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\centerline{\bf Central Forces\qquad Orbits}
\medskip
\centerline{\it Keep in your notebook}
\bigskip

In the Maple worksheet, {\tt http://physics.oregonstate.edu/ph426/orbits.mws}, you
will be examining how various parameters affect orbits.

\begin{enumerate}
\item  {\bf Work through the worksheet until you have plotted the effective
potential.}  Look at the graph of the effective potential.  Draw your
prediction of the shape of the orbit using information from the graph of the
effective potential.  Indicate on your plot the vectors $\vec r_{\rm min}$ and
$\vec r_{\rm max}$.
\vfill\vfill

\item  {\bf  Continue through the worksheet.}  Compare the plot of the orbit
to your prediction.
\vfill

\item  The blue dots on the orbit plot
are points of the orbit at equal time intervals.  Why are the dots more widely
spaced in some places?  What information about the spacing can you get from
the effective potential diagram?
\vfill

\item  {\bf Go through the worksheet several times, experimenting with
different parameters.}  What values of the parameters give you elliptic
orbits? hyperbolic? circular?
\vfill

\item  (Challenge)  Try some other potentials such as:

{\bf Harmonic Oscillator:}  $U(r)={kr^2\over 2}$

{\bf First Order General Relativistic Correction:} $U(r)=-{k\over
r}+{\delta\over r^3}$, for $\delta$ very small.
\end{enumerate}

\vfill
\leftline{\it by Corinne Manogue, Jason Janesky, and Kerry Browne}
\leftline{\copyright 2000 Corinne A. Manogue}
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