<p><span class="math-container">$f_{GW}$</span> changes because the binary system radiates energy. It could also gain energy through mass transfer. <span class="math-container">$f_{GW}$</span> can also be phase modulated. When <a href="https://en.wikipedia.org/wiki/Kepler-47" rel="nofollow noreferrer">planets orbit</a> a binary system, the binary system cannot remain at rest. Since it orbits the common center of mass, <span class="math-container">$f_{GW}$</span> is not constant but phase modulated. If you measure this PM, you can determine the orbital period of the planets and their masses. The PM is calculated using this equation:</p>
<p><span class="math-container">$$f_{GW}=f_{GW0}+t\cdot\dot f_{GW0}+a_{planet}\cdot sin(2\pi t f_{planet}+\phi_{planet})$$</span></p>
<p>The parameters have the following meaning:</p>
<p><span class="math-container">$f_{GW0}$</span> is the frequency of the undisturbed GW. This is calculated from the circulation period.</p>
<p><span class="math-container">$\dot f_{GW0}$</span> is the frequency drift of <span class="math-container">$f_{GW0}$</span></p>
<p><span class="math-container">$a_{planet}$</span> is the modulation index of the PM assuming that the planet describes a circular orbit around the GW source.</p>
<p><span class="math-container">$f_{planet}$</span> is the orbital frequency of the suspected planet.</p>
<p>From the phase <span class="math-container">$\phi_{planet}$</span> it follows when the planet is in front of or behind the GW source from the point of view of the earth.</p>
<p>A GW may also transport other information. You only know this when you manage to receive continuous GW.</p>

CC BY-SA 4.0
2023-11-18T10:26:31.560Z
2023-11-18T10:26:31.560Z
9herbert9
<p>Obviously they can, in the sense that at least the presence or absence of a gravitational wave can be detected. Hence you could send information by generating one or not, for example by either rotating two enormous masses around each other or not. Practically this is unlikely to be very useful.</p>
<p>What is the bandwidth you could send? Actually detected waves have had frequencies reaching a few hundred Hz, so that would give you a few hundred bits per second at most. Rotating deformed neutron stars might produce kHz waves, getting up to a kilobit per second at most. As noted in <a href="https://physics.stackexchange.com/questions/247513/gravitational-waves-frequency">this answer</a>, the frequency behaves roughly like <span class="math-container">$\sim\sqrt{G\rho}$</span> for gravitationally bound systems and hence to get decent bandwidth you need extremely high density objects. But to get a strong signal that you can detect at a distance they need to be very heavy and fast. So this is unlikely to be a very effective means of communication.</p>
<p>The theoretical maximum is likely given by a variant of <a href="https://arxiv.org/abs/cond-mat/9907500v1" rel="noreferrer">Lachman's formula for electromagnetic waves</a>, taking into account that these waves have slightly different statistics. One interesting observation is that this bound will scale with the energy: you need a lot of energy in the wave to have many gravitons that can carry information separately.</p>

CC BY-SA 4.0
2023-05-06T10:12:33.167Z
thanks, you mentioned it is roughly like Gp, what do you mean by Gp?
Hamidreza Abdollahi
CC BY-SA 4.0
2023-05-06T12:24:43.820Z
G times by rho.  G is the gravitational constant  and rho is the density of the two orbiting bodies. More dense bodies can orbit more closely without colliding, and so can produce higher frequency gravitational radiation.
James K
CC BY-SA 4.0
2023-05-05T08:36:33.027Z
2023-05-05T08:36:33.027Z
Anders Sandberg
<p>Gravitational waves can carry information about its source but for further information. Is there any equation which shows that gravitational waves can carry information and data?</p>

CC BY-SA 4.0
2023-05-04T20:17:43.670Z
Good question! However, could you possibly add a bit more information, in the question's current state, it's a little hard to understand exactly what you mean (or at least in my mind).
Deko Revinio
CC BY-SA 4.0
2023-05-04T20:26:15.693Z
i meant, how it is possible load data in GW, for example EM wave can carry data but how about GW flux? it is better to say, i meant what we have in documents and papers about carry data in GW science ... i read only they can deliver us data about their source , but how? what kind of data? ...
Hamidreza Abdollahi
CC BY-SA 4.0
2023-05-04T20:28:15.477Z
Alright, now I understand.
Deko Revinio
CC BY-SA 4.0
2023-05-04T20:39:34.440Z
This is kind of trivially "yes".  There's no practical way of doing this, as we are unable to produce detectable gravitational waves.  But as a simple thought experiment: place a ball on a string.  whirl about yourself (this produces gravitational radiation) then stop (radiation stops)  use this "on-off" to send a message in morse code
James K
CC BY-SA 4.0
2023-05-05T06:06:39.407Z
This question reminded me of the article published by the VIRGO Collaboration on april 1st entitled "A coded message from a remote galaxy in a gravitational wave": https://www.virgo-gw.eu/news/a-coded-message-from-a-remote-galaxy-in-a-gravitational-wave/ :)
Albert
CC BY-SA 4.0
2023-09-24T13:58:52.040Z
If you tell us what equation would be the equivalent for electromagnetic waves then you might get a sensible answer.
ProfRob
<gravitational-waves>
What is the formula that shows that gravitational waves can carry information and data?
Hamidreza Abdollahi
# What is the formula that shows that gravitational waves can carry information and data?

