# Would 2 stars in binary star formation with same mass and no velocity collide into each other? [closed]

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.

• Are there additional details missing here? Sounds like they would eventually collide thanks to gravity (assuming they're close by and no other bodies interfere). – user10106 Oct 19 '17 at 9:01
• 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 Oct 19 '17 at 13:38
• 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 Oct 19 '17 at 13:47
• 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 Oct 19 '17 at 15:12
• @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 Oct 20 '17 at 3:34

## 1 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 - 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.