From: utzoo!decvax!duke!karn@eagle.UUCP
Newsgroups: net.space
Title: Re: Pioneer 10 leaves solar system - (nf)
Article-I.D.: eagle.926
Posted: Mon May  2 22:04:50 1983
Received: Tue May 17 07:52:05 1983
References: pur-phy.751

Relay-Version:version B 2.10 delta 4/26/83; site burl.UUCP
Path:burl!spanky!hocda!houxz!houxm!mhuxa!mhuxj!mhuxt!eagle!karn
Message-ID:<926@eagle.UUCP>
Date:Mon, 2-May-83 22:04:50 EDT

Yes, a spacecraft is indeed interstellar when it exceeds the sun's
escape velocity, unless of course it impacts some object standing in the
way.  Braking into orbit around a planet takes a considerable
amount of energy. The best look at a planet that can be achieved without
braking in a two-body situation (which is a very good approximation) is a
hyperbolic flyby.

The velocity required to reach the moon is not quite earth escape
velocity; it is approximately the velocity required to inject the
spacecraft into an elliptical orbit with the apogee at the moon's orbit
and perigee at the parking orbit altitude.  In fact, this is how lunar
missions were planned.  A simple two-body approximation was first made
(ignoring the moon) followed by computationally intensive numerical
integrations in which the various orbital parameters were iterated
until the "best" results for lunar orbit insertion were obtained.
There are still no simple analytic ways to optimize arbitrary multi-body
trajectory problems.

Phil