Gravity Assist – “Slingshot”

Why is a gravity assist or “slingshot” effect different than just ordinary orbital mechanics?

A rock on a string produces centripetal force similar to a ship orbiting a planet. However, gravity assist does not seem to follow this same line of logic. Why not?

What are the fundamental differences?

Well, for one thing, a rock on a string can produce only a circular orbit, and a gravitational slingshot is hyperbolic. Also, you have to consider two frames of reference in the slingshot scenario. Maybe think of someone running as they wind up the rock. When they release it forward, it goes faster than if they release it backward.

A gravity assist involves three objects: A primary such as the sun, an orbiting body such as one of the sun’s planets, and the object to get the assist, such as a spaceprobe.

Let’s say you want to send a spaceprobe to Neptune. After getting free of the Earth’s gravity, your spaceprobe is now in an independent orbit around the sun, in approximately the same orbit as the Earth. To get to Neptune, you have to accellerate the spaceprobe enough so that it climbs up away from the sun out to Neptune. This would not only take lots of energy, but would involve coasting for decades as the probe slowly climbs up in an elongated elliptical path like a pop fly in baseball.

Fortunately, there’s a better way. You accellerate your spaceprobe just enough to reach Jupiter, which is faster and easier. Now Jupiter’s gravity pulls on the spaceprobe, pulling it toward the planet. If your probe doesn’t actually impact Jupiter, it whips past and out again. In the process, the spaceprobe gains speed in it’s path away from the sun at Jupiter’s expense: Jupiter is dragged back (by maybe the width of an atom) while the probe is flung forward. In fact, the probe can gain enough velocity to escape from the solar system altogether. If you time it right, you probe flys by the outer planets as it goes.

Your explanation leaves one key element a little fuzzy. If Jupiter were standing still, you couldn’t gain any velocity. While your probe would speed up falling into the gravity well, it would slow down by precisely the same amount as it climbed out again.

Jupiter, however, is moving in orbit around the sun. The “slingshot” works because it couples the space probe to Jupiter’s orbital velocity. In other words, as the probe is being accelerated towards Jupiter, it is also being “dragged” around the sun by Jupiter. Because of the disparity in mass, this results in Jupiter traveling a tiny amount more slowly around the sun but results in a big increase in the speed of the probe. The “extra” energy need to speed up the probe is, therefore, being captured from Jupiter’s orbital velocity.

Is there a difference between what is happening from a classical point of view as opposed to general relativity?

With centripetal force there is acceleration towards the center of the planet. Is there acceleration if you looked at from a GR perspective?

Is there a difference between what is happening from a classical point of view as opposed to general relativity?

With centripetal force there is acceleration towards the center of the planet. Is there acceleration if you looked at it from a GR perspective?

Quantitatively, there is a very slight difference in the acceleration of the satellite between Newtonian theory and GR. However, qualitatively, the same thing is happening. The scientists who calculate the orbit probably have to worry about relativistic effects, but you and I trying to understand the phenomenon don’t.

If the gravity of Jupiter is enough to pull the probe into it’s orbit, then how does the spaceprobe get the necessary escape velocity to exit? It would seem that if the pull was enough to suck it in the first time then it’s orbital spin couldn’t add enough velocity to allow it to escape. Know what I mean?

I am not sure what you said is correct. One of the NASA probes, the Galileo IIRC, used the Sun for the slingshot.

“Slingshot effect” is nothing more than an elastic collision. Say you have two baseballs in outer space flying towards each other at 10 meters/sec. After the collision the direction of travel of each ball has changed, but not the speed. So there’s no gain or loss of energy.

Now imagine the same thing happening on earth. Two balls are flying horizontally towards each other at 10 m/s. If the balls hit slightly off center, one ball will be propelled upwards at 10 m/s while the other flies downwards at 10 m/s. There is no exchange of kinetic energy. However, the one flying upwards has more potential energy and can reach a higher altitude. That ball has stolen some potential energy from the other ball.

The same thing happens when a satellite encounters Jupiter. The satellite will fall towards Jupiter at, say, 20 km/s, and emerge out of Jupiter’s gravitational field at 20 km/s. But the direction of travel is now pointed more outwards, away from the sun. So it will be able to travel farther out into space.

Here’s anothe way to look at it.

If the spacecraft passes behind the planet’s direction of motion it gains speed and changes direction. If it passes in front of the motion of the planet it loses speed and changes direction.

An easy way to see this is to visualize a planet passing by a stationary spacecraft; would the spacecraft stay stationary or would it gain speed via being dragged along in the planets wake.

The Sun cannot be used for a slingshot, since it is effectively the center of mass of the solar system (Achernar, can you comment? You know more about this than I do). You may be thinking of the Ulysses probe, which used Jupiter to swing it into a solar polar orbit.

If you want to get all technical about it, the sun could be used to alter a space probe’s velocity. However, could not be used to alter its speed. A velocity vector is both a speed and a direction. In effect, this means you can use the sun to “re-aim” a spacecraft but not to speed it up.

It’s actually pretty difficult to insert something in an orbit. Most trajectories will either smack directly into the body or miss it and be sent off in a different direction.

Certainly the Sun can be used for slingshoting, how else do they travel in time in Star Trek and the rest.

On a more serious note, for whatever energy in imparted to the object being slingshotted, that same energy is lost from the slingshotting body. So, every time Jupiter is used in this way, it loses a tiny fraction of its momentum - negligible of course, when u consider the difference in masses of the two bodies, the probe and the planet.

You can use stars for slingshot acceleration/deceleration because they are in orbit around the centre of the galaxy. If you are approaching a star at speed from interstellar space you could impart a small amount of your momentum to the star, and make it orbit the galaxy a tiny bit faster.
It is a tiny effect though, not enough to slow a starship down from relativitic speeds.
Many stars are double, so you have a bit more of a chance…

Doesn’t the probe do an orbit around the planet or is that just in the movies? If so, and if it doesn’t gain any velocity, how does it escape?

You need an open-ended orbit, i.e. parabolic or hyperbolic. If you enter a closed orbit, and do a loop around the planet, that’s it, you’re trapped there.

I’ve always conceived it like older baseball or tennis ball launchers - two large wheels turn at very high rpms. A ball comes down the launch chute at a certain speed. When it encounters the wheels, it’s velocity is increased by a certain magnitude, depending on the rpms of the wheel, how fast the ball comes down the chute, etc, and exits the launcher at an appropriate speed and angle for a baseball player or tennis player to practice against.

I know this isn’t exactly correct, but I think it’s similar enough to the slingshot effect to grasp the concept. Just substitute the sun and Jupiter for the wheels, the probe for the tennis/baseball, the satellites course for the chute guiding the balls in and out of the launcher.


BTW, if you dig into this excellent thread, you can see that gravity assist can also be used to slow down a probe:

The baseball launcher analogy is exactly how I always envisioned it too but if scr4 is right then it’s not a good analogy. Unless the spin of the planet imparts “english” to the planet.