% -*- latex -*-
% FILE: "/home/evmik/jobs/wm/2013_spring_Modern_Astrophysics_476/hw03/hw03.tex"
% LAST MODIFICATION: "Mon, 28 Jan 2013 12:39:16 -0500 (evmik)"
% (C) 2010 by Eugeniy Mikhailov, <evgmik@gmail.com>
% $Id:$
\documentclass[letter,12pt]{article}

%---------------------------------------------------------------
\usepackage{listings}
\usepackage{color}
\usepackage{fullpage}
%---------------------------------------------------------------

\begin{document}
\newcommand{\problem}[1]{%
	{\flushleft  \bf #1\\}
}
\newcommand{\hw}[1]{%
	\begin{center}
		\Large  \bf Homework #1%
	\end{center}%
}
\newcommand{\mat}[1]{% matlab code
{\color{blue}\texttt{#1}}%
}

%---------------------------------------------------------------
\hw{03}

\problem{Problem 1 (5 points)}
%---------------------------------------------------------------
Prove that for an orbit governed by
\begin{eqnarray*}
	\frac{p}{r} &=& 1 + e \cos(\theta)
\end{eqnarray*}
the semiminor axis ($b$) is given by $p/\sqrt{1-e^2}$.


\problem{Problem 2 (5 points)}
%---------------------------------------------------------------
Plot an orbit in x,y coordinates for $p=1$ and $e=.5$


\problem{Problem 3 (5 points)}
%---------------------------------------------------------------
Suppose two masses with $m_1=1$ and $m_2=1$ orbit each other,
suppose also that the semimajor axis $a=10^4$ m and the eccentricity $e$=0.2.
Plot orbits of both masses on the same plot as they orbit each other.


\problem{Problem 4 (5 points)}
%---------------------------------------------------------------
Solve problem 2.12 from the text book.


%---------------------------------------------------------------
\end{document}
%---------------------------------------------------------------