<p>YES!</p>

<p>Gravity will eventually pull them together. 
The thing is that gravity exerts itself over very vast distances, although the force decreases exponentially over distance. BUT, two motion less massive objects will attract each other, without any other influence whatsoever.</p>

CC BY-SA 4.0
2019-02-15T09:08:32.140Z
"Exponentially" in a casual day to day sense but not in a mathematical sense.  Gravitational attraction decays more quickly than inverse linear, doubling the distance more than halves the attraction, but not as fast as exponential.  In is inverse quadratic which, in the world of maths, is slow compared to exponential.
badjohn
CC BY-SA 4.0
2019-02-13T05:30:53.563Z
2019-02-13T05:30:53.563Z
Khawar Ali Sher
<p>Yes, they would experience gravitational attraction. It would take a long time for them to collide... the formula (derived <a href="https://physics.stackexchange.com/a/14718/83380">here</a> and shown <a href="https://physics.stackexchange.com/a/90722/83380">here</a>) is:</p>

<p><span class="math-container">$$t = \frac{\pi}{2} \sqrt{\frac{d^3}{2G(m_1+m_2)}}$$</span></p>

<p>where <span class="math-container">$d$</span> is the initial distance between the two planets of mass <span class="math-container">$m_1$</span> and <span class="math-container">$m_2$</span> and <span class="math-container">$G$</span> is the <a href="https://en.wikipedia.org/wiki/Gravitational_constant" rel="nofollow noreferrer">Gravitational constant</a>. This gives a time of about <span class="math-container">$10^{23}$</span> years, much much longer than the universe has existed. This assumes Newtonian mechanics. Relativity would not change the conclusion much.</p>

<p>There is no known upper limit to gravity, and plenty of indirect evidence that it has no upper limit.</p>

CC BY-SA 4.0
2019-02-09T20:16:29.220Z
The collision speed of a test particle falling to Earth from infinity is equal to the escape velocity, about 11 km/s. For 2 Earth-mass bodies, the speed will be similar, I *think* you can just multiply it by $\sqrt 2$, but I'm too sleepy to do the algebra right now. ;)
PM 2Ring
CC BY-SA 4.0
2019-02-12T21:39:36.220Z
What (indirect) evidence is available that gravity still acts 5 billion light years away?
Sextus Empiricus
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2019-02-13T21:05:13.570Z
I just did the algebra. The relative collision speed of 2 Earths is identical to the terminal speed of a test particle, so 11.186 km/s.
PM 2Ring
CC BY-SA 4.0
2019-02-15T11:38:13.633Z
"long time for them to collide" they'll only collide certainly if they are both "stationary" to begin with, or, have certain relative vectors.  if they are moving to begin with, they'll be attracted but in many cases will end up in a (huge, mammoth) orbit around each other.
Fattie
CC BY-SA 4.0
2019-02-28T08:33:30.837Z
There is still the problem that there is indeed an *effective upper limit* to gravity. If two objects are too far apart, due to expansion their separation will increase faster than the speed of light. There are parts of the universe that will never experience gravity or light from other parts of the universe. See [this answer](https://physics.stackexchange.com/a/330115/83380) and answers to [Am I attracting Pluto?](https://physics.stackexchange.com/q/200635/83380)
uhoh
CC BY-SA 4.0
2019-02-09T12:36:12.867Z
2019-02-28T08:21:15.387Z
2019-02-28T08:21:15.387Z
James K
<p>For this question assume that the entire universe is completely empty. The universe is not expanding or contracting, it is completely motionless since time immemorial and has never moved before.</p>

<p>Only two identical earths without moon are left in this entire universe and they are 5 billion light years apart. From their starting position the earths do not spin or move at all they are completely motionless.</p>

<p>Would these planets ever meet or at least be pulled together?  Or are the their respective gravities too small to have any meaningful effect?</p>

CC BY-SA 4.0
2019-02-09T12:34:34.167Z
For a good 5 billions ly they ignore each other.
Alchimista
CC BY-SA 4.0
2019-02-09T12:54:36.680Z
I want to say that probably you consider the entire universe as to be the entire visible and/or observable universe. The accepted answer is indeed satisfactory only under several assumption. It is more to answer about two generic masses in a static enormous room. Else cosmology sets in
Alchimista
CC BY-SA 4.0
2019-02-09T13:24:58.210Z
I am familiar with the differences, but for this question to work i needed to be sure there where no outside factors affecting the two planets.
Tom Sol
CC BY-SA 4.0
2019-02-09T15:05:26.510Z
Is the universe expanding?
userLTK
CC BY-SA 4.0
2019-02-09T17:41:59.090Z
It is not I'm sorry this was not mentioned.
Tom Sol
CC BY-SA 4.0
2019-02-09T18:50:45.943Z
Do the planets have a charge? Equal or opposite? That could offset any gravitational attraction.
Wayfaring Stranger
CC BY-SA 4.0
2019-02-10T03:53:29.323Z
@Alchimista I almost added a second answer, then I realized what you meant. Indeed if the planets just pop into an empty space 5 Gly apart, it takes each one 5 Gy to first experience gravity or anything else from the other.
uhoh
CC BY-SA 4.0
2019-02-10T08:00:36.617Z
When things magically pop up or disappear is always tricky. At a first glance I am even not sure about escape velocity as limit. Plus as I said having just two planet can be a totally different universe. There is expansion to be accounted for, and it should be even faster. Surprising enough, thinking of two test masses separated by a very huge distance or two planets in an otherwise empty univ. can lead to errors in thinking ( or even different correct answers ???)....
Alchimista
CC BY-SA 4.0
2019-02-12T14:50:11.790Z
Surely this is more of a physics question?
Fattie
<gravity><universe><observable-universe><rogue-planet>
Can two planets in an empty universe meet/be pulled together?
Tom Sol
# Can two planets in an empty universe meet/be pulled together?

