<p>My opinion (and I think there has to be a large element of that) is that the presence, and ultimately identification of the orbital period, of exomoons is going to come from very precise transit photometry.</p>
<p>If a sufficiently large moon orbits a planet, then this will leave its signature in the transit light curve. A &quot;Fourier-type analysis&quot; of the light curve might then reveal a periodic nature to the light curve shape during transit that could be attributed to the orbit of the moon. The requirements here would be a sufficiently large moon that its relative position alters the transit shape. The exoplanet also needs to be in a short period orbit so that you can observe lots of transits.</p>
<p>A related (and better) technique, that in practice would be used simultaneously, would be to look for the signature of a moon using changes in the duration and timing of transits that recur in a periodic way. The exoplanet-exomoon barycentre is what follows a Keplerian orbit; but the area-weighted &quot;centre of opacity&quot; of the system will, in general, not coincide with this barycentre because mass is proportional to <span class="math-container">$r^3$</span>, while obscuring area is proportional to <span class="math-container">$r^2$</span>. This will lead to a wobbling of both the time of  transit
and the transit duration that may again yield a periodic signal which could be identified with the exomoon period. These methods are discussed extensively by <a href="https://arxiv.org/abs/0810.2243" rel="noreferrer">Kipping 2009</a>, who point out that the transit timing and transit duration signatures have different dependencies on the exomoon mass and separation from the exoplanet and thus a careful measurement of both could yield the exomoon mass. i.e. Each method in its own has a degeneracy which means the exomoon mass/period could not be determined, but measured together, the degeneracy is broken.</p>
<p>There is a trade-off here. A wide exoplanet-exomoon separation will give bigger signatures, but of course by Kepler's third law, the orbital period will be longer and so you would likely need a longer dataset of transits to identify any periodicity and pin down the amplitude of these signatures.</p>
<p>At this stage, I don't think there is any likelihood of hearing about an exomoon period/mass in the next few years. Exomoon <em>detection</em> by these methods is though a possibility and may already have occurred (see <a href="https://ui.adsabs.harvard.edu/abs/2018SciA....4.1784T/abstract" rel="noreferrer">Teachey &amp; Kipping 2018</a>) . Perhaps the PLATO mission, which will produce better light curves than TESS or Kepler, and have long datasets will stand a better chance (and indeed exomoon detection is one of the mission goals - see <a href="https://arxiv.org/abs/1310.0696" rel="noreferrer">Rauer et al. 2014</a>).</p>

CC BY-SA 4.0
2020-09-30T07:33:00.117Z
2020-09-30T08:30:11.187Z
2020-09-30T08:30:11.187Z
ProfRob
<p>Comments below <a href="https://astronomy.stackexchange.com/a/39074/7982">this answer</a> to <em>How do we weigh a planet?</em> point out that we currently cannot (or at least have not) detect moons around exoplanets, much less measure the sizes and periods of their orbits around their planets.</p>
<p>I commented there that:</p>
<blockquote>
<p>...detecting exoplanets wasn't possible, nor did direct imaging of planetary systems, nor did making parallax measurements from the Kuiper belt, nor was the detection of gravitational waves...</p>
</blockquote>
<p>my point being that impossibly challenging observations keep getting done.</p>
<p>So I'd like to ask what the most likely extension of observational Astronomy would be that would allow for the measurement of the period of exomoons thereby weighing exoplanets.</p>
<p>Is it simply a pair of space telescopes in a halo orbit with laser interferometry between them and plenty of time? Could it be done from Earth? After all, exoplanetary systems are <em>already</em> imaged from Earth.</p>

CC BY-SA 4.0
2020-09-29T03:36:14.650Z
@AyushBhatt thanks for the edits! I like "didn't used to be possible" and I think it's not *incorrect* but only stylized, but your wording is better and more proper.
uhoh
CC BY-SA 4.0
2020-09-29T08:13:36.000Z
@antispinwards the challenge is to find enough to satisfy your request yet not enough to completely answer the question. The reason that I feel that challenge is that if I know the complete answer and don't post it, some will say that I ask in bad faith and yet others will have the opportunity to learn something, write an answer and collect some reuptation points (which [I'm not after](https://meta.stackexchange.com/q/345482)). On the other hand if I find the complete answer and do post it as an answer, *others* will complain that I'm gaming the system by asking and then quickly answering...
uhoh
CC BY-SA 4.0
2020-09-29T08:14:56.367Z
@antispinwards and on the *third hand* if I find out the answer and then don't post the question because I know the answer, then *everybody loses* except me, and that's the worst outcome from my point of view. The first two have each happened to me more than once over the years, they are not hypothetical. I feel that an answer here will be a good thing, so I've done something to make that answer possible. Without the question, the answer can't be posted.
uhoh
CC BY-SA 4.0
2020-09-29T08:18:37.833Z
@antispinwards based on my understanding of optics and interferometry, the proposed "pair of space telescopes in a halo orbit with laser interferometry between them" will certainly work *in principle* though quite challenging both in the hardware and the algorithms necessary to reduce the data in a model-dependent way. If you like I can elaborate on that in the question but it's simply an extension of current interferometry as addressed in answers to several of my previous questions and answers here: https://astronomy.stackexchange.com/search?q=user%3A7982+interferometry
uhoh
<observational-astronomy><exoplanet><optics><space-telescope>
What's still needed before we can observe orbits of exomoons thereby weighing exoplanets?
uhoh
# What's still needed before we can observe orbits of exomoons thereby weighing exoplanets?

