eli5 How does a spacecraft slingshotting around a planet increase it’s speed?

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Shouldn’t the gravity of the planet force the craft to expend fuel to escape the gravity?

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Well you are already travelling at a velocity that escaped one planet’s gravity before you even start.

Then you calculate it so that the boost to speed caused by the gravity well as you approach is higher than the cost to speed caused by the gravity well as you depart.

No fuel should be required at all, except for minor course corrections.

If you approach the planet at the correct angle, you would get pulled by the planet’s gravity, but your trajectory wouldn’t change enough to crash into it. You would approach, gain speed from gravity, and “miss” the planet if you aimed your spacecraft correctly.

Here is a depiction of the Juno probe sent to Jupiter.

https://i.imgur.com/EHTN00d.gif

When something “falls” it accelerates.

Gravity is only so strong.

When this “slingshot” maneuver is used, they basically do a whole lot of math that calculates at juuust what distance they need to enter the planet”s gravity well to circle and escape the drain rather than spiral into it. For the brief moment it is ” falling” toward the planet, it picks up just enough extra speed that it is able to reach the escape velocity of the relative altitude to the planet and sling off in a line or tangent from the brief orbit it created.

Its the same that can happen with a basketball circling a net. Or a golf putt circling the hole.

If there is enough energy in the ball and its on juuust the right (wrong for the player, lol) part of the rim, it can loop the rim, gain a bit of extra speed from starting to fall into the basket, then use that extra speed to actually skip back up and out if the angle was right.

It’s because the ship is in a constant fall the entire time and doesn’t get slowed down. The ship never has a path that leads to or away from the actual surface of the planet and as such never has to “loose” any velocity escaping the gravity. Any orbit is a constant fall and a spacecraft has initial velocity that allows it to make an orbit so big and lopsided that it’s more of a slingshot than an orbit

It’s not the gravity we’re using, but the planet’s motion around the sun. Throw a ball against the wall, it comes back at about the same speed. Throw a ball against a truck moving towards you, and the ball bounces back faster than the truck itself is going. Kind of the same thing, but using gravity to impart the energy instead of bouncing.

The planet actually loses energy in speeding up a spacecraft, although it’s a meaningless amount given the mass of the planet. The planet gains energy if the slingshot is used to slow the spacecraft by coming at it from the other direction.

The reason that gravitational slingshot works is because the planet move relative to the sun.

If you compared speed with the planet as the frame of reference it does not increase but if you compare it to the sun there is a change.