(Asked by: username_0 on 2019-02-09)

For this question assume that the entire universe is completely empty. The universe is not expanding or contracting, it is completely motionless since time immemorial and has never moved before.

Only two identical earths without moon are left in this entire universe and they are 5 billion light years apart. From their starting position the earths do not spin or move at all they are completely motionless.

Would these planets ever meet or at least be pulled together? Or are the their respective gravities too small to have any meaningful effect?

**Tags:** gravity, universe, observable-universe, rogue-planet

> **Comments:**
> **username_1**: For a good 5 billions ly they ignore each other.  
> **username_1**: I want to say that probably you consider the entire universe as to be the entire visible and/or observable universe. The accepted answer is indeed satisfactory only under several assumption. It is more to answer about two generic masses in a static enormous room. Else cosmology sets in  
> **username_0**: I am familiar with the differences, but for this question to work i needed to be sure there where no outside factors affecting the two planets.  
> **username_2**: Is the universe expanding?  
> **username_0**: It is not I'm sorry this was not mentioned.  
> **username_3**: Do the planets have a charge? Equal or opposite? That could offset any gravitational attraction.  
> **username_4**: @username_1 I almost added a second answer, then I realized what you meant. Indeed if the planets just pop into an empty space 5 Gly apart, it takes each one 5 Gy to first experience gravity or anything else from the other.  
> **username_1**: When things magically pop up or disappear is always tricky. At a first glance I am even not sure about escape velocity as limit. Plus as I said having just two planet can be a totally different universe. There is expansion to be accounted for, and it should be even faster. Surprising enough, thinking of two test masses separated by a very huge distance or two planets in an otherwise empty univ. can lead to errors in thinking ( or even different correct answers ???)....  
> **username_5**: Surely this is more of a physics question?  

---

## 2 answers

### Answer by username_8 on 2019-02-09. Score: 7 | Accepted answer

Yes, they would experience gravitational attraction. It would take a long time for them to collide... the formula (derived [here](https://physics.stackexchange.com/a/14718/83380) and shown [here](https://physics.stackexchange.com/a/90722/83380)) is:

$$t = \frac{\pi}{2} \sqrt{\frac{d^3}{2G(m\_1+m\_2)}}$$

where $d$ is the initial distance between the two planets of mass $m\_1$ and $m\_2$ and $G$ is the [Gravitational constant](https://en.wikipedia.org/wiki/Gravitational_constant). This gives a time of about $10^{23}$ years, much much longer than the universe has existed. This assumes Newtonian mechanics. Relativity would not change the conclusion much.

There is no known upper limit to gravity, and plenty of indirect evidence that it has no upper limit.

> **Comments:**
> **username_9**: The collision speed of a test particle falling to Earth from infinity is equal to the escape velocity, about 11 km/s. For 2 Earth-mass bodies, the speed will be similar, I *think* you can just multiply it by $\sqrt 2$, but I'm too sleepy to do the algebra right now. ;)  
> **username_10**: What (indirect) evidence is available that gravity still acts 5 billion light years away?  
> **username_9**: I just did the algebra. The relative collision speed of 2 Earths is identical to the terminal speed of a test particle, so 11.186 km/s.  
> **username_5**: "long time for them to collide" they'll only collide certainly if they are both "stationary" to begin with, or, have certain relative vectors.  if they are moving to begin with, they'll be attracted but in many cases will end up in a (huge, mammoth) orbit around each other.  
> **username_4**: There is still the problem that there is indeed an *effective upper limit* to gravity. If two objects are too far apart, due to expansion their separation will increase faster than the speed of light. There are parts of the universe that will never experience gravity or light from other parts of the universe. See [this answer](https://physics.stackexchange.com/a/330115/83380) and answers to [Am I attracting Pluto?](https://physics.stackexchange.com/q/200635/83380)  

---

### Answer by username_6 on 2019-02-13. Score: 0

YES!

Gravity will eventually pull them together.
The thing is that gravity exerts itself over very vast distances, although the force decreases exponentially over distance. BUT, two motion less massive objects will attract each other, without any other influence whatsoever.

> **Comments:**
> **username_7**: "Exponentially" in a casual day to day sense but not in a mathematical sense.  Gravitational attraction decays more quickly than inverse linear, doubling the distance more than halves the attraction, but not as fast as exponential.  In is inverse quadratic which, in the world of maths, is slow compared to exponential.  

---

