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If a ship successfully absorbs a planet's kinetic energy to increase its speed, can it add to that speed by firing its thrusters? Thank you very much.

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    $\begingroup$ "In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed." en.wikipedia.org/wiki/Oberth_effect $\endgroup$ Commented Sep 22, 2023 at 20:12
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    $\begingroup$ Yep, Oberth Maneuver, it's quite a powerful technique, massive fuel savings and much more flexibility regarding the trajectory than a passive gravity assist. $\endgroup$
    – SF.
    Commented Sep 22, 2023 at 21:35
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    $\begingroup$ Burn as deep in a gravity well as you can. If you have low-thrust engines it can even be worthwhile to split your burn to put it deeper in the gravity well. (Burn to raise your apoapsis, then shut down and wait until you're back near periapsis to continue. Obviously this can only be done while you are below escape velocity, anything beyond that must be done in a single burn.) $\endgroup$ Commented Sep 25, 2023 at 3:29

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Yes, and in fact you get more benefit from doing this than you'd think. It's called the Oberth Effect, and it basically means your fuel is worth more kinetic energy when you use it while moving at high speed than when at low speed, because of the way momentum and kinetic energy relate to each other.

In orbital mechanics, the easy way to get to high speed is diving into a gravity well. Fire your engines at the bottom, and you get an extra kick. You'll come out of the gravity well and end up going faster than if you'd just performed a gravity assist and then fired the engines later on.

We don't often hear about space probes taking that much advantage of this during gravity assists, though. There are two big reasons for that, even aside from the general public finding it fairly esoteric: First, space probes usually don't carry a great deal of fuel along with them, because it's more efficient to burn everything you can at the bottom of Earth's gravity well, which is to say during launch. Second, whatever propulsion a probe does have is usually of the high-efficiency, low-impulse kind, like an ion drive or Hall-effect thruster. Lots of delta-V per fuel mass, but the impulse it produces is on roughly the same level as laying a sheet of paper on the probe under earth gravity, and you need to fire it constantly for hours or days to get any meaningful movement out of it. And that's fine when you're tweaking your orbit somewhere between Jupiter and Saturn or very slowly spiraling towards the moon, but makes it really hard to take advantage of a twenty minute window while you're at the bottom of a gravity assist.

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