(Asked by: username_0 on 2020-09-28)

Comments below [this answer](https://astronomy.stackexchange.com/a/39074/7982) to *How do we weigh a planet?* point out that we currently cannot (or at least have not) detect moons around exoplanets, much less measure the sizes and periods of their orbits around their planets.

I commented there that:

> ...detecting exoplanets wasn't possible, nor did direct imaging of planetary systems, nor did making parallax measurements from the Kuiper belt, nor was the detection of gravitational waves...

my point being that impossibly challenging observations keep getting done.

So I'd like to ask what the most likely extension of observational Astronomy would be that would allow for the measurement of the period of exomoons thereby weighing exoplanets.

Is it simply a pair of space telescopes in a halo orbit with laser interferometry between them and plenty of time? Could it be done from Earth? After all, exoplanetary systems are *already* imaged from Earth.

**Tags:** observational-astronomy, exoplanet, optics, space-telescope

> **Comments:**
> **username_0**: @AyushBhatt thanks for the edits! I like "didn't used to be possible" and I think it's not *incorrect* but only stylized, but your wording is better and more proper.  
> **username_0**: @antispinwards the challenge is to find enough to satisfy your request yet not enough to completely answer the question. The reason that I feel that challenge is that if I know the complete answer and don't post it, some will say that I ask in bad faith and yet others will have the opportunity to learn something, write an answer and collect some reuptation points (which [I'm not after](https://meta.stackexchange.com/q/345482)). On the other hand if I find the complete answer and do post it as an answer, *others* will complain that I'm gaming the system by asking and then quickly answering...  
> **username_0**: @antispinwards and on the *third hand* if I find out the answer and then don't post the question because I know the answer, then *everybody loses* except me, and that's the worst outcome from my point of view. The first two have each happened to me more than once over the years, they are not hypothetical. I feel that an answer here will be a good thing, so I've done something to make that answer possible. Without the question, the answer can't be posted.  
> **username_0**: @antispinwards based on my understanding of optics and interferometry, the proposed "pair of space telescopes in a halo orbit with laser interferometry between them" will certainly work *in principle* though quite challenging both in the hardware and the algorithms necessary to reduce the data in a model-dependent way. If you like I can elaborate on that in the question but it's simply an extension of current interferometry as addressed in answers to several of my previous questions and answers here: https://astronomy.stackexchange.com/search?q=user%3A7982+interferometry  

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## 1 answers

### Answer by username_1 on 2020-09-30. Score: 6 | Accepted answer

My opinion (and I think there has to be a large element of that) is that the presence, and ultimately identification of the orbital period, of exomoons is going to come from very precise transit photometry.

If a sufficiently large moon orbits a planet, then this will leave its signature in the transit light curve. A "Fourier-type analysis" of the light curve might then reveal a periodic nature to the light curve shape during transit that could be attributed to the orbit of the moon. The requirements here would be a sufficiently large moon that its relative position alters the transit shape. The exoplanet also needs to be in a short period orbit so that you can observe lots of transits.

A related (and better) technique, that in practice would be used simultaneously, would be to look for the signature of a moon using changes in the duration and timing of transits that recur in a periodic way. The exoplanet-exomoon barycentre is what follows a Keplerian orbit; but the area-weighted "centre of opacity" of the system will, in general, not coincide with this barycentre because mass is proportional to $r^3$, while obscuring area is proportional to $r^2$. This will lead to a wobbling of both the time of transit
and the transit duration that may again yield a periodic signal which could be identified with the exomoon period. These methods are discussed extensively by [Kipping 2009](https://arxiv.org/abs/0810.2243), who point out that the transit timing and transit duration signatures have different dependencies on the exomoon mass and separation from the exoplanet and thus a careful measurement of both could yield the exomoon mass. i.e. Each method in its own has a degeneracy which means the exomoon mass/period could not be determined, but measured together, the degeneracy is broken.

There is a trade-off here. A wide exoplanet-exomoon separation will give bigger signatures, but of course by Kepler's third law, the orbital period will be longer and so you would likely need a longer dataset of transits to identify any periodicity and pin down the amplitude of these signatures.

At this stage, I don't think there is any likelihood of hearing about an exomoon period/mass in the next few years. Exomoon *detection* by these methods is though a possibility and may already have occurred (see [Teachey & Kipping 2018](https://ui.adsabs.harvard.edu/abs/2018SciA....4.1784T/abstract)) . Perhaps the PLATO mission, which will produce better light curves than TESS or Kepler, and have long datasets will stand a better chance (and indeed exomoon detection is one of the mission goals - see [Rauer et al. 2014](https://arxiv.org/abs/1310.0696)).


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