Applying GLS to Keplerian function

[telmonteiro]

I am trying to apply the GLS algorithm (from here [https://pyastronomy.readthedocs.io/en/latest/pyTimingDoc/pyPeriodDoc/gls.html#]) to two sets of RV(t) data. The first one is a planet with a circular orbit with a signal function of the type

$$ RV(t) = K \sin (2\pi(t-T)/P) + \gamma $$

For this simple function, had no problem in applying the GLS. The second set of RV(t) data was from an eccentric orbit (around e=0.4) with a signal function of the type:

$$ RV (\nu) = \gamma + K[e \cos \omega + \cos (\omega + \nu(t))] $$

For this one I'm not able to apply the GLS, even after checking the original paper. Is there some simple and direct way of applying the GLS so I can obtain the orbital parameters and their errors?

[mzechmeister]

The task of GLS is to find periods, albeit various versions also estimate parameter errors. For very eccentric orbits you may still find the period or a harmonic with the GLS (e=0.4 is moderate eccentric). The Keplerian version (much slower), which is also described in the paper, is only implemented in the fortran version and a final fit can be done with a gnuplot script, which also should provided least square fit errors.

For more sophicated orbit fitting you may consider other packages, e.g. exostriker. For period search they often employ the GLS, too.

[telmonteiro]

Thank you kindly for your answer. I will look into it!