<p>It seems the crux of your question lies in a misunderstand of how gravity works. So I'll try to answer your question by correcting your perceptions about gravity.</p>

<p>Gravity is a force imparted by objects with mass on all other objects with mass. The range of a gravitational force is infinite which means that galaxies millions and billions of light years away are technically applying a gravitational force on you, its just so infinitesimally small as to be not noticeable. The general equation for the force of gravity between two objects of mass $M_1$ and $M_2$ at a separtion of $r$ is given by</p>

<p>$$F_g = G\frac{M_1M_2}{r^2}$$</p>

<p>where $G$ is the gravitational constant equal to $6.67\times10^{-11}\ \mathrm{m^3\ kg^{-1}\ s^{-2}}$.</p>

<p>If you had nothing in the universe except the Earth ($M_1 = 5.97\times10^{24}\ \mathrm{kg}$) and the Moon ($M_2 = 7.35\times10^{22}\ \mathrm{kg}$) at their current distance of $r = 3.8\times10^7\ \mathrm{m}$, you'd find that $F_g = 2\times10^{22}\ \mathrm{N}$ where $N$ a <a href="https://en.wikipedia.org/wiki/Newton_(unit)" rel="nofollow noreferrer">Newton</a> - a unit of force equivalent to $\mathrm{kg\ m\ s^{-2}}$.</p>

<p>So in this scenario you calculate the gravitational force experienced by each body. The important point here is that <em>both bodies experience this singular force</em>. The Moon is pulled towards the Earth with a force equal to $2\times10^{22}\ \mathrm{N}$ and the Earth is likewise pulled towards the Moon by the same force equal to $2\times10^{22}\ \mathrm{N}$. They cannot and do not cancel each other out because each body is feeling one and only force of gravity. The Moon knows it experiences a gravitational force from the Earth and so it responds to that force by moving towards the Earth. It also happens to apply a gravitational force on the Earth to pull the Earth towards itself, but that force is the <em>same force</em>.</p>

<p>So in your scenario, two neutron stars which are just sitting next to each other in space would experience a singular gravitational force between them and pull themselves towards each other, eventually colliding. You can hopefully see the above argument works whether the two objects are the Moon and Earth, two neutron stars, or even Earth and you. Due to the mutual, single gravitational force within the system, the two bodies will be attracted to one another.</p>

<p>Of course, everything I've just said is the "Newtonian" description of gravity. A more complete and accurate picture is achieved by considering this from a General Relativity standpoint.</p>

CC BY-SA 3.0
2017-10-19T15:30:44.917Z
2017-10-19T15:30:44.917Z
zephyr
<p>Velocity decides if 2 stars with different masses in a binary star formation will collide or not, but if 2 stars with same mass existed but with no velocity (i.e they are not orbiting each other, just staying at their places at some distance), would they collide ? I guess the answer is no, but just not sure of how and where do the gravitational wave friction come into the scenario.</p>

CC BY-SA 3.0
2017-10-19T13:38:17.257Z
If you just placed two stars next to each other with no initial velocity, they would definitely collide as they'd be gravitationally attracted to one another just like you're gravitationally attracted to the Earth. And it is not because of the orbiting velocities that they collide in the normal case. It is because gravitational waves steal energy from the orbit slowly over time, forcing them to get closer and closer together until they collide.
zephyr
CC BY-SA 3.0
2017-10-19T13:44:15.220Z
They should not collide. Let's take and example. Say, you and I were holding a rope and we both had same power (same mass in case of star), you and  I would be pulling each other with the same force and hence neither would you be able to pull me towards you and neither would I be able to pull you towards me. The force cancels out. Then how do you expect these 2 stars with same mass (same gravitational pull) to collide with each other  when no one is able to pull the other star closer. @zephyr
GypsyCosmonaut
CC BY-SA 3.0
2017-10-19T13:47:38.780Z
You're misunderstanding how gravity works. Your analogy does not correctly explain how gravity works. The gravitational forces do not cancel out like that. If they did, you wouldn't stay on the surface of Earth seeing as the attraction between you and the Earth is no different than two neutron stars.
zephyr
CC BY-SA 3.0
2017-10-19T15:07:41.330Z
@zephyr Don't get me wrong, I am not trying to argue over here, please enlighten me. Let's say there is no acting force in the universe and there are just two objects, the Earth and the moon. The mass of Earth, let's assume is the same as the moon. Neither the Earth, nor the moon is in motion, they both are still but moon is in gravitational radius of Earth and Earth is in gravitational radius of moon. Both exert same gravitational force on each other. Now just explain me why they should collide. I have the notion that they would not collide.
GypsyCosmonaut
CC BY-SA 3.0
2017-10-19T15:09:01.900Z
Earth would not be able to pull moon towards itself because moon is also pulling Earth towards itself with the same force, hence they should remain in their places at the same distance. Please enlighten me.
GypsyCosmonaut
CC BY-SA 3.0
2017-10-19T15:12:38.883Z
This question does not deserve a close vote as being unclear. I believe the question is perfectly clear. Nor does it deserve a downvote. I'm assuming the close votes and downvotes are from those who believe this to be a stupid question, but that goes against the purpose of this site which is to ask questions and attain knowledge. Not everyone has the same knowledge.
zephyr
CC BY-SA 3.0
2017-10-20T03:34:29.000Z
@GypsyCosmonaut does your rope-pulling thought experiment work the sane way in a frictionless environment like space? Without something to push against (like the ground) in order to resist motion, the two people pulling on the rope should approach each other *twice* as fast as only one pulling.
Asher
CC BY-SA 3.0
2017-10-20T04:08:01.397Z
Yes you're correct, I couldn't think of the friction I'd be exerting against ground. Thank you @Asher ツ
GypsyCosmonaut
CC BY-SA 3.0
2017-10-20T08:36:50.097Z
I'm voting to close this question as off-topic because it is fundamentally a misunderstanding of basic physics that has caused the question to be asked in the first place.
Rory Alsop
<binary-star>
Would 2 stars in binary star formation with same mass and no velocity collide into each other?
GypsyCosmonaut
# Would 2 stars in binary star formation with same mass and no velocity collide into each other?

