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I've stumbled upon an answer to a question about square power in Newton's law of gravity. After reading it I got a question whether the flux of gravitational field has actually any physical meaning.

Fluxes I know arise in a context of balance equations. The change of a certain physical quantity $a$ is comprised of change due to a flux $\boldsymbol j_a$ and due to a source $\sigma_a$:

$$\frac{\partial a}{\partial t} + \operatorname{div} \boldsymbol j_a = \sigma_a $$

But as for me the flux of gravitational field is actually nothing but a gravity field itself:

$$j_g = \mu(\boldsymbol g)$$

$\mu$ being the volume form. It doesn't bear the meaning of a flux propagating the gravity field $\boldsymbol g$ or anything else.

The question is specifically about gravity, and about classical gravity. Not about electromagnetic phenomena, general relativity or quantum gravity.

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The "flux" in this case just refers to the surface integral of the vector field. It has nothing really to do with flux in the sense of electromagnetic radiation. Have a look at this link. The math is clearly explained there. –  Kitchi Dec 21 '12 at 10:10
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up vote 1 down vote accepted

The word "flux" is something of an accident of history. See for example it's use in Gauss' law or as a magnetic flux. Nothing is actually flowing e.g. for a static charge we would still refer to the flux through a surface surrounding the charge even though the system is time independant.

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so no physical meaning? –  Yrogirg Dec 21 '12 at 10:34
    
Yes, it has a physical meaning. It's the integrated field strength over the surface. –  John Rennie Dec 21 '12 at 10:38
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