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From: KFL@MIT-MC.ARPA ("Keith F. Lynch")
Newsgroups: net.space
Subject: Slingshot effect
Message-ID: <[MIT-MC.ARPA].726285.851121.KFL>
Date: Thu, 21-Nov-85 00:20:37 EST
Article-I.D.: <[MIT-MC.ARPA].726285.851121.KFL>
Posted: Thu Nov 21 00:20:37 1985
Date-Received: Sun, 24-Nov-85 06:12:58 EST
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    Date: 19 Nov 85 20:00:07 GMT
    From: decwrl!dec-rhea!dec-tle!crimmin@ucbvax.berkeley.edu  (DTN 1-2015)
    Subject: slingshot effect

    Is the trajectory a hyperbola while the probe is en route
    to Jupiter, or only after it misses? 

  The trajectory isn't really a simple curve, since it is influenced
by both the Sun and Jupiter.  At first, you can regard it as being an
ellipse about the Sun.  If Jupiter didn't get in the way, it would
continue to orbit the Sun in an elliptical orbit with perihelion near
Earth's orbit and a aphelion near Jupiter's orbit.  Eventually, it
would get close enough to either Jupiter or Earth that its orbit would
be perturbed (or it would crash into one of those planets, or perhaps
into an asteroid - not into Mars though, it passes above or below
Mars' orbit).
  But of course the elliptical orbit is so designed that Jupiter will
be at the apogee when the probe is there, so it never completes even
one full elliptical orbit of the Sun.  This, by the way, is called a
Hohmann minimum energy orbit - the least energy way to get from here
to Jupiter.
  The probe does not quite hit Jupiter, but it does pass so close that
Jupiter's effect on the probe greatly overwhelms the Sun's effect.  If
we now switch to a frame of reference in which Jupiter is stationary
(we were in a frame of reference in which the Sun was stationary), we
see the probe coming almost directly towards Jupiter in nearly a
straight line.  As the probe gets closer it speeds up and curves
towards Jupiter.  It swings past, the path straightens out in a new
direction, and it slows down.  Once more it is in a nearly straight
line, going almost directly away from Jupiter, and is going at the
same speed it came in at.  Note that since it 'fell' to Jupiter from a
great altitude, it had more than Jupiter-escape-velocity at every
distance from Jupiter, so it could not possibly have become a
satellite of Jupiter.  No matter how it was aimed, unless it hit
Jupiter it had to leave the vicinity of Jupiter as fast as it came in.
In the vicinity of Jupiter and in the reference frame in which Jupiter
is stationary, the path of the probe was a hyperbola with Jupiter at
one focus.
  Switching back to a Sun centered reference frame we see that the
velocity is not the same as it was.  After passing by Jupiter the
probe is now going much faster.  Once it becomes distant enough from
Jupiter that the Sun's gravity is the only significant force on the
probe, the path of the probe is a hyperbola with the Sun at one focus.
If nothing gets in the way, the probe will continue out of the solar
system and into interstellar space to wander among the stars for
countless eons.  The chances of it ever running into a star or a
planet in another solar system are vanishingly small, even though it
will be roaming entirely within our galaxy - it doesn't have galactic
escape velocity.  It is an interesting exercise to imagine how one
would go about detecting a Voyager/Pioneer type probe in interstellar
space, even assuming there are several in each cubic light year
(launched by other civilizations).

    Watching from Jupiter, the probe approaches and departs at
    the same velocity.

  Right.

    Does the probe perceive a faster velocity in relation to Jupiter?
    to the Sun?

  After leaving the vicinity of Jupiter, the probe is going faster
relative to the Sun than relative to Jupiter.  A few years later, when
Jupiter is on the other side of the Sun, the probe is going faster
relative to Jupiter than to the Sun, not that that is especially
relevant.

    What is the meaning of *zero* the orbital speed of the 
    planet relative to the Sun?

  I meant that if the probe was in the vicinity of Jupiter and was at
rest relative to the Sun, Jupiter could accelerate the probe to twice
Jupiter's orbital velocity, relative to the Sun.  That alone is faster
than solar escape velocity.
  The Voyager and Pioneer probes were not at rest relative to the Sun,
however their velocity relative to the Sun in the vicinity of Jupiter
WAS less than Jupiter's, i.e. Jupiter overtook the probes.
  It's kind of confusing.  One could, in principly, go anywhere simply
by aiming your rocket in the right direction.  But we don't have
anywhere near enough energy to do it that way.  So it is done in the
most energy efficient way possible, hence the various Hohmann orbits
and slingshot effects.

    Is this correct? From the Sun, the probe appears to
    accelerate to a speed twice that of Jupiter in its orbit 
    of the Sun. But from Jupiter, the probe appears to come 
    and go at a constant velocity.

  Right.  Not really twice Jupiter's speed, that is the theoretical
maximum.  Anyway, you don't really want to go that fast if you want to
get to Saturn and to pass both Jupiter and Saturn as SLOWLY as
possible, to have lots of time for observations.
  Also (in the Jupiter frame), the probe does come and go at the SAME
velocity, but it isn't really a CONSTANT velocity.  It increases to a
maximum at the closest point to Jupiter and then decreases back to the
original value.
  I think there is an out-of-ecliptic-plane probe being planned, that
will pass underneath Jupiter so as to rise up out of the plane which
all the planets travel around the Sun.  This will give us the first
clear view of the Sun's north and south poles.  It is ironic that a
probe meant to study the Sun has to go past Jupiter first, since
Jupiter is four times further than the Sun, and in the opposite
direction.  But it is the most energy efficient way to get a probe out
of the ecliptic plane.  It would be done in the same way if the probe
was to drop straight into the Sun.  In space it is just as hard to
lose velocity as to gain it, and any probe to the Sun has to lose the
Earth's orbital velocity about the Sun or it will just continue to
orbit the Sun in the vicinity of Earth.
  Hope this answers your question.
								...Keith