Topic:  2 body problem

1. For Thurs 9.22:
 --read pp. 22-32 
 --scan pp. 33-34 
 --read pp. 48-49

2. For Tues 9.27 (but try get started before Thursday--download the code
and bring in a laptop if you have one on Thursday).
 --Download the mercury6 code from here: http://www.arm.ac.uk/~jec/ and
read the instruction file ("mercury6.man") (If you really insist, you
may use a different N-body code.  Some
other codes which you can google are SWIFT/SWIFTER, HNbody, and 
Hut's hermite code.)
 --Simulate the Sun and Mercury for a few orbital times with an N-body
code, and show that Mercury's orbit produced by the code has a=.39,
e=.2, and that it traces the analytical expression for the ellipse r =
a*(1-e^2)/(1+ecos(theta-pomega)). Do that by plotting both r vs. theta
from the code, and overplotting the analytic expression. Note:  you will
need to modify the following files 
     (a) big.in (to remove all planets other than
Mercury; you may also make mercury coplanar by setting its z=vz=0, and
set epoch=0) 
    (b) small.in (to remove all small bodies)
    (c) param.in (to change algorithm--I recommend bs2 for now; and to change 
start time, stop time, etc) You will also need to modify element.in and 
compile and run element6.for after mercury6 has finished running.  That will create
a file MERCURY.aei, whose columns you can read and plot with a program
of your choice, e.g. supermongo, gnuplot, matlab, mathematica, python's
matplotlib, etc. If you
have never used a plotting program, gnuplot is probably the simplest to learn.
 For example, to plot column 1 vs. column 7 starting from the 5th line
in gnuplot, you would write "plot 'MERCURY.aei' every ::5 using 1:7" For
more help with gnuplot, see number 6 here:
http://faculty.wcas.northwestern.edu/yoram/phys252/lecture01/gnuplot.html 
as well as the links at the bottom of that page, and google.