\documentstyle[11pt]{article}
\textwidth 14.0cm
\oddsidemargin 0pt
\evensidemargin 0pt
\begin{document}
\begin{large}
\begin{center}
{\bf General Astronomy, 29:61\\
     Fall, 2004\\
Third Homework Set...September 12, 2004.\\ Due September 17, 2004}\\
\end{center}
\end{large}
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 {\em confiteor} of revealed truth. {\bf Note: Data for some of these problems can be found in the appendix of the textbook}.\\

\noindent
{\bf(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 23h 59m 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. {\em It will be a help to thinking about this problem if you first remember what kind of time a regular clock keeps}. \\

\noindent
{\bf (2)}  The latitude of Miami is $25^{\circ} 47^{'}$.  Calculate the maximum flux of solar heating of the ground (units Watts/m$^2$).  Note that I am asking for the {\em effective } heating of the Earth in Watts per unit of area on the ground, not the {\em solar constant} as defined in class.  What is the minimum solar heating flux? \\ 

\noindent
{\bf (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 days.  (a) What is the mean solar day on Minerva?  (b) What is the length of the year in mean solar days {\em 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?  \\

\noindent
{\bf (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?    \\ 

\noindent
{\bf (5)} The Central Time Zone is centered on $90^{\circ}$ West longitude.  On the average, how much will local apparent noon here in Iowa City differ from 12:00 noon, Central Standard Time? Give the sense of the error as well, i.e. local apparent noon being early or late with respect to CST.  Ignore daylight savings time.  \\ 

\noindent
{\bf (6)} What is the lowest declination of an astronomical object that can be seen here in Iowa City? \\ 

\noindent
{\bf (7)} Consider the solar flux incident on the ground, with units of Watts/m$^{2}$.  As in problem \# 2, this is the effective heating flux, not the ``solar constant'', and takes into account the obliqueness of the Sun's rays.  Let $W_1$ be the solar heating flux at noon on the summer solstice, and $W_2$ be the solar heating flux at noon on the winter solstice.  The difference $\Delta W = W_1 - W_2$.  Write down an equation describing how this depends on latitude.  For what latitude is $\Delta W$ a maximum?  For what latitude is $\Delta W$ a minimum?   \\

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



\end{document}
