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From: sgeels@athena.mit.edu (Scott A Geels)
Newsgroups: sci.space
Subject: Re: Slingshot effect
Message-ID: <1991Jun17.161730.13283@athena.mit.edu>
Date: 17 Jun 91 16:17:30 GMT
References: <1991Jun15.032840.23428@athena.mit.edu>
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Organization: Massachusetts Institute of Technology
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In article <1991Jun15.032840.23428@athena.mit.edu> brndlfly@athena.mit.edu (Matthew T Velazquez) writes:
>In <LA_CARLE.91Jun14203158@sol.brispoly.ac.uk> la_carle@sol.brispoly.ac.uk
>(Les Carleton) writes:
>
>>Can you please explain the "slingshot" effect as used on recent
>>probes. I understand that it increases the velocity of the vehicle by
>>making passes around the sun. I'm not a physics or Astrophysics major
>>so it may seem a naiive question. What I don't understand is why the
>>velocity increases.  Surely if a pass of the sun is made, the energy
>>conservation law will come into play and the vehicle will end up with
>>the same velocity at its original distance from the sun as it had when
>>left there (after launch?).
>
pseudo-proof: (pardon the ascii attempts at notation)

V'(0,1) = velocity of spacecraft wrt the center of mass (CM),
          initial (0) and final (1)

V (0,1) = velocity os spacecraft wrt the Earth (or Sun, or Solar
          System), initial (0) and final (1)

V (CM)  = velocity of center of mass (Venus)

Definition of CM:  (this is elementary physics)

V(0) = V'(0) + V(CM)
V(1) = V'(1) + V(CM)

We want |V(0)| < |V(1)| , so that we gain energy

Ergo, we want:
|V'(0) + V(CM)| < |V'(1) + V(CM)|

Example of how this can be the case:
V'(0) = -5i(hat)
V'(1) = +5i(hat)
     (note: these must have the same magnitude, by conservation
            of energy)
V(CM) = +i(hat)

|V(0)| = 4
|V(1)| = 6

Disclaimer: the numbers used here are bogus

Therefore, net gain in velocity wrt the Earth!

You can also use this to lose velocity.


		Scott Geels

sgeels@athena.mit.edu
sgeels%fred.den.mmc.com@everest.den.mmc.com