We've been talking about Cassini with my 6-year old daughter recently and I've mentioned that it picked up more speed by passing close to Venus (twice), Earth and Jupiter. But then, I've struggled to explain how did it pick up speed, why and how does it work.
How would you recommend to explain/demonstrate the concept of "gravity assist" to a 6-year old?
I like the trowing a ball against a speeding train analogy.
The important factor is that Jupiter is moving, quite fast. About 13 km/s. The other important factor is that Jupiter is very massive, so it has a lot of gravity and it can draw objects towards it, causing their direction to bend.
The tricky concept for a 6 year old is that gravity is a zero-sum game. The object that falls towards Jupiter, in this case it's a hyperbolic orbit but regular orbits work too, so as it falls towards it, it adds velocity then flying away from it, it loses the same amount of velocity, so the net velocity relative to Jupiter is zero. No change.
But because Jupiter is moving, Jupiter can tug the spacecraft along with it. The velocity relative to Jupiter is unchanged but the velocity relative to the sun changes, Jupiter is like the train that the ball bounces off of.
The opposite can happen too. Jupiter can be used to slow a spacecraft down. It depends on the angle of approach, like throwing a ball against a train while it moves away from you.
You can also do this experiment below (with 2 balls not 3 to represent the gravity assist, though it's a cooler experiment with 3). It's the same principal. Bouncing off a moving object (Jupiter) is very different than bounding off a flat surface that isn't moving.
https://www.youtube.com/watch?v=2UHS883_P60
All that said, I'd still point out that this is a tricky concept and not to worry if they don't understand it.
I tend to think the best explanations are the simple ones which explain the core concepts of the concept without getting too fancy or detailed. That being said, I'd just explain what happens during a gravity assist.
Cassini flew by Jupiter and when it got close enough Jupiter's gravity began to pull Cassini towards it. This is exactly the same as what pulls things back to the ground on Earth. Because Cassini was being pulled towards Jupiter, it was basically "falling" onto Jupiter and was able to pick up some extra speed by falling. However, since Cassini was traveling sooo incredibly fast, it actually didn't fall onto Jupiter and was able to fly away instead with the extra speed it picked up.
I can't say I've explained something like that to a 6 year old (and confirmed they understood it) but I think that is both factually accurate and simple enough for a young child to understand.
I might modify Zephyr's answer just a hair -- and I have not tried this on a 6-year old, let alone the average adult, who is much more difficult to explain things to than any child is.
Gravity is understood, so show that gravity pulls both the satellite towards Jupiter and Jupiter towards the satellite. But since $ m_{Jupiter} >> m_{satellite} $, Jupiter speeds up a teensy bit while the satellite speeds up a whole lot in the opposite direction. (Plus they manage to miss colliding :-) )
