<p>It is not only possible, we have almost this situation in our neighborhood. Alpha Centauri only 4 lightyears away with two Stars. Alpha Centauri A and B. A has 1.1 times the mass of the sunn and B 0.9. This is very similar. And the distance is is 11 AU. 1.5 ~ 90 Lightminutes.</p>
<p><a href="https://en.wikipedia.org/wiki/Alpha_Centauri#Orbital_properties" rel="nofollow noreferrer">Alpha Centauri Wikipedia</a></p>

CC BY-SA 4.0
2020-09-13T19:37:36.217Z
2020-09-13T19:37:36.217Z
Tecnick3
<blockquote>
<p>Can two heavy objects circling around their C.M. be separated because of the speed of gravity?</p>
</blockquote>
<p>No. Newtonian mechanics does quite well assuming instantaneous gravity. You can get relativistically correct orbits either by doing a complete GR calculation, or using a simple approximation as already <s>eluded</s> alluded to in <a href="https://astronomy.stackexchange.com/a/38849/7982">@antispinward's answer</a>.</p>
<p><a href="https://space.stackexchange.com/a/21472/12102">This excellent answer</a> to <em>Besides retarded gravitation, anything else to worry about when calculating MU69's orbit from scratch?</em> in Space Exploration SE explains that we get the wrong answer if purely Newtonian mechanics is used except for slowing down the speed of gravity, but that's because one is neither treating gravity correctly nor using Newtonian mechanics correctly.</p>
<p>Many answers to <a href="https://space.stackexchange.com/q/23408/12102">How to calculate the planets and moons beyond Newtons's gravitational force?</a> include a way to treat this problem using a well-accepted <em>approximate treatment</em> of general relativity.</p>
<p>From <a href="https://space.stackexchange.com/a/23409/12102">this answer</a>:</p>
<blockquote>
<p>The acceleration of a body in the gravitation field of another body of <a href="https://en.wikipedia.org/wiki/Standard_gravitational_parameter" rel="nofollow noreferrer">standard gravitational parameter</a> <span class="math-container">$GM$</span> can be written:</p>
<p><span class="math-container">$$\mathbf{a_{Newton}} = -GM \frac{\mathbf{r}}{|r|^3},$$</span></p>
<p>where <span class="math-container">$r$</span> is the vector from the body <span class="math-container">$M$</span> to the body who's acceleration is being calculated. Remember that in Newtonian mechanics the acceleration of each body depends only on the mass of <em>the other body</em>, even though the force depends on both masses, because the first mass cancels out by <span class="math-container">$a=F/m$</span>.</p>
</blockquote>
<p>and later:</p>
<blockquote>
<p>The following approximation should be <em>added to</em> the Newtonian term:</p>
<p><span class="math-container">$$\mathbf{a_{GR}} = GM \frac{1}{c^2 |r|^3}\left(4 GM \frac{\mathbf{r}}{|r|} - (\mathbf{v} \cdot \mathbf{v}) \mathbf{r} + 4 (\mathbf{r} \cdot \mathbf{v}) \mathbf{v} \right),$$</span></p>
</blockquote>

