Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/26/83; site ihuxr.UUCP 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