argument, which could be geometrical.