CC BY-SA 4.0
2020-09-13T10:31:54.027Z
If I could give +10 (I mean 10 upvotes), I would!
Deschele Schilder
CC BY-SA 4.0
2020-09-13T10:34:31.817Z
By the way, I like what you said about the White Cube...
Deschele Schilder
CC BY-SA 4.0
2020-09-14T02:17:34.010Z
Gravity is instantaneous? Isn't this a total trip?!
Tom Russell
CC BY-SA 4.0
2020-09-14T02:21:03.980Z
@TomRussell no, information about gravity moves at the speed of light only. It's just that if you use purely Newtonian physics and just add a delay the simplest way possible you don't get the right answer because you're mixing apples and oranges while trying to make lemonade. If you use a purely general relativistic treatment, you get back to the right answer.
uhoh
CC BY-SA 4.0
2020-09-14T02:25:34.640Z
@TomRussell See [Have more recent LIGO/VIRGO gravitational wave measurements narrowed down the speed of gravity further?](https://astronomy.stackexchange.com/q/33009) for an experimental confirmation of the speed of gravity, and [this answer](https://space.stackexchange.com/a/39509/12102) for what happens when you mix apples and oranges trying to make lemonade :-)
uhoh
CC BY-SA 4.0
2020-09-14T02:57:39.970Z
Sigh. Foiled again. A certain Vonnegut quote comes to mind: "“Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. For he is full of murderous resentment toward the unlearned who have come by their ignorance the easy way."
Tom Russell
CC BY-SA 4.0
2020-09-14T07:39:14.920Z
@TomRussell see also a related question at Physics.SE: [Virtual Photon transmission speed of a Static Electric Field?](https://physics.stackexchange.com/q/156746/21441)
Ruslan
CC BY-SA 4.0
2020-09-16T03:29:08.623Z
"a simple approximation as already eluded to" alluded
Acccumulation
CC BY-SA 4.0
2020-09-16T03:51:08.010Z
@Acccumulation thanks! In the future please feel free to edit yourself if you like
uhoh
CC BY-SA 4.0
2020-09-13T00:31:08.817Z
2020-09-16T03:51:38.250Z
2020-09-16T03:51:38.250Z
uhoh
<p><a href="https://i.sstatic.net/5VWdk.png" rel="noreferrer"><img src="https://i.sstatic.net/5VWdk.png" alt="enter image description here" /></a></p>
<p>Imagine two massive objects, with the same mass (M) circling around their center of mass (C.M.). Let's assume that the distance between them is 1 light hour. Don´t the two bodies get accelerated and move away from each other because they feel the gravity of each other as it was 1 hour ago, because of which a force tangent to the direction of the speed develops?<br />
Can it be that gravity acts instantaneously? I've read about experiments proving the speed of gravity to be equal to the speed of light, but these were disputed.<br />
Isn't there both in Newtonian mechanics and GR there a time delay? The difference being though that space and time in Newtonian mechanics are separate and absolute (implying instantaneity?), while in GR the both are a whole and absolute.</p>

CC BY-SA 4.0
2020-09-13T11:38:10.600Z
Gravity isn't a force in GR. Gravity is a force in Newtonian mechanics and Newtonian gravity makes incorrect detailed predictions about orbits. I'm unclear what kind of answer you are expecting. In GR the bodies do not move away from each other (ignoring any tidal effects), they move closer together because the system radiates gravitational waves.
ProfRob
CC BY-SA 4.0
2020-09-13T18:42:41.630Z
@RobJeffries So the answer is no? Isn't the so-called force transmitted by gravitons in string theory, in a flat spacetime? Which is the same mechanism as the transmission of other forces? So, actually, we **can** speak of a force? Mass-energy (the energy-momentum tensor) being the charge?
Deschele Schilder
CC BY-SA 4.0
2020-09-13T20:35:28.330Z
I am not sure the position where the other mass was 1 hour ago is even well-defined.  It depends on the speed of the frame of reference.
Florian F
<gravity>
Can two heavy objects circling around their C.M. be separated because of the speed of gravity?
Deschele Schilder
# Can two heavy objects circling around their C.M. be separated because of the speed of gravity?

(Asked by: username_0 on 2020-09-12)

[![enter image description here](https://i.sstatic.net/5VWdk.png)](https://i.sstatic.net/5VWdk.png)

Imagine two massive objects, with the same mass (M) circling around their center of mass (C.M.). Let's assume that the distance between them is 1 light hour. Don´t the two bodies get accelerated and move away from each other because they feel the gravity of each other as it was 1 hour ago, because of which a force tangent to the direction of the speed develops?  
Can it be that gravity acts instantaneously? I've read about experiments proving the speed of gravity to be equal to the speed of light, but these were disputed.  
Isn't there both in Newtonian mechanics and GR there a time delay? The difference being though that space and time in Newtonian mechanics are separate and absolute (implying instantaneity?), while in GR the both are a whole and absolute.

**Tags:** gravity

> **Comments:**
> **username_1**: Gravity isn't a force in GR. Gravity is a force in Newtonian mechanics and Newtonian gravity makes incorrect detailed predictions about orbits. I'm unclear what kind of answer you are expecting. In GR the bodies do not move away from each other (ignoring any tidal effects), they move closer together because the system radiates gravitational waves.  
> **username_0**: @RobJeffries So the answer is no? Isn't the so-called force transmitted by gravitons in string theory, in a flat spacetime? Which is the same mechanism as the transmission of other forces? So, actually, we **can** speak of a force? Mass-energy (the energy-momentum tensor) being the charge?  
> **username_2**: I am not sure the position where the other mass was 1 hour ago is even well-defined.  It depends on the speed of the frame of reference.  

