How Does a Gravity Assist Work? Stealing Speed From a Planet

Measured relative to the planet itself, a gravity assist changes nothing about speed. The spacecraft approaches on a hyperbolic path, is deflected through some angle, and departs at exactly the same speed relative to the planet as it arrived, because gravity is conservative and gives back what it took. What changes is direction. The useful frame is the sun's, in which the planet is itself moving at tens of kilometres a second, and the spacecraft's velocity relative to the sun is the sum of its velocity relative to the planet and the planet's velocity relative to the sun. Rotating the first of those while the second stays fixed changes the total, and if the deflection points the spacecraft more nearly along the planet's direction of travel, the sum is larger. A standard analogy is a ball thrown at a moving train and bouncing off the front: relative to the train it leaves at the speed it arrived, and relative to the ground it leaves much faster, having taken momentum from the train.

Momentum is conserved exactly, so the planet loses precisely what the spacecraft gains. The disparity in mass makes the effect unmeasurable: a spacecraft weighing a tonne exchanging momentum with a planet weighing more than ten to the twenty-sixth kilograms changes the planet's orbital speed by an amount vastly smaller than anything that can be detected, and the same reasoning applies to the many assists flown to date. The manoeuvre is therefore free for practical purposes, which is why it is used constantly. It can also work in reverse: passing behind a planet rather than in front slows the spacecraft relative to the sun, which is essential for missions travelling inward, since falling towards the sun means gaining enormous speed that must then be shed to enter orbit around an inner planet. Missions to Mercury have used multiple braking assists at Earth, Venus and Mercury itself for precisely this reason.

The technique converted missions that were impossible into ones that were merely difficult:

• •Mariner 10 in 1974 was the first to use one deliberately, flying past Venus to reach Mercury, following calculations by Michael Minovitch and mission design by Giuseppe Colombo
• •The Voyager missions exploited a planetary alignment occurring roughly every 175 years, with Voyager 2 assisted by Jupiter, Saturn and Uranus in turn to reach Neptune, a journey that would otherwise have needed decades longer and a far larger rocket
• •Galileo reached Jupiter via Venus and two Earth flybys, a route nicknamed for its repeated inner-system loops
• •Cassini used Venus twice, Earth and Jupiter before arriving at Saturn
• •New Horizons took a single Jupiter assist that cut roughly three years from its journey to Pluto
• •The Parker Solar Probe uses repeated Venus flybys to remove orbital energy and spiral progressively closer to the sun, which is the braking version of the same manoeuvre
• •Modern missions increasingly combine assists with low-thrust ion propulsion, which trades thrust for efficiency and works well over long cruise phases

The manoeuvre is powerful and not flexible. The available deflection depends on how close the spacecraft can pass and how fast it is going, with slower approaches bending more, so there is a maximum gain per encounter, and passing too close means hitting the atmosphere or the surface. The planets must be in the right places, which means launch windows open and close on the timescale of planetary alignments and a missed window can cost years. Trajectory design becomes an optimisation problem across many possible sequences, solved with numerical methods and giving routes that look absurd on a diagram. Navigation must be precise, since an error of a few kilometres at the flyby compounds into millions by the next encounter, which is why deep space tracking measures spacecraft velocity to fractions of a millimetre per second. A curious unresolved detail is the flyby anomaly, a small unexplained velocity change observed in several Earth flybys during the 1990s and 2000s, which has not recurred clearly in later encounters and has no accepted explanation.

A gravity assist changes a spacecraft's direction relative to the planet without changing its speed in that frame, and because the planet is itself moving around the sun, the rotated velocity adds differently to the planet's motion, so the craft gains or loses speed relative to the sun. The energy comes from the planet's orbit and the effect on the planet is immeasurably small. Voyager 2 reached Neptune on three assists, and missions heading inward use the reverse to shed speed.