August 6, 2003

# Cosmic billiards

A probe can modify its trajectory, velocity and even its inclination relative to the ecliptic plane, without expending any extra energy. It does so by exploiting a principle of the laws of universal gravitation called gravitational assistance.

As the spacecraft passes in the vicinity of a planet, it comes within its gravitational influence and is pulled toward the planet. As a result, its trajectory curves and it picks up speed. The probe swings behind the planet and then slows down again as it moves away. Although the probe’s outbound velocity is the same as its velocity on arrival, the planet transfers a part of its Sun-relative velocity to the probe during the swingby.

Animation: how gravity assist works

The change in velocity and deviation of the spacecraft’s trajectory depend on the mass of the planet chosen for the flyby, and on the flyby altitude and relative velocity. If the probe swings by the planet in its direction of motion about the Sun, it picks up speed. If the flyby is in the opposite direction, the probe loses speed.
The trajectory is obviously calculated very precisely so that the spacecraft does not collide with the planet during a flyby.

This gravity assist technique is used by most interplanetary missions. For example, the Voyager probe would never have made it to Saturn, Uranus and Neptune without a gravity assist from Jupiter. And the Galileo probe used the gravity of Jupiter’s moon Io to decelerate and go into Jovian orbit.

The Cassini-Huygens probe, scheduled to go into orbit around Saturn in 2004, completed 2 flybys of Venus in 1998 and 1999, and a gravity assist from Earth in 1999. The velocity gained from these manoeuvres took it to the outer solar system. A final gravity assist from Jupiter in 2000 gave it the energy required to reach Saturn.

CASSINI-HUYGENS orbit (ESA website)

 Did you know? Transfer orbits for economy-class interplanetary travel The most economical way to transfer from one circular orbit to another, in the same plane and direction of travel, is to describe a half-ellipse with one end at a tangent to the initial orbit and the other to the final orbit. This type of manoeuvre—called a Hohmann transfer—in theory only requires two bursts of thrust. Hohmann transfers are used to position geostationary satellites or to send spacecraft to Mars.