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If you pass an object with negligible mass, your your path will remain unchanged and your deflection will be zero degrees.

if you pass a planet, your path will be bent in the direction of the planet. You'll speed up and the planet slows down.

enter image description here

My question is, what's the maximum angular deflection you can get from this operation? Can swinging around a planet change your path by 90 degrees?

How about a black hole? Can I whip around real close and leave moving in the opposite direction, 360 degrees?

I guess I want to understand the geometry of geodesics.

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    $\begingroup$ A deflection of 180° sends you back where you came from: a "hairpin" bend. $\endgroup$
    – PM 2Ring
    Commented Sep 4 at 15:19
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    $\begingroup$ The maximum deflection (in Newtonian gravity) is 180°, in the frame of the planet. But that calculation ignores the size of the planet. And in a gravity assist we want to know the deflection in the Sun frame. $\endgroup$
    – PM 2Ring
    Commented Sep 4 at 15:23
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    $\begingroup$ In GR, things get more interesting. Trajectories can loop multiple times around a black hole or neutron star. See my physics.stackexchange.com/a/805213/123208 & physics.stackexchange.com/a/810981/123208 for some diagrams of photon trajectories. And see rob's excellent answer for massive particle trajectories: physics.stackexchange.com/a/774043/123208 $\endgroup$
    – PM 2Ring
    Commented Sep 4 at 15:31

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