# Science: Gravity on two bodies [closed]

Let's say we have a situation like a universe completely empty except there are two rocks about a light year apart, these rocks are the same size and mass as Earth.

Now my question is will those two objects be drawn to each other due to their gravitational pull? or is the distance too great for gravity to have effect so they won't move at all?

if the answer to the first question is yes my follow-up question is the same scenario except now you have two rocks the same size and mass of the sun. Assuming that the gravity is enough to move them will they then accelerate towards each other faster or will they move at the same pace? i.e. do the planets move at X and the Suns move at Y or because the mass of both objects is equal will the Suns also move at X?

If it requires some clarifications to be made, as in the comments.

• physics.stackexchange.com/questions/11321/… You chose the wrong forum – Raditz_35 May 30 '17 at 11:58
• If any of your data is not 0 then you will always have some force. Same with the second. One of your data is changing (distance) so you have acceleration. – SZCZERZO KŁY May 30 '17 at 12:21
• VoteOpen: physics questions are not off topic on the WB by default. The question isn't the best on physics topic but ... Also, I would like you to read the meta answer written by Monica, especially parts of building community. And then read the meta post about community and notice that significant percentage of users are interested in math and physics. And then run the queries yourself and think about changes. – MolbOrg May 30 '17 at 14:19

It depends on what you believe about Gravity; which is not a settled question in physics. In fact most physicists believe Einstein's General Relativity will prove to be broken at very high gravity or very great distance; because its assumption of an infinitely divisible space (i.e. that there is no smallest distance) is at odds with, and provably wrong, in quantum physics.

Attempts to reconcile GR and QP include Loop Quantum Gravity; String Theory, etc.

All that said, for a single light year and the modest masses you propose (size of a planet or Sun), there should be no problem. (For examples of problems, individual atoms a light year apart might not attract each other at all, in some models of gravity; or planets a billion light years apart may not affect each other at all.)

They would attract each other. Gravity causes an acceleration proportional to the two masses and distance; so two equal mass objects move toward each other at the same speed. Whereas, given an apple and the Earth, the apple moves toward the Earth far faster than the Earth moves toward the apple; the acceleration of each is inversely proportional to their mass vs the other.

The stars would accelerate toward each other faster; the sum of their gravitational pulls is far greater than the sum of the gravitational pulls of the two planets.

In either case, the result may be collision, but not necessarily; they may also zoom past each other in symmetric "J" shape trajectories (like we use planetary bodies for gravitational acceleration), or end up orbiting each other for many billions of years before colliding or moving apart.

• Assuming a starting position at rest, a "J" shaped trajectory is not possible : given that there is only 2 bodies, they can only accelerate toward each other. Of course, if the bodies have a starting velocity, things are different, but I think the question is about motionless rocks (though not explicitly stated). – Keelhaul May 30 '17 at 12:27
• they would in every case collide, if they don't start with an impluse in a different direction. – Fl.pf. May 30 '17 at 12:34
• Agreed, and probably what the OP meant. If they begin at rest with zero relative spin to each other. If they spin, I think there is a relativistic differential gravitational force across the diameter; right? One side of object A is approaching Object B, while the the other side of Object A is receding from it. I thought perhaps over the distance of traveling a light year; that tiny effect might be amplified into a near miss. But I haven't done the math; that was just my speculation. Maybe they balance out. – Amadeus-Reinstate-Monica May 30 '17 at 13:09
• @Keelhaul that is actually a funny part of the question, as there are only 2 bodies in the system we can't say if they have some angular momentum initially. There is no way to measure that, lol. And even when we state they are at rest, we assume that there is some coordinate system where they are at rest, but we can't say if the system is an inertial system or not :D and thus it might look like the Gravitational constant is slightly different, speed of light is little different, but in fact the coordinate system is not entirely inertial. The question is funny as hell ))) – MolbOrg May 30 '17 at 15:10
• @MolbOrg "But we can't say do the system of those 2 bodies rotate around some 3rd axis." : well in this case, it doesn't matter. In fact, since there is no other referential, this rotation doesn't even exist : you can't move relative to nothing. – Keelhaul May 30 '17 at 17:41

Force between two equal bodies is $\Large F = \frac{G \cdot m^2}{R^2}$

m - mass
G - gravitational constant = 6,6720⋅10^(−11)
R - distance between bodies


1. every 2 bodies have gravitational force between them (doesn't matter how far they are), but as further you go as weaker it gets
2. bigger mass = greater force

but we can't really check if gravity works infinitely.

Calculations:

c = 3 * 10^8 - speed of light
t = 3.1536 * 10^7 - seconds in a year
m = 5.972 * 10^24 - mass of earth
G = 6,6720 * 10^(−11) - gravitational constant
F - force
a - acceleration


F = G * m^2 / (c * t)^2

a = f / m

combining them we get this:

https://www.wolframalpha.com/input/?i=((6.6720*10%5E(%E2%88%9211))*5.972e24+%5E2)%2F((3e8+*+3.1536e7)%5E2))%2F5.972e24


and calculations show we would get the acceleration of 4.45 * 10^-18 (m*s^2) for the planets

Sun is bigger than Earth by 333,000 times and acceleration will be 1.469 × 10^-12 (m*s^2)

to compare: size of a hydrogen atom is 5.3 * 10^-11 (m)

However, as $\text {distance}=\frac{a \cdot t^2}{2}$ it requires less than 1.46 billion years for the planets to meet each other. It is the time in case we assume that the acceleration does not change over time, but is do change over time, so more accurate calculations will have a lesser time interval.

Same for stars will give us less than 2.5 million years.