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I've spent an incredibly large amount of time trying to wrap my head around how the period is computed using just solely the raw data for the radial velocity. I've tried my hand with some nonlinear regression models but they seem to require an initial guess and knowledge of the period. Say, I had a star whose radial velocity data was available, how would I calculate an exoplanet's period? As well as that, how would one eliminate the influence of other neighboring stellar bodies in the radial vel data? Thank you.

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Fit a model of the RVs predicted from a Keplerian orbit to the data (a sine wave for a circular orbit). The period obtained is the period of the orbit. In terms of an initial guess for the period - just do a Fourier transform of the data and look for the peak in the power spectrum at the frequency of the exoplanet orbit.

If there are multiple planetary signals at different periods there will be tell-tale residuals to the fit above (and possibly multiple frequency peaks in the Fourier transform) . Add another planet to the Keplerian model with a different period and fit again.

If you are asking how do I mathematically/numerically go about that process, well I wouldn't bother to reinvent the wheel. There is at least one perfectly good, free resource called Systemic Console that can do exactly the procedure I described above. The latest version (Systemic 2.0) only runs on linux and MAC. There is a web version called Systemic Live, but this may be limited to the public RV datasets that it already has access to rather than your own datasets.

Screenshot from Systemic-live

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    $\begingroup$ You mentioned to fit a model of the RVs predicted from a Keplerian orbit to the data. How exactly would I proceed with that and what do you mean by "RVs predicted"? I'm sorry if this comes off as ignorant, I'm still in high school. Thank you for your help! $\endgroup$ Commented Nov 28, 2022 at 20:21

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