brndlfly@athena.mit.edu (Matthew T Velazquez) (06/15/91)
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?). It's easier to visualize if you consider flyby of a planet. Of course the planet is moving, so there's your energy source. Patched-conics principles approximate that if you do a Hohmann ellipse to the rendezvous body in the inertial frame, the trajectory is a hyperbola in the frame of the planet. Your visualization that the energy of the vehicle is the same at symmetric points on opposite sides of the hyperbola is correct, but in the PLANET frame. If you exit the rendezvous moving in the same direction as the planet, you gain velocity in that direction IN THE INERTIAL FRAME. Voila! Incidentally, if you exit the rendezvous moving opposite the direction of the planet, you lose inertial velocity. By this means it is possible to remove all Sun-relative velocity from a body, causing it to collide with the Sun, and this was one of the methods a group of students (including me) considered in our evaluation of space-based nuclear waste disposal for a sophmore-level course, Unified Engineering (aka Valley of the Shadow of Death) at MIT. Hope that makes any sense at all:o)# T Velazquez MIT Aero/Astro brndlfly@athena.mit.edu "The art of engineering is knowing when to lie, and by how much." -Ken Meltsner
sgeels@athena.mit.edu (Scott A Geels) (06/17/91)
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