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From: johnf@apollo.uucp (John Francis)
Newsgroups: net.puzzle,sci.physics
Subject: Re: Funny Orbits       (SPOILER INCLUDED)
Message-ID: <30e40c0c.917@apollo.uucp>
Date: Fri, 24-Oct-86 12:55:21 EST
Article-I.D.: apollo.30e40c0c.917
Posted: Fri Oct 24 12:55:21 1986
Date-Received: Sun, 26-Oct-86 01:18:57 EST
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Organization: Apollo Computer, Chelmsford, Mass.
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Xref: watmath net.puzzle:2108 sci.physics:51

> Assume that an object in a circular orbit suddenly has its mass cut in half.
> What happens to the orbit?
> By the way, the factor of 2 in the above question is critical. If it is
> greater than 2 something else happens and if it is less than 2 something else
> happens.

Both halves of the object continue in a circular orbit :-)

Assuming that what the problem *really* means is that the mass is reduced to 1/2
the original mass while something else is left unchanged - what does not change ?
Is it the momentum or the energy ?


        SPOILER FOLLOWS

As under Newtonian dynamics the orbits of all objects moving in a central
inverse-square field are conic sections, the original poser is obviously
looking for the answer "the orbit becomes a parabola". If the factor is
greater than 2 the orbit will become hyperbolic, and if less than 2 it will
become elliptical.

Given this fact, deduce whether the momentum or the energy should be assumed
not to have changed.