It seems too me there’s an analogy between the two, but I understand we have a loss of kinetic energy in the former and we can have a gain in the latter. What am I missing?
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This question is probably more well suited for r/askscience. The folks over there are better with technical questions, and they will take good care of you!
I’m no expert, but to me the difference seems to be that Bremstrahlung is only one part of a gravity swing-by.
A complete swing-by would consist of Bremsstrahlung, as well as Beschleunigungsstrahlung.
accelerating charged particles emit photons. gravity is too weak so that only happens with merging black holes. gravity assists are more similar to neutrons getting slowed down by water or just elastic collisions.
Bremsstrahlung radiation comes from charged particles quickly changing direction. A charged particle swinging past a planet would likely produce this as well, but most flybys of planets don’t happen with lots of electrical charge and the acceleration is too low.
Gravity slingshots work because the planet is moving and can donate some of its movement (a very small amount) to the rocket.
There is probably some gravitational analogue to bremsstrahlung that applies, generating gravitational waves, but it would be incredibly weak.
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