Slingshot Orbit to Asteroid Bennu

The Voyager 1 and Voyager 2 spacecraft have now left the solar system and will continue into deep space. How did we manage to send them so far? The Voyager spacecraft used gravity assists to visit Jupiter, Saturn, Uranus and Neptune in the late 1970s and 1980s. Gravity assist manoeuvres, known as slingshots, are essential for interplanetary missions. They were first used in the Soviet Luna-3 mission in 1959, when images of the far side of the Moon were obtained. Space mission planners use them because they require no fuel and the gain in speed dramatically shortens the time of missions to the outer planets.


Artist’s impression of OSIRIS-REx orbiting Bennu [Photo Credit: NASA]

Asteroid Bennu

A small spacecraft known as OSIRIS-REx is en route to an asteroid called Bennu. Bennu is about 500 metres across and in a near-Earth orbit. The aim is to collect rock samples from the asteroid, returning them to Earth in 2023. NASA scientists have used Earth’s gravity to slingshot OSIRIS-REx onto Bennu. In an Earth flyby in September 2017, the plane of the spacecraft’s orbit changed by about 6 degrees, aligning it with the orbit of Bennu. As it approached Earth, it stole some momentum, boosting its speed. Relative to the Sun, its speed increased by about 14,000 km/h without any fuel being burned. The spacecraft is on target to arrive at Bennu in autumn 2018.

Two Points of View

Gravity assists seem to be magic, providing something for nothing. Since energy is conserved, how can a spacecraft obtain a boost in speed by passing a planet? Reasoning from energy conservation, we would argue that a spacecraft should speed up on approach to a planet, but decelerate while departing. The paradox can be resolved by looking at the problem from two different reference frames. We compare the view from the planet and from the Sun.

To an observer on the planet, the energy of the spacecraft (kinetic energy plus potential energy) is conserved. The spacecraft speeds up on approach, accelerating towards the planet. On departure, it must climb again, losing the kinetic energy that it gained on approach, and its final speed is the same as the speed before the encounter. However, it will be heading in a different direction, the angle of change depending on how close it comes to the planet.

Now we take the view of an observer on the Sun. The planet’s velocity must be added to that of the spacecraft; normally, the two velocities will have different directions. Since the direction changes, the speed of the spacecraft, as measured by the observer on the Sun, is different before and after the encounter: the spacecraft may speed up or slow down. The spacecraft accelerates as it gets closer, and can “slingshot” around the planet, gaining velocity comparable to that of the planet itself.

The figure below shows a simple example of vector addition that illustrates the gravity assist effect. The left panel is in the planet frame: the spacecraft approaches from south with velocity vJ. It departs “eastward” with velocity vI. The right panel shows the view in the Sun frame. To keep things simple we assume that the planet moves eastward with constant velocity vI. The spacecraft approaches from south-west with velocity vI + vJ and speed 2 v. It departs eastward with velocity vI + vI = 2vI and speed 2v. It has gained 60% of planet’s speed v.


What is the source of the energy needed to accelerate the spacecraft? It cannot appear from nowhere. It comes from the energy of the moving planet. There is a transfer of kinetic energy from the planet to the spacecraft. If the spacecraft speeds up, the planet must slow down very slightly. However, since Earth is massive compared to OSIRIS-REx, the effect on the orbit of our planet is completely negligible.

Planetary Alignment

The Voyager missions took advantage of a fortuitous configuration of the outer planets: about once every 175 years, they line up in such a way that a mission to all four planets is practicable, with the help of gravity assist. Voyager 2 (launched in 1977) used gravity assists to fly by all the outer planets: Jupiter, Saturn, Uranus and Neptune. In its encounter with Jupiter, it gained about ten kilometres per second or 36,000 km/h, speeding it towards the outer planets and onwards, beyond the solar system and heading for the stars.


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