---

## 2 answers

### Answer by username_4 on 2020-09-13. Score: 14 | Accepted answer

> Can two heavy objects circling around their C.M. be separated because of the speed of gravity?

No. Newtonian mechanics does quite well assuming instantaneous gravity. You can get relativistically correct orbits either by doing a complete GR calculation, or using a simple approximation as already ~~eluded~~ alluded to in [@antispinward's answer](https://astronomy.stackexchange.com/a/38849/7982).

[This excellent answer](https://space.stackexchange.com/a/21472/12102) to *Besides retarded gravitation, anything else to worry about when calculating MU69's orbit from scratch?* in Space Exploration SE explains that we get the wrong answer if purely Newtonian mechanics is used except for slowing down the speed of gravity, but that's because one is neither treating gravity correctly nor using Newtonian mechanics correctly.

Many answers to [How to calculate the planets and moons beyond Newtons's gravitational force?](https://space.stackexchange.com/q/23408/12102) include a way to treat this problem using a well-accepted *approximate treatment* of general relativity.

From [this answer](https://space.stackexchange.com/a/23409/12102):

> The acceleration of a body in the gravitation field of another body of [standard gravitational parameter](https://en.wikipedia.org/wiki/Standard_gravitational_parameter) $GM$ can be written:
>
> $$\mathbf{a\_{Newton}} = -GM \frac{\mathbf{r}}{|r|^3},$$
>
> where $r$ is the vector from the body $M$ to the body who's acceleration is being calculated. Remember that in Newtonian mechanics the acceleration of each body depends only on the mass of *the other body*, even though the force depends on both masses, because the first mass cancels out by $a=F/m$.

and later:

> The following approximation should be *added to* the Newtonian term:
>
> $$\mathbf{a\_{GR}} = GM \frac{1}{c^2 |r|^3}\left(4 GM \frac{\mathbf{r}}{|r|} - (\mathbf{v} \cdot \mathbf{v}) \mathbf{r} + 4 (\mathbf{r} \cdot \mathbf{v}) \mathbf{v} \right),$$

> **Comments:**
> **username_0**: If I could give +10 (I mean 10 upvotes), I would!  
> **username_0**: By the way, I like what you said about the White Cube...  
> **username_5**: Gravity is instantaneous? Isn't this a total trip?!  
> **username_4**: @username_5 no, information about gravity moves at the speed of light only. It's just that if you use purely Newtonian physics and just add a delay the simplest way possible you don't get the right answer because you're mixing apples and oranges while trying to make lemonade. If you use a purely general relativistic treatment, you get back to the right answer.  
> **username_4**: @username_5 See [Have more recent LIGO/VIRGO gravitational wave measurements narrowed down the speed of gravity further?](https://astronomy.stackexchange.com/q/33009) for an experimental confirmation of the speed of gravity, and [this answer](https://space.stackexchange.com/a/39509/12102) for what happens when you mix apples and oranges trying to make lemonade :-)  
> **username_5**: Sigh. Foiled again. A certain Vonnegut quote comes to mind: "“Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. For he is full of murderous resentment toward the unlearned who have come by their ignorance the easy way."  
> **username_6**: @username_5 see also a related question at Physics.SE: [Virtual Photon transmission speed of a Static Electric Field?](https://physics.stackexchange.com/q/156746/21441)  
> **username_7**: "a simple approximation as already eluded to" alluded  
> **username_4**: @username_7 thanks! In the future please feel free to edit yourself if you like  

---

### Answer by username_3 on 2020-09-13. Score: -1

It is not only possible, we have almost this situation in our neighborhood. Alpha Centauri only 4 lightyears away with two Stars. Alpha Centauri A and B. A has 1.1 times the mass of the sunn and B 0.9. This is very similar. And the distance is is 11 AU. 1.5 ~ 90 Lightminutes.

[Alpha Centauri Wikipedia](https://en.wikipedia.org/wiki/Alpha_Centauri#Orbital_properties)


---

