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From: bs@linus.UUCP (Robert D. Silverman)
Newsgroups: net.puzzle,sci.physics
Subject: Re: Funny Orbits       (SPOILER INCLUDED)
Message-ID: <359@linus.UUCP>
Date: Tue, 28-Oct-86 14:15:52 EST
Article-I.D.: linus.359
Posted: Tue Oct 28 14:15:52 1986
Date-Received: Wed, 29-Oct-86 05:20:13 EST
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Xref: mnetor net.puzzle:1545 sci.physics:73

> > 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.

As a followup one can assume 3 separate conditions:

(1) Momentum is conserved
(2) Kinetic energy is conserved
(3) Momentum changes from mv to mv/2 and energy from 1/2mv^2 to 1/4mv^2

What happens in each????

Bob Silverman