(Asked by: username_0 on 2017-10-19)

Velocity decides if 2 stars with different masses in a binary star formation will collide or not, but if 2 stars with same mass existed but with no velocity (i.e they are not orbiting each other, just staying at their places at some distance), would they collide ? I guess the answer is no, but just not sure of how and where do the gravitational wave friction come into the scenario.

**Tags:** binary-star
> **Comments:**
> **username_1**: If you just placed two stars next to each other with no initial velocity, they would definitely collide as they'd be gravitationally attracted to one another just like you're gravitationally attracted to the Earth. And it is not because of the orbiting velocities that they collide in the normal case. It is because gravitational waves steal energy from the orbit slowly over time, forcing them to get closer and closer together until they collide.  
> **username_0**: They should not collide. Let's take and example. Say, you and I were holding a rope and we both had same power (same mass in case of star), you and  I would be pulling each other with the same force and hence neither would you be able to pull me towards you and neither would I be able to pull you towards me. The force cancels out. Then how do you expect these 2 stars with same mass (same gravitational pull) to collide with each other  when no one is able to pull the other star closer. @zephyr  
> **username_1**: You're misunderstanding how gravity works. Your analogy does not correctly explain how gravity works. The gravitational forces do not cancel out like that. If they did, you wouldn't stay on the surface of Earth seeing as the attraction between you and the Earth is no different than two neutron stars.  
> **username_0**: @zephyr Don't get me wrong, I am not trying to argue over here, please enlighten me. Let's say there is no acting force in the universe and there are just two objects, the Earth and the moon. The mass of Earth, let's assume is the same as the moon. Neither the Earth, nor the moon is in motion, they both are still but moon is in gravitational radius of Earth and Earth is in gravitational radius of moon. Both exert same gravitational force on each other. Now just explain me why they should collide. I have the notion that they would not collide.  
> **username_0**: Earth would not be able to pull moon towards itself because moon is also pulling Earth towards itself with the same force, hence they should remain in their places at the same distance. Please enlighten me.  
> **username_1**: This question does not deserve a close vote as being unclear. I believe the question is perfectly clear. Nor does it deserve a downvote. I'm assuming the close votes and downvotes are from those who believe this to be a stupid question, but that goes against the purpose of this site which is to ask questions and attain knowledge. Not everyone has the same knowledge.  
> **username_2**: @GypsyCosmonaut does your rope-pulling thought experiment work the sane way in a frictionless environment like space? Without something to push against (like the ground) in order to resist motion, the two people pulling on the rope should approach each other *twice* as fast as only one pulling.  
> **username_0**: Yes you're correct, I couldn't think of the friction I'd be exerting against ground. Thank you @Asher ツ  
> **username_3**: I'm voting to close this question as off-topic because it is fundamentally a misunderstanding of basic physics that has caused the question to be asked in the first place.  

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## 1 answers

### Answer by username_1 on 2017-10-19. Score: 4 | Accepted answer

It seems the crux of your question lies in a misunderstand of how gravity works. So I'll try to answer your question by correcting your perceptions about gravity.

Gravity is a force imparted by objects with mass on all other objects with mass. The range of a gravitational force is infinite which means that galaxies millions and billions of light years away are technically applying a gravitational force on you, its just so infinitesimally small as to be not noticeable. The general equation for the force of gravity between two objects of mass $M\_1$ and $M\_2$ at a separtion of $r$ is given by

$$F\_g = G\frac{M\_1M\_2}{r^2}$$

where $G$ is the gravitational constant equal to $6.67\times10^{-11}\ \mathrm{m^3\ kg^{-1}\ s^{-2}}$.

If you had nothing in the universe except the Earth ($M\_1 = 5.97\times10^{24}\ \mathrm{kg}$) and the Moon ($M\_2 = 7.35\times10^{22}\ \mathrm{kg}$) at their current distance of $r = 3.8\times10^7\ \mathrm{m}$, you'd find that $F\_g = 2\times10^{22}\ \mathrm{N}$ where $N$ a [Newton](https://en.wikipedia.org/wiki/Newton_(unit)) - a unit of force equivalent to $\mathrm{kg\ m\ s^{-2}}$.

So in this scenario you calculate the gravitational force experienced by each body. The important point here is that *both bodies experience this singular force*. The Moon is pulled towards the Earth with a force equal to $2\times10^{22}\ \mathrm{N}$ and the Earth is likewise pulled towards the Moon by the same force equal to $2\times10^{22}\ \mathrm{N}$. They cannot and do not cancel each other out because each body is feeling one and only force of gravity. The Moon knows it experiences a gravitational force from the Earth and so it responds to that force by moving towards the Earth. It also happens to apply a gravitational force on the Earth to pull the Earth towards itself, but that force is the *same force*.

So in your scenario, two neutron stars which are just sitting next to each other in space would experience a singular gravitational force between them and pull themselves towards each other, eventually colliding. You can hopefully see the above argument works whether the two objects are the Moon and Earth, two neutron stars, or even Earth and you. Due to the mutual, single gravitational force within the system, the two bodies will be attracted to one another.

Of course, everything I've just said is the "Newtonian" description of gravity. A more complete and accurate picture is achieved by considering this from a General Relativity standpoint.


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