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Slingshot or gravity assist

The effect known as the gravity assist or slingshot effect is a way of using the motion of a planet to accelerate a space probe on its journey towards the outer planets.

Think of a space probe on a journey to Neptune. On its way it will have to pass Jupiter the largest planet in the Solar System.
Imagine first that Jupiter is at rest. As the probe nears Jupiter it accelerates because of the gravity pull of the planet. It swings round Jupiter and moves away slowing down as it does so. Assuming that there is no energy lost the speed of the space probe will be same at equal distances from Jupiter before and after the encounter. Not a lot of use if we are trying to give the space probe some extra energy.

However Jupiter is not stationary! It is moving in its orbit around the Sun at about 48000 km/hr. (See Figure 1(b)). As it space probe moves towards the planet it will accelerate as before but because Jupiter is moving it is "dragged along" by the planet, having its speed increased considerably by the planets motion. Its speed after the encounter is much greater than it was before. The gravity pull of the planet has given the space probe some additional energy. Of course the gravity pull of the space probe will have slowed down Jupiter but by only a tiny amount because the planet is so much more massive than the space probe.

The space probe will have had its speed in the direction of Jupiter's motion increased greatly. It has gained energy from the planet.

To get the best gravity effect or slingshot it is vital to launch the space craft at the right time so that it gets the slingshot effect in the right direction, hurling it towards its destination rather than whipping it out away from the Solar System into deep space.

It is thought that the gravity assist of Jupiter in the past may have been responsible for protecting the Earth from some asteroid collisions.

A little maths
If you think about the velocity vectors in Figure 1(b) you can see that the vector in the direction of motion of the planet has been increased by an amount almost equal to the velocity of the planet.

An analogy with the slingshot

Imagine a child throwing a ball at a train. First with the train stationary and then with it moving (See Figures 2(a) and 2(b)).

Assume that in both cases the ball was moving at 5 m/s as it hit the train.

Case (a) the ball rebounds from the train (not losing any energy in the collision) and moves back at 5 m/s.

Case (b) now assume that the train is moving from left to right at 10 m/s. The ball moves at 5 m/s relative to the ground (that is 15 m/s relative to the train). It hits the train and rebounds at 15 m/s relative to the train. But the train is moving at 10 m/s relative to the ground and so the ball rebounds at 15+10 = 25 m/s relative to the ground.

The ball has gained kinetic energy from the train.

schoolphysics slingshot animation

To see an animation of the sligshot click on the animation link.

A useful site to shown the motion of a slingshot effect is:

© Keith Gibbs 2020