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From: henry@utzoo.UUCP (Henry Spencer)
Newsgroups: net.space
Subject: Re: Galileo mission to Jupiter
Message-ID: <5592@utzoo.UUCP>
Date: Sun, 12-May-85 01:16:05 EDT
Article-I.D.: utzoo.5592
Posted: Sun May 12 01:16:05 1985
Date-Received: Sun, 12-May-85 01:16:05 EDT
References: <1671@mordor.UUCP> <24@escher.UUCP>, <10563@brl-tgr.ARPA>
Organization: U of Toronto Zoology
Lines: 64

> 	Ok, I've heard lots of times about the 'gravity assist'
> maneuver used to sometimes dramatically increase the speed of
> a spacecraft by flying close to a bigger mass.  Now the question
> is, how does this work?  I understand that you would gain energy
> by dropping weight when inside a gravity well (and having the
> velocity vector pointed so that you could make it out, now lighter
> and requiring less energy), but is that the ONLY cause of the
> acceleration?  I thought that this effect was also due to rotating
> the velocity vector of the spacecraft.

There are two separate types of maneuver here.  One, classically called
a "gravity-well" maneuver, flies very close to a large mass so that an
engine burn can be made at the lowest possible potential energy.  The
other, often called a "gravity-boost" maneuver, is a three-body maneuver
(the Sun is usually the third body) using gravity alone to transfer some
momentum from a large body to the spacecraft.

The gravity-well maneuver exploits the difference between momentum and
kinetic energy to give the spacecraft higher final velocity.  How much
velocity you gain from an engine burn is a matter of momentum; how much
you gain or lose to a gravity field is a matter of energy.  Since energy
is proportional to the *square* of velocity, and leaving a gravity field
subtracts a fixed amount of energy, the higher the velocity with which
you start to leave a gravity field, the less velocity you lose to gravity.
So an engine burn's effect is magnified if you fly into a handy gravity 
field before making it.  The scales remain balanced:  you carry the fuel
down with you and don't bring it back up, so it loses energy.

The gravity-boost maneuver exploits relative motions.  With respect to
Jupiter, flying past Jupiter will only rotate your velocity vector, and
cannot change its magnitude.  The key is the words "with respect to
Jupiter".  If what you care about is velocity with respect to something
else, and Jupiter is moving with respect to that something else, then
you can gain or lose velocity.  In the limiting case, an extremely tight
hyperbola whips you around an almost 180-degree turn with respect to
Jupiter.  You leave heading almost exactly back along your approach path.
So Jupiter-relative Vdepart = -Vapproach.  If your approach was, say,
along Jupiter's orbit in the reverse direction, then viewed from the Sun
you were moving at Vapproach-Vjupiter on the way in, and on the way out
you're at Vdepart-Vjupiter = -Vapproach-Vjupiter = -(Vapproach+Vjupiter).
So your Sun-relative velocity vector has been flipped 180 degrees (hence
the minus sign), but has also had 2*Vjupiter added to it.  There is nothing
magic about it, since Jupiter has lost the same amount of Sun-relative
momentum you've gained.  But considering the relative masses, a given
amount of momentum matters a lot more to you than to Jupiter!

It is, of course, possible to combine the two effects.

> 	I've also heard that the maneuver works best when you get
> closest to the object being slingshot off of.  Is this true?
> (it would seem so)

Both types of maneuver work best if you get as close as you can.  The
gravity-well maneuver works best if you convert as much potential energy
as possible into kinetic energy first.  The gravity-boost maneuver's
results depend on how far your velocity vector rotates with respect to
the body you're flying past; the closer the approach, the sharper the
turn.  Of course, you can only fly so close without hitting something.
There was some interest in arranging Voyager 2's Neptune flyby to send
it on to Pluto, but somebody calculated the approach distance and it
came out to be several hundred kilometers *below* the cloud tops...
-- 
				Henry Spencer @ U of Toronto Zoology
				{allegra,ihnp4,linus,decvax}!utzoo!henry