<p>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:
<span class="math-container">$$
  T_{event} = T_0 + P\times E
$$</span>
where <span class="math-container">$T_{event}$</span> is the time of the given event (time maximum or minimum light, maximum positive radial velocity etc), <span class="math-container">$T_0$</span> is a reference time when the particular event occurred in the past, <span class="math-container">$P$</span> is the period and <span class="math-container">$E$</span> is an integer &quot;cycle count&quot; of how many times the particular event has recurred.</p>
<p>In this specific example, your 'event' is a time of maximum light, <span class="math-container">$T_0=2454767.4648$</span>, <span class="math-container">$P=0.4737$</span>. If you wanting to calculate the next time of maximum light, you need to:</p>
<ol>
<li>calculate the HJD for the time of interest (<span class="math-container">$T_{now}$</span>),</li>
<li>obtain an estimate of the cycle count <span class="math-container">$E=\textrm{int}(\frac{T_{now}-T_0}{P})$</span></li>
<li>Add 1 to <span class="math-container">$E$</span> to obtain the next time of maximum light</li>
<li>Plug the new <span class="math-container">$E$</span> into your ephemeris which will give the HJD of the new/next <span class="math-container">$T_{max}$</span></li>
</ol>
<p>As a worked example, for &quot;now&quot;:</p>
<pre><code>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
</code></pre>

CC BY-SA 4.0
2021-05-25T02:52:25.243Z
Thank you very much for your explanation. It helped a lot.
Elena Greg
CC BY-SA 4.0
2021-05-24T22:20:10.583Z
2021-05-24T22:20:10.583Z
astrosnapper
<p>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</p>
<p><a href="https://i.sstatic.net/YXYNr.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YXYNr.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-05-24T20:52:10.330Z
There's not near enough context here to be able to answer this question.
David Hammen
CC BY-SA 4.0
2021-05-24T23:17:50.113Z
@DavidHammen and yet... :-)
uhoh
CC BY-SA 4.0
2021-05-25T00:44:42.610Z
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
<ephemeris>
Linear ephemeris
Elena Greg
# Linear ephemeris

(Asked by: username_0 on 2021-05-24)

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

[![enter image description here](https://i.sstatic.net/YXYNr.png)](https://i.sstatic.net/YXYNr.png)

**Tags:** ephemeris
> **Comments:**
> **username_1**: There's not near enough context here to be able to answer this question.  
> **username_2**: @DavidHammen and yet... :-)  
> **username_3**: 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  

---

## 1 answers

### Answer by username_3 on 2021-05-24. Score: 5 | Accepted answer

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:

calculate the HJD for the time of interest ($T_{now}$),
obtain an estimate of the cycle count $E=\textrm{int}(\frac{T_{now}-T_0}{P})$
Add 1 to $E$ to obtain the next time of maximum light
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

> **Comments:**
> **username_0**: Thank you very much for your explanation. It helped a lot.  

---

