# Laws of gravity for a universe that only consists of two objects?

So, we know that when two objects of normal matter get away from each other, the gravitational pull they feel from each other, decreases.

I wanted to see how that would work. And in my over-simplistic understanding of physics, there could be two mechanisms that would create that phenomenon.

One is, simply, each body of mass stretches the fabric of space-time in a spherical fashion, relative to its mass, regardless of other bodies. Now, if another body of mass is in the vicinity, it would be pulled towards the first body, and also create the same effect for its own mass, so the first body would feel a pull too. If the second body moves away from the first one, it's moving out of the spherical pull, and its moving its own pull away, so the two bodies feel less gravitational pull.

The other mechanism would be somehow different. I should put it this way:
There is a certain amount of gravitational force in each body of mass. And all of that force gets "spent" on other bodies that have the force of the same type.

If there are only two bodies in the whole universe, their distance wouldn't affect the amount of pull they feel. But when there are other bodies around too (plus all the particles moving around), their distance would affect the gravitational pull that they feel from each other. But only because other "things" in the universe get a bigger "chance" of "catching" the gravitational force of those two bodies. Which means the force of those bodies get spent on other things around them, and less force remains to create pull between the first two bodies.

I don't know which one of those two explanations is closer to the current consensus on the workings of gravity, but to get an answer, I'd just simply ask:

If only two bodies of mass (earth and mars) make up the whole universe, and there is nothing around or between them (no photons or neutrinos or anything, hypothetically), would their distance affect how much pull they feel?

If you need more explanation:
Basic definitions of gravity (like $GmM/r^2$) only consider the mass of the two objects and their distance from each other as the playing factors in how much gravitational pull they feel. Based on those definitions, the answer to the question would be yes, obviously.

But are there other theories that would predict differently? If not, let's just assume that the answer to the question is "No, their distance wouldn't affect how much pull they feel." If so, are there any observations that would contradict this answer?

• Well the first problem is that your guesses are not written mathematically. Commented Jul 21, 2012 at 17:29
• By definition of $GmM/r^2$, the answer is yes. Commented Jul 21, 2012 at 17:31
• That's one definition. But is that the consensus? Are there other theories that describe gravity in other ways? Perhaps the second way that I described?
– Aria
Commented Jul 21, 2012 at 17:53
• Are you trying to develop your own physics for gravity? And trying to do it without using mathematics?? Your descriptions are 1) vague, 2) non-math based, and *3) use the term "gravitational force" and hence it must be defined. Commented Jul 21, 2012 at 18:08
• Your update 1) doesn't remedy anything I said, and 2) this basically asks if we have theories contradicting the Einstein/Newton ones, at least for some hypothetical universe -- but this universe must have some axioms, and you seem to say it's just our universe with only two objects, thus a theory contradicting Newton in the fake universe would also contradict Newton in the real one... There are no such theories (and if one were to exist, it would not be credible) Commented Jul 21, 2012 at 19:04

## 2 Answers

If you have a universe consisting of just Mars and Earth then Newton's law of gravitation would be an essentially perfect description of the system. The GR description of the system would be marginally more accurate, but since the densities and velocities are low GR and Newton's law would predict virtually the same behaviour.

I can't think of any even marginally plausible theory that would predict otherwise. If you scaled up to two neutron stars then you'd need GR to describe the loss of energy due to gravity waves, or to describe a collision, but Newton's law would still be a good long distance approximation.

There is such thing as Mach principle. In an universe with only two bodies the bodies will have the same mass $\frac{m_1 m_2}{m_1+m_2}$ (where $m_1$ and $m_2$ are the masses of the respective bodies in an universe with infinite mass) regardless of their composition.

• This is not reasonable--- Mach's principle can only be formulated properly including horizons, and it doesn't work when you have asymptotically flat backgrounds. You can't just have two bodies--- they will emit gravitational waves, which are some sort of bodies too. What does it mean for the bodies to have the reduced mass if there is no other body with which to measure the mass? If there is such a measuring device, then it will be able to mass the objects separately. Commented Jul 22, 2012 at 7:40