I understand that as a spacecraft approaches a planet, star or moon their gravity speeds up the craft. But why doesn’t exiting the bodies gravity slow it back down with equal force?
Planetary gravitational assist (“swing-by”) manuevers work by transfering momentum between the planet and the spacecraft in order to effect a change in velocity for the spacecraft. The resulting change in momentum on the planetary body is negligable but can be dramatic for the spacecraft (up to twice the velocity difference between the spacecraft and planet, although in practice it is significantly less). It is true that the spacecraft will accelerate as it falls into the planetary body’s sphere of influence (SOI) and decelerate as it leaves, but the difference acquired while in the gravitational potential, plus additional impulse by a spacecraft amplified by the Oberth effect can make a substantial difference in spacecraft trajectory. Nearly all of the outer planet missions have used swing-by maneuvers to obtain course changes unavailable by direct impulse, and in several cases have used multiple swing-bys, e.g. Cassini-Huygens.
A long time ago I wrote a Mailbag article on the topic of gravitational assist maneuvers which appears to have been lost in the aether as it is no longer visible on the Straight Dope homepage, but I actually spoke with mission planners at JPL as well as drawing from my own experience to discuss the tools, methods, and required precision to perform these maneuvers. JPL has this down to a science, and has been completely successful in high precision swing-by maneuvers going back to the Pioneer missions, which is pretty remarkable given the required precision is hitting a target box of a few square kilometers after travelling hundreds of millions of kilometers over several years. It’s akin to playing beer pong across the Grand Canyon and making every shot.
Stranger
If the planet was stationary that would be true. But the planet is traveling at some velocity. Which can be added to the object doing the slingshot at the right angle etc. You can also add a bit of propulsion at the right time to maximize things.
This is where I intuitively lose the concept. It seems like, in my limited understanding, you go down the well then you come back out the well and energy in equals energy out without net gain.
This site gives a pretty good explanation: https://solarsystem.nasa.gov/basics/chapter4-1
This is true, and if the planet were fixed in position there would be no net gain in speed (although you could still get a change in velocity). However, planets are in motion, and they move quite fast. By selecting an approach vector with a significant velocity difference you can obtain a significant change in both speed and direction, which makes a miniscule difference in the orbital speed of the planet. Most swing-bys make only relatively modest changes in the speed of the object as it leaves the planetary body’s SOI compared to when it enters, but the change in direction is often quite dramatic and would require a mass of propellant greater than that of the spacecraft itself to perform with direct impulse.
Stranger
Imagine you are on roller skates travelling at 10mph and along comes a moped travelling at 20mph.
Now get the moped to travel in a steady straight line and angle your skating so that you intercept its path. When you reach it, grab hold of the back of it for a split second and then release. It the time you were “attached” to the moped your speed has increased a bit, the mopeds speed has reduced a bit and you are now shooting off at higher speed in a different direction.
Very loosely you might think of it like this. If you approach the planet from behind you will be accelerated towards the planet as you get close, and you gain energy. As you leave the planet, it takes back the energy equivalent to falling into its gravitational well, but what it doesn’t take back is the energy it gave you accelerating you up to the velocity of its gravitational well, only the energy it gave you to make you go faster than it.
Now the above doesn’t really cover it accurately, but you can intuitively see that because the planet is moving there is an asymmetry in the way it affects your motion depending upon how you are moving relative to it. You could of course also slow yourself down.
In case, after all of the above answers, you still aren’t getting it:
Ignore the slingshot aspect. Think of a billiard ball bouncing off a wall. In an idealized world where there’s no friction, no flexing, etc., the ball would bounce off the wall at the same angle in the opposite reflection without any gain nor loss.
But now imagine that the wall is moving towards the ball. When the ball hits, it’s not just going to bounce off with its own energy, it’s going to have the energy in the wall added into the equation. Or like a tennis ball getting hit with a racket, the ball doesn’t just bounce off at the same speed it came in at, it gains all of the force that the tennis player has added in by swinging the racket in at the ball.
When you slingshot around a planet, you’re in an idealized situation because there’s (practically) no friction in the vacuum of space and very little of the energy of the sling is lost in bending your craft. As you said, the ship goes in at one speed and then comes out at basically the same speed. Except, the planet is moving. If you simply rammed your ship into the planet, and your ship was a bouncy ball, it would get rocketed out in the same way that a tennis ball does on getting hit by a racket that’s moving. But, with today’s ships, trying that would just get you killed. Angling your ship to just miss the planet will give you the same effect without having to die. You have adjusted your angles correctly, the force of the planet, cruising through space at umpty-thousand miles per second, is going to transfer a little bit over to your ship while the two objects are interacting with one another, giving you a speed boost and slowing the planet down just a fraction.
Here it is, courtesy of the Wayback Machine and a bit of dumb luck on my part.
The dumbed down version that helped me understand is: Yes, the spacecraft’s speed (relative to the planet) doesn’t change, but its direction changes. Imagine two people throwing bouncy balls at each other; the balls collide in the air with a very slight vertical offset, so one bounces upwards and the other downwards. In this analogy, the other ball (that goes down) is the planet, and “upwards” is further from the Sun.
This article might also be helpful Voyager
Wow, thanks everyone for the explanations and the links. The thing I didn’t take into account was the speed of the body being used for propulsion. In the last link the ‘bouncing a tennis ball off of a passing truck’ explanation helped too.
When I explain this I do it similar to what Sage Rat did.
It’s very easy for people to understand delta speed stuff involving reflective collisions. But for “refractive” type collisions such as a spacecraft and a planet’s field, it’s harder for most people to suss out.
It’s basically still a collision. The probe is just “hitting” the gravitational field of the planet instead of a surface.