How do gravity assists work?

A letter to the “Ask Astro” column, and answer, were published in the Dec 2007 Astronomy magazine.

How do gravity assists work?
ALEX FORBES, CASTRO VALLEY, CALIFORNIA

By passing near a large body, a spacecraft can radically alter its speed and trajectory without expending any fuel. This may sound like a free lunch, but it isn’t.

A spacecraft that speeds up during a gravity assist does so by taking away some of the planet’s orbital energy. An imperceptible slowing of the planet results in a vast speed boost for a spacecraft. Mission designers also can select trajectories that slow a spacecraft or alter its orbital inclination.

In 1961, Michael Minovitch, a mathematics and physics graduate student working during the summer at the Jet Propulsion Laboratory in Pasadena, California, discovered this technique. It was first employed in February 1974, when NASA’s Mariner 10 mission to Mercury used Venus to alter the craft’s course and speed. — FRANCIS REDDY, SENIOR EDITOR

After submitting the question to Astronomy, I did some research on the web, as usual quickly ending up at Wikipedia. The reason a gravity assist or “slingshot” sounds like a free lunch is because we (or I) tend to think of the planet as a stationary object, which of course we really know isn’t and can’t be. This works because the planet itself is also in motion.

So, if we sneak up on the planet from its “rear” – accelerating toward it in the same direction it is orbiting – my oversimplified understanding is that we get a speed boost from two sources: gravitational acceleration toward the planet, yes, but the planet is also receding from us as we approach, “dragging” us to higher speeds, so we get extra velocity from that.

As we pass the planet, the gravitational boost works in reverse, canceling itself out. But we retain the additional velocity from piggybacking on the planet’s orbital velocity, our speed boost. As Astronomy explains, conservation of momentum is not violated because we have slowed down the planet infinitesmally.

This also works in reverse, slowing us down if we approach the planet going against its orbital direction. Also, “powered slingshots” appear to enhance the effect, according to Wikipedia.

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