Now let’s look at how the laws of conservation of energy and momentum apply to spaceflight. To propel probes into deep space it is advantageous to use the energy of orbiting planets to add velocity, like a slingshot. This means that we do not have to use as much expensive and heavy fuel to reach our goal and we can use a smaller, less expensive, rocket to boost the spacecraft toward the intended planet, asteroid, moon, etc.

 

The idea is to have a spacecraft fly close to a planet and use a tiny portion of the planet’s orbital energy to accelerate the spacecraft. It might seem at first glance that this violates the conservation of energy laws. The spacecraft falls into the gravitational field of the planet, thus accelerating, but then slows down as it passes the planet, having done work against the pull of the planet’s gravity. It would seem that the net gain in velocity is zero! However, this is only true for a reference frame where the planet is not moving, as for a person observing the spacecraft from the surface of the planet. However, the planet is in motion around the Sun. For a Sun-centered observer, the spacecraft picks up a small portion of the planet’s angular momentum. It is this motion that accelerates the spacecraft. Energy and momentum are again conserved, as the amount of kinetic energy picked up by the spacecraft is exactly equal to the amount lost by the planet. The planet, however, is barely affected because its much, much larger mass means its orbital velocity is reduced by only a very tiny amount.

 

Here is an animation of the trajectory of Voyager 2, which visited all four outer planets. This was only possible because of gravity assists: