\documentstyle[11pt]{article}

\textheight 22cm
\textwidth  16cm
\hoffset= -0.6in 
\voffset= -0.5in   
\setlength{\parindent}{0cm}
\setlength{\parskip}{15pt plus 2pt minus 2pt}
\pagenumbering{roman} 
\setcounter{page}{-9}


\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\bd}{\begin{displaymath}}
\newcommand{\ed}{\end{displaymath}}
\begin{document}


\begin{center}
{\Large ASTR430 Midterm\\
75 minutes in class\\
  160 Points\\}
\end{center}

These are three questions from ASTR430 midterms that I have given in
the past. This year there will be three problems with about this level
of difficulty. As here, I will often ask you to apply what you have
learned in ASTR430 to problems that we haven't considered in class
yet. There will not be a descriptive question this year.

Draw nice pictures and show your work! If you run out of time, explain
where you are stuck, and/or what you would have done.  Good luck!

1. {\bf [30 pts]} Two-Body Motion. Find the place along an elliptical
orbit where $v_r = dr/dt$, the radial velocity, is maximum.

2. a) {\bf [25 pts]} Reading from The New Solar System. In a short
paragraph, describe Plate Tectonics.  What drives it?  On which
object(s) does it appear to be operating?\\ b) {\bf [25 pts]} In a
short paragraph or two, describe how the solar wind and cosmic rays
cause the aurora and the Van Allen radiation belts on Earth.

3. a) {\bf [20 pts]} 
Dimensional Analysis. Find an approximate expression
for the central pressure of the Earth using Dimensional Analysis and
assuming that the answer depends only on the Earth's mass
$M_E\approx6\times10^{24}$kg, its radius $R_E\approx 6\times10^6$m,
and the gravitational constant $G\approx
7\times10^{-11}$m$^3$s$^{-2}$kg$^{-1}$. Assume that the arbitrary
dimensionless constant is one, and evaluate your expression in bars --
$10^5$pascals (mks unit) = 1bar. The atmospheric pressure at sea level
is 1bar.\\ b) {\bf [10 pts]} Repeat part a) to get the form for the
pressure a distance $r$ from the center of the Earth. 


\enddocument}