Can anyone offer a reason why the force due to gravity decreases as the inverse square of a distance as opposed to some other function. For instance, sound waves propogate in a spherical manor, thus sound intensity decreases as a function of the surface area associated with that sphere. The gravitational field extends in a kind of "infinate sphere" so it seems reasonable that force due to gravity might decrease in a similar fassion but it doesn't. Why?

It does. Gravity goes like [math]\sim \frac{1}{r^2}[/math] and the surface of a sphere goes like [math]\sim r^2[/math]. I don't see your problem.....?

By analogy, think of the intensity of light, which varies inversely with the square of the distance from the source. If you're one meter from the source and a little patch of light hits your eye, the intensity of the light is basically the number of photons in the little patch divided by its area. But if you're two meters from the source, the area of the same little patch is four times as great, because the surface area of a sphere is proportional to the square of the radius. Since the number of photons in the patch is the same, the density of light at two meters is one fourth what it is at one meter.

 

Gravity works the same way - its "intensity" is inversely proportional to the distince from the source.

 

http://home.comcast.net/~paultrow/writing.htm

It does. Gravity goes like [math]\sim \frac{1}{r^2}[/math] and the surface of a sphere goes like [math]\sim r^2[/math']. I don't see your problem.....?

 

Severian! so glad you are around. over in Relativity form we were having trouble intuitively handling the "twin paradox"

Explaining in not-too-mathical terms why it is that the twin who undergoes acceleration comes back feeling younger and more chipper and indeed BEING younger

 

and both the old grey twin and the young twin can agree that that is how it is

 

If you see anything wrong or misleading in what I said over there, I would appreciate it if you would flag the trouble. It is not the kind of thing I ordinarily post about but the problem seemed to be festering and in need of first aid.

 

here's a link in case you have time and are willing to take a look

http://www.scienceforums.net/forums/showthread.php?t=8190

No, light from a "point source" propogates outwards spherically. This means that the function which governs light (and sound) intensity is the is relative to the inverse of the surface area of a sphere with the radius being the distance from the center of the light source. My problem lies in the fact that gravity also propogates outward spherically however it varies relative to the inverse square rule... This just doesn't jive with me. My thought on the matter was that modern physics still doesn't really know what gravity is thus, lacks the tools to explain its effets. FYI, the equation which giverns sound and light intensity is 1/(4*pi*r^2), similar to the inverse square law but off by a factor of 1/(4*pi). So I guess my question is what happened do the (4*pi)^-1 in gravitys case. Perhaps it is covered in the universal grevitational constant (G) ??? I hadn't thought about that untill just now hmm...

4pi is a constant, so it doesn't vary and doesn't matter where it is incorporated in the equation. the variable is r, which varies as an inverse square.