Do hot Jupiter's violate Kepler's laws?
No, of course not. Why would you think that they do?
I'm not really sure about this. Let me ask a similar question: Are Keplars Laws consistent with general relativity at the energy level of hot jupiters? Most hot Jupiters lie far inside of Mercurys orbit, which itself does not follow Newtons laws.
I guess it depends on the level of accuracy you are talking about. No object follows Kepler's laws exactly, since there are deviations from simple orbital mechanics, of which GR is only one. That's why I wanted the OP to specify why he thought the hot Jupiters would violate Kepler's laws. Perhaps I should not have said "of course".
Just as comparison: While the effect of general relativity on the orbit of Mercury is measurable, the impact of the other planets (mainly Jupiter) is at least 10 times larger. "At least" because there are multiple ways to quantify the impact, with different results.
Nothing follows laws based on classical mechanics exactly, but the deviations are tiny if things orbit regular stars.
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