\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 ASTR450 Homework \# 4 -- Central Force Motion\\
Due Tuesday, October 15}
\end{center}

Reading: Finish reading Danby's Chapter 6. You can skim sections 6.6 \&
6.7, and skip sections 6.8-6.13.

1. Danby: Page 136, Problem 2. This is a hard problem. The
relationships between $\nu$, $E$ and $M$ will be useful as will the
discussion and plot on page 133.

2. Danby: Page 136, Problem 6. For what value of q is the time spent
inside 1 AU maximum, and what is the maximum time?  Give a physical
reason for why this value of q is ``reasonable'' (draw a picture).

3. Danby: Page 137, Problem 9. The problem is asking for the time
average of $r$.

4. Danby: Page 137, Problem 12. If we increase Earth's orbital
eccentricity while leaving its semimajor axis constant, does it
receive more sunlight over a year or less?

5. Read the text and the worked example problems for sections 1-6 in the
``Building Physical Intuition in Mechanics'' handout. Try to do some
of the problems for practice!  An answer to one of these problems
consists of a statement for EACH of the multiple choice possibilities
indicating either a) why it cannot be correct or b) that it might be
correct. Remember, checking limits, units, and symmetries can rule out
wrong answers, but cannot prove correct ones. The techniques that you
will learn by doing these problems will help you avoid math mistakes
on your homeworks. You can also expect one of these problems on the
midterm! For this homework, write up your solution to {\bf problems 9
  and 26} (for 26, H and L are the heights when the iceberg is not
oscillating).
 



\enddocument{}