A Question About The Slingshot Effect (Not Related To Visiting The 1980's To Collect Whales)

[jotasbrane]

The stuff I've read about using gravity assists say that you fly in close to a planet, and if your angle is right, you'll swing around in a hyperbolic orbit and fly off in the opposite direction. And they also say that the reason you don't break any laws of physics doing this is because you're stealing some of that planet's kinetic energy from its

Comments

[radiotelescope]

You don't have to bring potential energy in; kinetic energy *is* conserved in this process. (If you measure from when the spaceship is Far Away to when it's Far Away Again, that is. In the *middle* of the slingshot, the spaceship is speeding close to the planet, so potential has been temporarily turned to kinetic.)

Measuring kinetic energy of two bouncing objects is just a non-intuitive process, because all the numbers depend on your reference frame. If you consider the planet as stationary, then the spaceship comes in at speed X, nudges the planet into a very slow movement Y (almost zero), and itself rebounds at Z (slightly less than X). It will be true that mS*X*X = mP*Y*Y + mS*Z*Z. You also have to conserve momentum, so mS*X = mP*Y - mS*Z (minus sign because Z points the other way). You can throw in numbers and work an example.

From this point of view, the spaceship has slowed down. But it's also reversed course, so this can be a big win *from the point of view of the sun*. If you translate the above example into the spaceship's *initial* frame of reference, then the spaceship starts at speed zero; the planet comes whizzing along at X; bounce; and then the planet slows down to X-Y, while the spaceship speeds up to X+Z, which is almost 2X.

None of this math changes if the planet isn't orbiting. It's just a different frame of reference in which the big win occurs. Possibly a less useful one.

[jotasbrane]

Hmm, OK. That makes sense. So the actual orbiting doesn't come into it; it's just that the spaceship gains the speed of the planet, in whatever frame of reference you're measuring the speed of the planet.