Gravity Assist Analogy I'm having tremendous difficulty accepting the reality of this phenomenon. I have read countless analogies of balls hitting trains and moving walls, etc but I still cannot reconcile why the rebounding object gains TWICE the larger mass's velocity WRT the sun/station platform/whatever. It feels like it is gaining something from nothing. 
 A: Let's consider a ping pong ball and a paddle. First throw the ball at a stationary paddle. The ball bounces back. The ball approaches the paddle with speed v and leaves with speed v. 
Important point 1: The ball doesn't end up at the speed of the paddle (which is $0$ in this case). As it hits and slows to a stop, it flattens. Then it springs back to a round shape. It leaps off of the paddle. 
Important point 2: The speed of separation is the same as the speed of approach. 
Now consider the paddle hitting a stationary ball. 
Important point 3: If you run alongside the paddle, this looks a lot like a ball being thrown at a stationary paddle. From this point of view, you would expect the ball to approach with speed v and leave with speed v. 
The ball is flattened as it matches the speed of the paddle, and then spring back, leaping off of the paddle. 
To repeat this a little differently, the paddle approaches the ball at speed v. As the paddle hits, the ball is flattened and speeds up to speed v, matching the paddle. Then the ball springs back, leaping off the paddle increasing its speed by v again. So it has a speed of 2v.
A: The Planet’s orbit is basically adding its knetic energy to the craft.Here’s an analogy.
Imagine trying to throw a ball.If you throw the ball while standing still,it’s going to go pretty far.But if you throw the ball while moving,it’s going to go really far.
