Gravity assists explained simply— How the Voyagers escaped the Solar System

If nature offers some free help to reach our destination, we should take it

Traveling the vast distances of space isn’t cheap. It costs spacecraft time, fuel and money. Fortunately, nature offers free help along the way and mission designers always take it.

They’re called gravity assists.

Gravitational slingshots/assists allow spacecrafts to save on all those factors using a simple physical law. NASA’s Voyager 1 & 2 spacecrafts are famous for using the gravity of Jupiter & Saturn to go fast enough to escape the Sun’s gravity and study interstellar space.

Voyager 1 approaching Jupiter. Source: Wikipedia

Why use gravity assists?

Instead of using gravity assists to navigate to a destination, a spacecraft can simply carry more fuel to power itself. But adding more fuel makes it weigh more. This means more fuel needs to be added to the rocket to launch the now-heavier spacecraft. Since including extra fuel also increases the rocket’s mass, more fuel is needed to carry that fuel, and so on. Rocket science.

As a thumb rule, the fuel requirements increase exponentially with more mass added to the spacecraft. Heavier spacecraft may require a more complex rocket to be built to meet the demands. Such increases in cost and technological complexity can be saved by using gravity assists. They also allow us to do things that are beyond our current abilities.

How the Voyagers did it

In the 1970s, some of the most ambitious spacecraft in history were launched: Voyager 1 and 2, both by NASA. They would go on to escape the Sun’s gravity and exit the Solar system. Voyager 1 entered interstellar space in 2013 and Voyager 2 is expected to do the same soon. And it wouldn’t have been possible without gravity assists.

After launch, the twin Voyagers didn’t have enough velocity to escape the Sun’s gravity straightaway. It was and remains impossible for us to build a rocket powerful enough to achieve that. The Titan III rockets that launched the Voyagers (10 days apart) left with them enough energy just to get to Jupiter.

To overcome this problem, the Voyagers were made to swing around the gas-giant to acquire the velocity boost needed to escape the Sun. As each spacecraft approached Jupiter, the planet’s gravity sped it up. Such a close gravitational encounter with a planet is called a flyby.

Voyager 1 & 2 trajectories, showing gravity assist maneuvers at Jupiter & Saturn to escape the Solar system. Credit: NASA

It’s easy to prove how the spacecraft velocity increases in the above case using vectors. Unlike scalar quantities (like speed) which only have magnitude, vectors (like velocity) have both magnitude & direction. A change in direction implies change in velocity, which was quite useful to the Voyagers.

Consider the Voyager spacecraft approaching Jupiter as shown in the diagram below. Let the planet’s velocity around the Sun be v . The spacecraft’s velocity on approaching the planet is v(in) and when leaving the planet is v(out) , as shown in cases 1 and 2 respectively.

A spacecraft’s trajectory (dashed lines) when approaching and leaving a planet. Beautifully self-drawn.