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The giant planets, particularly Jupiter, are notorious for bringing about changes in eccentricities and inclinations of smaller bodies(asteroids and KBOs). Jupiter, in fact, throws almost all the objects that come sufficiently close to it, out of the Solar System.
My question is, how?
Gravity is an attractive force and has a negative potential energy associated with it. If it has any role, all gravity must be able to do is reduce the total energy of the small bodies, eventually circularising it-not doing the opposite job!
Also, I can't imagine how the giant planets manage to alter the inclinations of these small objects. Gravity would, of course, pull these small objects towards the giant planets, but again, that's only bringing it closer to the plane of the Solar System, not increasing its inclination
Or have I got it wrong altogether?I would be glad if you could break this down for me.

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    $\begingroup$ The premise that jupiter only throws out objects is false. It can do both. It's the main cause for changing long - period comets into short - period ones $\endgroup$ Jan 15, 2022 at 14:14
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    $\begingroup$ The answer is gravity from multiple sources, primarily the Sun and Jupiter, and nothing else. $\endgroup$ Jan 15, 2022 at 22:05
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    $\begingroup$ en.wikipedia.org/wiki/Gravity_assist $\endgroup$ Jan 16, 2022 at 3:41
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    $\begingroup$ This is a good starting point: astronomy.stackexchange.com/q/28900/35206 $\endgroup$ Jan 16, 2022 at 6:03
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    $\begingroup$ My understanding is that this is a consequence of destabilising orbital resonances. The gravity of Jupiter may in some cases exert periodic tugs on some asteroids which are in orbital resonance with it, and over time this can compound to throw the asteroid's orbit off course. (Not making this an answer as I'm not an expert.) $\endgroup$
    – YiFan
    Jan 31, 2022 at 8:50

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