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What percentage of planets have a near sinusoidal shape radial velocity graph?
Any planet with an elliptical orbit will have a sinusoidal shape radial velocity graph. But this does not take into account factors such as the gravitational pull of the other planets, and Einstein’s General relativity, which will make the orbit rather more complex- they are very small effects. So, within the accuracy parameter described above, I’d have to say 100% of them.
Difficult one! From what I found out, observations of a real star would produce a sinusoidal graph, although eccentricity in the orbit will distort the curve and complicate the calculations. I couldn’t find anything about planets however!