A gravitational slingshot, also called a gravity assist, is a flyby maneuver that changes a spacecraft's speed and direction by passing close to a moving planet. It matters because rockets carry limited fuel, while planets already have enormous orbital motion around the Sun. By choosing the right approach path, mission designers can send spacecraft to distant worlds with far less propellant.
The key idea is that the spacecraft borrows a tiny amount of momentum from the planet.
Key Facts
- Gravity assist changes a spacecraft's heliocentric velocity by using a planet's orbital motion.
- In the planet's reference frame, the spacecraft's speed before and after an ideal flyby is the same, but its direction changes.
- In the Sun's reference frame, the spacecraft can gain or lose speed depending on the flyby geometry.
- Momentum is conserved: m_spacecraft Δv_spacecraft + M_planet Δv_planet = 0.
- Kinetic energy in the Sun frame can change for the spacecraft because energy is exchanged with the moving planet.
- A larger turn angle and a faster moving planet can produce a larger change in heliocentric velocity.
Vocabulary
- Gravity assist
- A maneuver in which a spacecraft uses a planet's gravity and orbital motion to change its speed and direction.
- Heliocentric frame
- A reference frame measured relative to the Sun, commonly used for spacecraft traveling through the solar system.
- Hyperbolic trajectory
- An open curved path followed by an object that passes a massive body and escapes instead of entering a closed orbit.
- Momentum
- The quantity of motion of an object, calculated as p = mv.
- Flyby
- A close pass near a planet or moon that allows gravity to bend a spacecraft's path.
Common Mistakes to Avoid
- Thinking the planet gives free energy, which is wrong because the spacecraft gains energy by taking a tiny amount from the planet's orbital motion.
- Ignoring the reference frame, which is wrong because the spacecraft's speed may stay the same in the planet frame but change in the Sun frame.
- Assuming every flyby speeds up the spacecraft, which is wrong because the spacecraft can also slow down if it passes in front of the planet's motion.
- Treating the path as a circular orbit around the planet, which is wrong for most gravity assists because the spacecraft usually follows an open hyperbolic path.
Practice Questions
- 1 A spacecraft approaches a planet in the planet's frame at 8.0 km/s and leaves at 8.0 km/s after its velocity direction turns by 60 degrees. What quantity stayed the same in the planet's frame, and what quantity changed?
- 2 In the Sun frame, a spacecraft enters a flyby with speed 18 km/s and exits with speed 23 km/s. If its mass is 900 kg, by how much did its kinetic energy change?
- 3 A spacecraft passes behind a planet relative to the planet's orbital motion. Explain why this geometry can increase the spacecraft's speed in the Sun frame even though gravity is the only force during the flyby.