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Path: utzoo!linus!philabs!cmcl2!floyd!vax135!ariel!houti!hogpc!houxm!ihnp4!ihuxr!lew
From: lew@ihuxr.UUCP
Newsgroups: net.space
Subject: Re: many body calculations
Message-ID: <468@ihuxr.UUCP>
Date: Mon, 13-Jun-83 16:39:03 EDT
Article-I.D.: ihuxr.468
Posted: Mon Jun 13 16:39:03 1983
Date-Received: Wed, 15-Jun-83 12:32:59 EDT
Organization: BTL Naperville, Il.
Lines: 26

There have been several inquiries about calculating planetary movements
and many-body behavior. I not sure if this fills the bill, but you can
get excellent results with a straight-forward application of "F=ma",
combined with "F=m1*m2/r^2" (vector versions, of course). One simple
trick which increases the accuracy tremendously is the following.

Calculate the positions of the bodies half a time unit from the current
time (ignoring acceleration), and use these positions to calculate the
gravitational forces during that time unit. This comes much nearer to
providing the correct accelerations than using the positions at the
beginning of the time interval.

When I was a TA at Lehigh in the introductory physics course,
the students were given this method to calculate one period
of a planet, given an initial position and velocity. I computed the
orbital elements and compared them with the simulation and found a
really fine agreement with a few hundred time units per orbit.

I later used this method to estimate the magnitude of Jupiter's
perturbation of Mars's orbit. My preliminary conclusion was that it was
great enough that it should have defeated Kepler in his "war on Mars".
Maybe Kepler had data points near nodes of the cyclic variation
of the perturbative effects. Anyway, I've never resolved this question
to my own satisfaction.

		Lew Mammel, Jr. ihuxr!lew