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I'd like to know how to calculate the size of the planet's orbit, given that it is the only one orbiting around a star, and that this star is oscillating with an amplitud of 0.026'' in 25 year periods. (The star is located at 1.83 pc from observer and has a given mass M). Also, the star is oscillating due to the planet.

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    $\begingroup$ Are you implying that the period of the planet's orbit is 25 years. This kind of specific question looks like homework. That's not a problem, but please acknowledge that this is a homework question, if that is the case. Otherwise explain some more context on where these specific values come from. $\endgroup$
    – James K
    Nov 10, 2022 at 6:18

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Assume the planet is much less massive than the star and use Kepler's third law assuming 25 years is the orbital period.

The amplitude of the star's motion is only needed if you want to explicitly calculate the planet mass.

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