# All matter has a mass but does all matter have a gravitational pull?

I know that all planets and stars have a gravitational pull but does a simple much smaller object have a gravitational pull for example a pebble?

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All matter has a mass but does all matter have a gravitational pull?

Yes. One way to see this is that we observe all mattet to have the same acceleration in a given gravitational field, which means that the gravitational force acting on an object is strictly proportional to the object's inertia as measured by its mass. By Newton's third law, this force is also equal in strength to the force made by the object.

It's not even restricted to matter. Relativity says that energy is equivalent to mass, so for example a ray of light makes a gravitational field. (It's not actually the mass-energy but the stress-energy tensor that's relevant. The mass-energy is one part of the stress-energy tensor.)

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Every matter and field we know has a stress-energy tensor which acts as a source for the gravitational field via Einstein's field equations. The gravitational field is described in terms of the curvature of space-time. Everything that moves in it "feels" it. Taken together this means everything interacts gravitationally with everything else.

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Yes, even a neutrino has a gravitational force, although it's so small that no experiment is likely to measure it in the foreseeable future.

The potential $V$ at a distance $x$ from a point mass of mass $m$ is:

$$V = - \frac {Gm}{x}$$

where G is the gravitational constant (this is the non-relativistic expression, which is valid under most circumstances). The mass $m$ can have any value. As long as $m$ is greater than zero there will be a finite potential.

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I would add that even photons are sources of gravitation. Indeed, in the early universe that would have dominated over baryonic matter. In addition, most of the mass in nucleons are due to the energy in the colour field, as the bare masses of quarks are extremely small (a few MeV). – genneth Mar 27 '12 at 10:02
Yes, but I don't know how to write the gravitational potential for a photon ;-) – John Rennie Mar 27 '12 at 11:19

## protected by Qmechanic♦Sep 7 '13 at 21:56

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