# Linear ephemeris

What is the T in the formula for the linear ephemeris T_max = T + P*E, please? P stands for the period; E, for ephemeris. How to determine T? I have T_max and P. Or is it a referent epoch? Many thanks • There's not near enough context here to be able to answer this question. – David Hammen May 24 at 20:52
• @DavidHammen and yet... :-) – uhoh May 24 at 23:17
• Sometimes having done exactly this is in a previous life help with "matched filtering" what's behind the question... ;-) Remains for the OP to judge whether it actually answers their question – astrosnapper May 25 at 0:44

This is a fairly standard ephemeris for e.g. times of maximum light of a variable star but you are getting some of the symbols mixed up. The ephemeris is normally written as: $$T_{event} = T_0 + P\times E$$ where $$T_{event}$$ is the time of the given event (time maximum or minimum light, maximum positive radial velocity etc), $$T_0$$ is a reference time when the particular event occurred in the past, $$P$$ is the period and $$E$$ is an integer "cycle count" of how many times the particular event has recurred.

In this specific example, your 'event' is a time of maximum light, $$T_0=2454767.4648$$, $$P=0.4737$$. If you wanting to calculate the next time of maximum light, you need to:

1. calculate the HJD for the time of interest ($$T_{now}$$),
2. obtain an estimate of the cycle count $$E=\textrm{int}(\frac{T_{now}-T_0}{P})$$
3. Add 1 to $$E$$ to obtain the next time of maximum light
4. Plug the new $$E$$ into your ephemeris which will give the HJD of the new/next $$T_{max}$$

As a worked example, for "now":

T_now = 2459359.4269246464
E = (2459359.4269246464-2454767.4648)/0.4737 = 9693.81913583739
int(E)+1 = 9694
Next T_max = 2454767.4648 + 0.4737 * 9694
= 2459359.5126

• Thank you very much for your explanation. It helped a lot. – Elena Greg May 25 at 2:52