# When graphing radial velocity measurements, whats the relationship between days and the orbital phase

I graphed the radial velocity measurements for various planets, however, I am able to calculate the RV and the phase but whats the translation between phase and days. I want it to be days vs RV.

• obviously you need the orbital period in order to convert phase to days. And you need to know the velocity for one date in order to determine the offset; that could be the transition time Jul 8, 2020 at 20:24
• How about using a period vs power periodogram.
– Oop
Jul 8, 2020 at 20:36

If the orbital period is $$P$$ (in units of days) and the time of periastron passage (a specific date when the stars are closest together) is $$T_0$$ (generally given as a Julian Date, or JD), then the conversion from orbital phase $$\phi$$ to JD (days) will be:
$$JD = T_0 + \phi P$$
In other words, $$\phi$$ is just the fraction of the orbital period, so multiplying it by the period gives the number of days since periastron within the orbit.
If the orbit is circular, there is no specific periastron date so $$T_0$$ can be set to any arbitrary date, but is generally chosen to be a date when the radial velocity is zero (or at the systemic velocity if that is non-zero) and crossing from negative to positive radial velocities.