Can somebody summarize gravity assist slingshot for me?
A ship heads for the moon and gains energy from gravity. It circles round and leaves. It seems like the energy gained by gravitational acceleration should be lost leaving against the moon's gravity.
I have an idea. Suppose the ship is under power, accelerating by throwing reaction mass, and also because the moon is pulling it. So, as the ship goes away from the moon, it won't be nearby for as long as it was on its approach. So the moon will have longer to speed it up than it had to slow it down. So there's a net gain in velocity.
If the ship is just coasting toward the moon while the moon speeds it up, and then still just coasting away while the moon slows it down, then I don't see how there would be any long-term gain in speed. The ship should lose as much speed while departing as it gained while approaching.
I'm not saying that I'm right. I'm just saying that either I'm right or I'm confused.