Earth Flybys - how do they work?

[mellojoe]

How is it possible to gain orbital velocity by doing an Earth flyby? Don't you expend energy to get into orbit? How do you gain additional velocity by returnning right back where you left? I know I must be missing something simple.

The Cassini probe did two Venus flyby's plus an Earth flyby. That makes total sense. Leave Earth, gain gravity assist from Venus, do an oribital manuever at Apoapsis, catch Venus on the return trip, and use an Earth flyby at that point to slingshot you to the outer planets.

But how do you gain anything by leaving Earth, then simply returnning? Where is momentum gained?

[Nikolai]

How is it possible to gain orbital velocity by doing an Earth flyby?

You're right that from Earth's perspective, you appear to leave as fast as you arrived -- no gain in momentum.

However, if you come up on Earth from "behind", from the Sun's perspective, you gained momentum and the Earth lost an equal amount. (That's because the Earth was moving away from you, and pulled you as you approached for more time than it pulled you as you sped away.)

If you come up on Earth from "ahead", from the Sun's perspective, Earth gains momentum and you lose an equal amount.

[stupid_chris]

How is it possible to gain orbital velocity by doing an Earth flyby? Don't you expend energy to get into orbit? How do you gain additional velocity by returnning right back where you left? I know I must be missing something simple.

The Cassini probe did two Venus flyby's plus an Earth flyby. That makes total sense. Leave Earth, gain gravity assist from Venus, do an oribital manuever at Apoapsis, catch Venus on the return trip, and use an Earth flyby at that point to slingshot you to the outer planets.

But how do you gain anything by leaving Earth, then simply returnning? Where is momentum gained?

That all depends on how you encounter Earth, and from how far you encounter it. You won't be necessarily coming back exactly in the way you were. If you set yourself in an eccentric orbit around the sun, with an apoapsis outside Earth's orbit and a periapsis inside it, depending on how you could encounter it, you could bend your path effectively and get ejected at Earth's prograde vector while not coming from it's retrograde vector, thus gaining velocity. When you enter in an hyperbolic orbit, you will exit the object's SOI at the same speed you entered it, but you can use the object's gravity to pick up speed by changing your ejection orientation