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From: karn@eagle.UUCP
Newsgroups: net.space
Subject: Re: many body calculations
Message-ID: <998@eagle.UUCP>
Date: Tue, 14-Jun-83 02:51:12 EDT
Article-I.D.: eagle.998
Posted: Tue Jun 14 02:51:12 1983
Date-Received: Wed, 15-Jun-83 03:48:42 EDT
Lines: 28

This is a topic that has lately come near and dear to my heart (I'm
doing the kick motor calculations for the amateur satellite Phase 3-B,
due to be launched this Thursday morning). The method which Lew Mammel
describes is known in the literature as the "Cowell Method", which is
just the numerical integration of the second-order differential
equations that describe an orbit.  The beauty of this method is its
simplicity and the ease with which it can include perturbing factors
(other planets, air drag, earth oblateness, etc.)

On the other hand, if the problem you're solving is a good approximation
to two-body motion (i.e., one large body dominates the motion of your
satellite) then you can integrate just the perturbing forces with
respect to a reference two-body orbit, updating the reference orbit
when you get too far away.  This is Encke's method, and it allows larger
step sizes (increasing program speed and reducing accumulated roundoff error)
than Cowell's method.

There are lots of methods for doing the numerical integration that these
models require.  Having no formal training in the subject, I'm only now
becoming familiar with the Runge-Kutta method, which is apparently the
simplest (but not the fastest or most accurate) algorithm available.  It
is, however, a refinement of the method which Lew describes, and is
probably much more accurate.

I'm learning to distrust anything a computer prints out with a decimal
point wedged between digits...

Phil Karn