# Why is Gravitational force proportional to the masses?.

We know that two mass particles attract each other with a force

$$F~=~\frac{G M_1 M_2}{r^2}.$$

But what is the reason behind that? Why does this happen?

• Is there a particular part of the equation that you are asking about, like are you asking where say G comes from? Or why all mass attracts? – DJBunk Jul 24 '12 at 20:35
• I am not asking about the equation.I am asking why all mass attracts. – orange Jul 24 '12 at 20:46
• If you have a physics background Zee in 'QFT in a Nutshell' gives a rough explanation of this in chapter I.5. And Peskin mentions this on pg 126. Otherwise I don't know of a good heuristic explanation for this. – DJBunk Jul 24 '12 at 20:58

One could explain "well, gravity is the curvature of spacetime due to the mass-energy". But that would only lead to "well, why does mass-energy curve spacetime?" And, should someone produce a proposed answer to that, the follow-up question would have to be "but why is that so?" etc.

At some point though, one must accept that there are genuine fundamentals, genuine primaries that cannot be explained in terms of something "more" fundamental, "more" primary.

Gravity is considered one of those fundamentals. But the question "what is the reason for gravity" presumes that gravity isn't fundamental. So, the only proper "answer" to your question is "to the best of our knowledge, gravity is fundamental".

• I wonder if you would like to have a crack at this question – Floris Apr 2 '15 at 13:53

The masses in that equation play two different roles. Depending on which object you are interested in, one is a mass producing the field, and one is a mass experiencing the gravitational field.

The acceleration of an object due to a force is the force divided by the inertial mass of the object. Take that force and divide by M1. Then you get the acceleration of M1. You get the effect of the gravity of M2 on M1. In this case M2 is the active gravitational mass. It's responsible for the force acting on M1. Anlayzing the motion of M2 results in the same analysis, only then M1 is the active mass and M2 is the passive, or inertial mass.

Now gravity isn't a force, it's a pseudo force due to the curvature of space time. Like any pseudo-force, its proportional to the inertial mass of what it acts upon. The Equivalence Principle is helpful here. The curvature of space time is due to the presence of mass-energy, on small scales roughly proportion to the active gravitational mass.

So why do masses effect each other that way?

M1 produces a space-time curvature proportional to M1. M2 experiences that pseudo-force in proportion to its inertial mass. By the same analysis a symmetric effect produces the change in motion of M1.

As to why mass-energy causes space-time to curve, I'm not sure. I think we'd need a quantum theory of gravity for that.