<p>An <a href="https://en.wikipedia.org/wiki/Ephemeris" rel="nofollow noreferrer">ephemeris</a> (plural ephemerides) is a collection of predictions of the positions of one or more celestial objects.  An <a href="https://en.wikipedia.org/wiki/Epoch" rel="nofollow noreferrer">epoch</a> is a reference point from which time is measured.  The <a href="https://en.wikipedia.org/wiki/Phase_(waves)" rel="nofollow noreferrer">phase</a> represents the fraction of the period of a periodic phenomenon that has passed, omitting whole periods.  Phase is often represented as an angle (between 0 and 360 degrees or <span class="math-container">$2\pi$</span> radians), or as a number between 0 and 1.  Your question is based on that latter convention.  So the phase <span class="math-container">$\phi$</span> is</p>
<p><span class="math-container">\begin{equation} \phi = \dfrac{t - t_\text{epoch}}{P} \bmod 1 \end{equation}</span></p>
<p>where <span class="math-container">$t$</span> is the time of interest, <span class="math-container">$t_\text{epoch}$</span> is the epoch, <span class="math-container">$P$</span> is the period, and <span class="math-container">$\text{mod}$</span> is the <a href="https://en.wikipedia.org/wiki/Modulo" rel="nofollow noreferrer">modulo operator</a>.</p>
<p>You can take the MJD (<a href="https://en.wikipedia.org/wiki/Julian_day#Variants" rel="nofollow noreferrer">Modified Julian Date</a>) from your flux table as <span class="math-container">$t$</span>; it represents time since the epoch of MJD in units of a day.  You can choose any epoch that is convenient.  If you use the epoch of MJD as your epoch then <span class="math-container">$t_\text{epoch} = 0$</span>, so then the phase formula becomes</p>
<p><span class="math-container">\begin{equation} \phi = \dfrac{t}{131.05} \bmod 1 \end{equation}</span></p>
<p>The phase of the first observation from your flux table is then</p>
<p><span class="math-container">\begin{equation} \phi = \dfrac{55018.52594}{131.05} \bmod 1 = 419.8285077 \bmod 1 = 0.8285077 \end{equation}</span></p>
<p>As an aside: Do not confuse the phase described above with the <a href="https://en.wikipedia.org/wiki/Phase_angle_(astronomy)" rel="nofollow noreferrer">phase angle</a> that is mentioned in your bottom graph.  The phase angle describes the distribution of light and dark across the celestial object as seen by the observer, not the location of the celestial object in its orbit independent of any observer.  The (orbital) phase increases at a fixed rate (between the sudden drops from 1 to 0) but the rate of increase of the phase angle usually varies, especially when the orbit is not a perfectly circular one.</p>
<p>Follow-up answer:</p>
<p>Phases are a bit like a circle that has been cut and then unwound into a flat line segment.  Instead of going round and round the circle you repeatedly go from beginning to end along the line and then instantaneously jump back to the beginning.  You have to cut the circle somewhere in order to turn it into a flat line segment.  Changing the epoch corresponds to picking another point on the circle where to cut it (instead of cutting at the first point).  It would be better to explain this with a few graphs, but I cannot quickly construct them.</p>
<p>If the phase varies from 0 to <span class="math-container">$F$</span> then the phase formula is</p>
<p><span class="math-container">\begin{equation} \phi = \left( F \dfrac{t - t_\text{epoch}}{P} \right) \bmod F \end{equation}</span></p>
<p>If you plot your flux as a function of phase then changing <span class="math-container">$F$</span> doesn't change the graph but only changes the range of numbers along the x axis.</p>

CC BY-SA 4.0
2023-04-03T02:39:42.563Z
This was great thank you so much, I do have a follow up question though if you don't mind expanding on it a bit, why is it I can just use Tep = 0? Would it matter then if I used Phase as an angle? And if so how would the equation change? Thanks!
chris trejo
CC BY-SA 4.0
2023-04-04T20:36:22.113Z
See the follow-up answer that I added.
Louis Strous
CC BY-SA 4.0
2023-04-02T09:15:51.770Z
2023-04-04T20:35:48.960Z
2023-04-04T20:35:48.960Z
Louis Strous
<p>So I'm currently researching Star-planet Interactions for HD 156279, I'm taking the flux of the Ca II H&amp;K lines and trying to plot them against the phase of the planet, looking for evidence of magnetic or tidal interactions.</p>
<p>Now I have my flux as show below:
<a href="https://i.sstatic.net/17zyG.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/17zyG.png" alt="enter image description here" /></a></p>
<p>And I know the Phase=(time-ephem)/period. Now my professor said I can find the ephemeris from this site:
<a href="http://exoplanet.eu/ephemeris/hd_156279_b/" rel="nofollow noreferrer">http://exoplanet.eu/ephemeris/hd_156279_b/</a>
<a href="https://i.sstatic.net/VVbSY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VVbSY.png" alt="enter image description here" /></a></p>
<p>The problem I'm having is figuring out what the ephemeris is? I know the Period is 131.05, I assume the Time parameter is 2455525.59 as given by the webpage although I'm not sure about that either. I understand that phase should be between 0.0-1.0 and if I use 2455525.59 for time and using a converter for JD for my first flux in the table above (2009-07-06 12:41:11 = 2455019.0285995 and I assume this is the ephem I'm looking for) if I plug those into my equation I get 3.865...so I'm guessing that's not what I'm looking for. Any help would be greatly appreciated. I would ask my advisor but he's out sick with covid...so I'm trying to figure this out on my own.</p>
<p>Thanks!</p>

