Gravity Assist Orbits 

Slingshot effect: Spacecraft can use a planet's gravitational field to boost orbital velocities and change direction. Energy efficient!

Used by Voyager to do a "Grand Tour" of the outer planets:

How?


Consider an encounter between a planet and satellite:

What is the final velocity Vf? Watch this!

Before the encounter, an outside observer sees

But in the center of mass frame, we have


Assume a perfectly elastic collision: energy, linear momentum are both conserved
 
 

After the collision we have

In the center of mass frame

 
 

To the outside observer


 

So the spacecraft has been boosted in velocity by 2Vp!
 

This is an extreme case -- 180 degree recoil. Not usually possible in reality.  More typical boosts are ~ Vp.

Is this a free lunch? Where did the energy come from?
 
 
 
 
 

Galileo used the Earth to do a gravity assist to Jupiter, getting a velocity boost of 5 km/s.
How did this change the Earth's speed?