# Calculate the orbital phase when plotting the Radial Velocity data of a transitting exoplanet

I'm not quite sure how I find the orbital phase ($$\phi$$) of a transitting exoplanet. For example, I have this RV data in this article:

First of all, I don't know how that phase or "cycles" is derived. But that's not the phase $$\phi$$ I'm looking for but this (in the same article):

As you see, that phase goes from 0 to 1, and I know it has to do with the time of passage from the periastron and the data time (the HJD column), but I'm not able to derive this number in the interval [0,1]. So, if we assume the orbital parameters are known, how can we derive that number?

In this case, the first row in Table 1 has time $$t = \mathrm{HJD}\ 2455107.37937$$, while in Table 2 the transit time is given as $$E = \mathrm{HJD}\ 2454967.27571$$ and the orbital period as $$P = 4.885525\ \mathrm{days}$$. So the number of cycles can be calculated as $$\mathrm{cycles} = (t-E)/P$$ giving 28.677 (to 3 decimal places).