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From: bill@utastro.UUCP (William H. Jefferys)
Newsgroups: net.physics
Subject: Re: slingshot effect (Clarification)
Message-ID: <89@utastro.UUCP>
Date: Thu, 21-Nov-85 11:18:34 EST
Article-I.D.: utastro.89
Posted: Thu Nov 21 11:18:34 1985
Date-Received: Sat, 23-Nov-85 10:08:31 EST
References: <395@wuphys.UUCP> <693@lasspvax.UUCP> <88@utastro.UUCP>
Organization: U. Texas, Astronomy, Austin, TX
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> 
> In the center-of-mass frame of reference of the planet and the probe,
> the two bodies approach and recede on symmetrically placed hyperbolic
> orbits.  The two bodies approach and recede with the same speed.
> (The massive planet hardly moves at all in this encounter and to
> a first approximation we can regard it as fixed, i.e., on a degenerate
> hyperbolic orbit).

Rereading this, I notice that it is a little ambiguous.  I meant to
say that the probe leaves the encounter with the same speed (at infinity)
that it enters with.  The above might be interpreted to mean that the
planet and the probe had the same speed, which is obvously wrong.
The two hyperbolas are symmetric in shape, but not in size, and in
the limit as the mass of the planet goes to infinity, the planet's
hyperbolic orbit shrinks to a point.