(Asked by: username_0 on 2023-05-04)

Gravitational waves can carry information about its source but for further information. Is there any equation which shows that gravitational waves can carry information and data?

**Tags:** gravitational-waves
> **Comments:**
> **username_1**: Good question! However, could you possibly add a bit more information, in the question's current state, it's a little hard to understand exactly what you mean (or at least in my mind).  
> **username_0**: i meant, how it is possible load data in GW, for example EM wave can carry data but how about GW flux? it is better to say, i meant what we have in documents and papers about carry data in GW science ... i read only they can deliver us data about their source , but how? what kind of data? ...  
> **username_1**: Alright, now I understand.  
> **username_2**: This is kind of trivially "yes".  There's no practical way of doing this, as we are unable to produce detectable gravitational waves.  But as a simple thought experiment: place a ball on a string.  whirl about yourself (this produces gravitational radiation) then stop (radiation stops)  use this "on-off" to send a message in morse code  
> **username_3**: This question reminded me of the article published by the VIRGO Collaboration on april 1st entitled "A coded message from a remote galaxy in a gravitational wave": https://www.virgo-gw.eu/news/a-coded-message-from-a-remote-galaxy-in-a-gravitational-wave/ :)  
> **username_4**: If you tell us what equation would be the equivalent for electromagnetic waves then you might get a sensible answer.  

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## 2 answers

### Answer by username_6 on 2023-05-05. Score: 5 | Accepted answer

Obviously they can, in the sense that at least the presence or absence of a gravitational wave can be detected. Hence you could send information by generating one or not, for example by either rotating two enormous masses around each other or not. Practically this is unlikely to be very useful.

What is the bandwidth you could send? Actually detected waves have had frequencies reaching a few hundred Hz, so that would give you a few hundred bits per second at most. Rotating deformed neutron stars might produce kHz waves, getting up to a kilobit per second at most. As noted in [this answer](https://physics.stackexchange.com/questions/247513/gravitational-waves-frequency), the frequency behaves roughly like $\sim\sqrt{G\rho}$ for gravitationally bound systems and hence to get decent bandwidth you need extremely high density objects. But to get a strong signal that you can detect at a distance they need to be very heavy and fast. So this is unlikely to be a very effective means of communication.

The theoretical maximum is likely given by a variant of [Lachman's formula for electromagnetic waves](https://arxiv.org/abs/cond-mat/9907500v1), taking into account that these waves have slightly different statistics. One interesting observation is that this bound will scale with the energy: you need a lot of energy in the wave to have many gravitons that can carry information separately.

> **Comments:**
> **username_0**: thanks, you mentioned it is roughly like Gp, what do you mean by Gp?  
> **username_2**: G times by rho.  G is the gravitational constant  and rho is the density of the two orbiting bodies. More dense bodies can orbit more closely without colliding, and so can produce higher frequency gravitational radiation.  

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### Answer by username_5 on 2023-11-18. Score: 0

$f\_{GW}$ changes because the binary system radiates energy. It could also gain energy through mass transfer. $f\_{GW}$ can also be phase modulated. When [planets orbit](https://en.wikipedia.org/wiki/Kepler-47) a binary system, the binary system cannot remain at rest. Since it orbits the common center of mass, $f\_{GW}$ is not constant but phase modulated. If you measure this PM, you can determine the orbital period of the planets and their masses. The PM is calculated using this equation:

$$f\_{GW}=f\_{GW0}+t\cdot\dot f\_{GW0}+a\_{planet}\cdot sin(2\pi t f\_{planet}+\phi\_{planet})$$

The parameters have the following meaning:

$f\_{GW0}$ is the frequency of the undisturbed GW. This is calculated from the circulation period.

$\dot f\_{GW0}$ is the frequency drift of $f\_{GW0}$

$a\_{planet}$ is the modulation index of the PM assuming that the planet describes a circular orbit around the GW source.

$f\_{planet}$ is the orbital frequency of the suspected planet.

From the phase $\phi\_{planet}$ it follows when the planet is in front of or behind the GW source from the point of view of the earth.

A GW may also transport other information. You only know this when you manage to receive continuous GW.


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