<exoplanet><ephemeris>
Finding the Phase of an Exoplanet using the ephemeries
chris trejo
# Finding the Phase of an Exoplanet using the ephemeries

(Asked by: username_0 on 2023-04-01)

So I'm currently researching Star-planet Interactions for HD 156279, I'm taking the flux of the Ca II H&K lines and trying to plot them against the phase of the planet, looking for evidence of magnetic or tidal interactions.

Now I have my flux as show below:
[![enter image description here](https://i.sstatic.net/17zyG.png)](https://i.sstatic.net/17zyG.png)

And I know the Phase=(time-ephem)/period. Now my professor said I can find the ephemeris from this site:
<http://exoplanet.eu/ephemeris/hd_156279_b/>
[![enter image description here](https://i.sstatic.net/VVbSY.png)](https://i.sstatic.net/VVbSY.png)

The problem I'm having is figuring out what the ephemeris is? I know the Period is 131.05, I assume the Time parameter is 2455525.59 as given by the webpage although I'm not sure about that either. I understand that phase should be between 0.0-1.0 and if I use 2455525.59 for time and using a converter for JD for my first flux in the table above (2009-07-06 12:41:11 = 2455019.0285995 and I assume this is the ephem I'm looking for) if I plug those into my equation I get 3.865...so I'm guessing that's not what I'm looking for. Any help would be greatly appreciated. I would ask my advisor but he's out sick with covid...so I'm trying to figure this out on my own.

Thanks!

**Tags:** exoplanet, ephemeris


---

## 1 answers

### Answer by username_1 on 2023-04-02. Score: 2 | Accepted answer

An [ephemeris](https://en.wikipedia.org/wiki/Ephemeris) (plural ephemerides) is a collection of predictions of the positions of one or more celestial objects. An [epoch](https://en.wikipedia.org/wiki/Epoch) is a reference point from which time is measured. The [phase](https://en.wikipedia.org/wiki/Phase_(waves)) represents the fraction of the period of a periodic phenomenon that has passed, omitting whole periods. Phase is often represented as an angle (between 0 and 360 degrees or $2\pi$ radians), or as a number between 0 and 1. Your question is based on that latter convention. So the phase $\phi$ is

\begin{equation} \phi = \dfrac{t - t\_\text{epoch}}{P} \bmod 1 \end{equation}

where $t$ is the time of interest, $t\_\text{epoch}$ is the epoch, $P$ is the period, and $\text{mod}$ is the [modulo operator](https://en.wikipedia.org/wiki/Modulo).

You can take the MJD ([Modified Julian Date](https://en.wikipedia.org/wiki/Julian_day#Variants)) from your flux table as $t$; it represents time since the epoch of MJD in units of a day. You can choose any epoch that is convenient. If you use the epoch of MJD as your epoch then $t\_\text{epoch} = 0$, so then the phase formula becomes

\begin{equation} \phi = \dfrac{t}{131.05} \bmod 1 \end{equation}

The phase of the first observation from your flux table is then

\begin{equation} \phi = \dfrac{55018.52594}{131.05} \bmod 1 = 419.8285077 \bmod 1 = 0.8285077 \end{equation}

As an aside: Do not confuse the phase described above with the [phase angle](https://en.wikipedia.org/wiki/Phase_angle_(astronomy)) that is mentioned in your bottom graph. The phase angle describes the distribution of light and dark across the celestial object as seen by the observer, not the location of the celestial object in its orbit independent of any observer. The (orbital) phase increases at a fixed rate (between the sudden drops from 1 to 0) but the rate of increase of the phase angle usually varies, especially when the orbit is not a perfectly circular one.

Follow-up answer:

Phases are a bit like a circle that has been cut and then unwound into a flat line segment. Instead of going round and round the circle you repeatedly go from beginning to end along the line and then instantaneously jump back to the beginning. You have to cut the circle somewhere in order to turn it into a flat line segment. Changing the epoch corresponds to picking another point on the circle where to cut it (instead of cutting at the first point). It would be better to explain this with a few graphs, but I cannot quickly construct them.

If the phase varies from 0 to $F$ then the phase formula is

\begin{equation} \phi = \left( F \dfrac{t - t\_\text{epoch}}{P} \right) \bmod F \end{equation}

If you plot your flux as a function of phase then changing $F$ doesn't change the graph but only changes the range of numbers along the x axis.

> **Comments:**
> **username_0**: This was great thank you so much, I do have a follow up question though if you don't mind expanding on it a bit, why is it I can just use Tep = 0? Would it matter then if I used Phase as an angle? And if so how would the equation change? Thanks!  
> **username_1**: See the follow-up answer that I added.  

---

