Q&A: Gravitational Assists Explained

Question: When NASA says they’re doing a gravitational assist on one of their spacecraft, I get that means using the gravity of a planet to change the craft’s motion. I’m curious how that works, but everywhere I looked the explanations were too hard to follow. Hoping you can explain it in simpler terms, thanks. — DV, Dayton, OH

Answer: I have a great analogy that should make it clear without anything more than arithmetic. But before we get to that explanation let’s look at the three different types of gravitational assist. The term “gravitational boost” is sometimes used, but since the maneuver can also change direction or reduce speed, I prefer “assist”.

The top video shows a gravitational assist that only changes the direction of motion. We’ll use the Moon as the assisting body. You don’t see the Moon moving because this type of assist requires flyby in a plane perpendicular to the Moon’s motion (so imagine it moving straight at or away from you).

The craft has an incoming speed of 7 kps (kilometers per second). It accelerates from attraction by the Moon’s gravity, decelerates as it recedes, and eventually slows to its original 7 kps — but its direction of motion has changed by 90°. Other angles are possible depending on the spacecraft’s incoming trajectory.

Gravitational assists expend no fuel. Of course, the Moon has to be in the correct position for this to work so it’s not always an available option. Also note that gravitational assists are 3D maneuvers. The videos in this post are 2D simulations just to keep things simple.

Depending on mission goals, sometimes you want a gravitational assist to increase or decrease your speed. The amount of speed change possible depends on several factors:

  • speed and direction of motion of the Moon
  • gravitational strength of the Moon
  • how closely the craft approaches the Moon
  • the speed and direction of motion of the spacecraft

Here’s what a “speed increase” gravitational assist looks like:

For an increase in speed the spacecraft must approach the Moon from its trailing side in the plane of the Moon’s orbit. It will again accelerate as it approaches and decelerate as it recedes, but this time there will be a net gain in speed after the encounter. This speed change is often referred to as ΔV, and for this assist ΔV = +2 kps.

Lest you think this is an example of “getting something for nothing”, the Moon is actually slowed by this encounter to balance the spacecraft’s gain. Both interacting objects feel the same gravitational force according to Newton’s 3rd Law, but the 2nd Law says the effect of that force (acceleration) is inversely proportional to mass. So the low-mass satellite gains 2 kps, but the speed lost by the Moon is infinitesimal. No need to worry about “Moonfall” 🙂

The New Horizons spacecraft performed this maneuver with Jupiter and got a ΔV of +4 kps added to its original 10 kps. This ΔV enabled it to reach Pluto and beyond. Voyager 2 also used Jupiter but had a more favorable assist alignment with a ΔV of +7 kps, after which it repeated the maneuver with Saturn and got another ΔV of +5 kps. That was enough to carry it to Uranus and Neptune and beyond.

This final video shows a gravitational assist decreasing the spacecraft’s speed by a ΔV = −1 kps:

For a decrease in speed the spacecraft must approach the Moon from its leading side in the plane of the Moon’s orbit. Again we see acceleration followed by deceleration, and in this case there’s a net loss of speed. These types of gravitational assists are sometimes used when voyaging to the inner solar system (closer to the Sun than Earth). Speed must be decreased to fall closer to the Sun.

Earth orbits the Sun with a speed of 30 kps, so any spacecraft launched from Earth already has a speed of 30 kps (relative to the Sun) while it’s just sitting on the launch pad. If the rocket launches in the direction of Earth’s motion, that 30 kps is added to whatever ΔV is provided by the rocket engines (typically 11 kps to escape Earth’s gravity). That would give the spacecraft a net speed of 41 kps (relative to the Sun).

Launching in the direction opposite Earth’s motion with the same rocket ΔV nets a speed of 19 kps. This alone will put you into an elliptical orbit around the Sun that dives into the inner solar system, but sometimes you need to dive deeper. NASA’s Messenger spacecraft targeted Mercury, the innermost planet. Getting there requires a lot of −ΔV. Multiple flybys of Earth, Venus, and Mercury itself were required to get into orbit around Mercury.

To really understand why gravitational assists work you need Newton’s Laws of Motion. You don’t learn these laws until you take a physics class, so here’s a simple analogy that relates to a common phenomenon: collisions between moving objects. Granted, spacecraft don’t “collide” with anything during a gravitational assist (hopefully), but a gravitational interaction is the same as a physical collision in terms of Newton’s Laws.

Consider what would happen if you pitched a baseball into the front of an oncoming truck. We’ll assume perfectly elastic (bouncy) collisions and ignore friction:

Here the ball will rebound with a speed equal to its incoming speed plus the speed of the truck. If the ball was pitched at the back end of the truck (from behind the truck) the ball will rebound with a speed of 100 mph − 80 mph = 20 mph. If the ball was pitched at the side of the truck (from the shoulder of the road), the truck’s speed wouldn’t make a difference — the ball would rebound with a speed of 100 mph regardless.

Changing this to a no-contact situation (say, magnetizing the ball and truck to repel each other) would not change the collision results. Nor would changing it to a force that attracts (like gravity) — but you’d have to pitch the ball to miss the truck so the ball can be pulled around it.

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