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jimjam
2007-Mar-26, 05:43 PM
We know that Gravitational force works by an inverse square formula (double distance = 1/4 effect). The visual appearance of an object also follows the same rules. Is this coincidence, or is there a relationship?

NEOWatcher
2007-Mar-26, 05:58 PM
We know that Gravitational force works by an inverse square formula (double distance = 1/4 effect). The visual appearance of an object also follows the same rules. Is this coincidence, or is there a relationship?
The relationship is simple geometry. Draw any cone to represent the affect, and any cross section is a square of it's distance by a constant ratio.

There may be other quantum relationships, but on a realistic scale is irrellevent (or not determined).

trinitree88
2007-Mar-26, 06:05 PM
We know that Gravitational force works by an inverse square formula (double distance = 1/4 effect). The visual appearance of an object also follows the same rules. Is this coincidence, or is there a relationship?

jimjam. There are many things that are inverse square law. Illumination, gravitational force, radiation, sound, exposure to machine gun fire...etc. It actually comes out from the increase in the surface area of nested spheres...assuming the "stuff" is being shot through them at a constant rate. A spherical surface of 2R has 4 times the surface area of one of radius R.
pete

4 pi (2R)2 vs 4 pi (R)2

see:http://www.teacherschoice.com.au/Maths_Library/Area%20and%20SA/area_2.htm

The angle subtended on the sky also follows this relationship. Ernst Mach once commented something to the effect of....that "a Foucault pendulum has a priori no knowledge of the existence of a plane that is (fixed/inertial) with respect to the distant stars, before you release it, yet it always assumes that plane when released. Since it can in no way know of the distant stars time shifted positions, it must therefore be the distant stars that somehow determine the plane the pendulum assumes....

Nereid
2007-Mar-26, 08:24 PM
Of course, this assumes certain things about surface area, spheres, distances, etc.

It works just fine in flat, Euclidean geometry, but could fail if the space you inhabit has a different geometry.

For example, General Relativity is a background-independent theory, which means that the 'shape' of spacetime depends (solely) upon what's 'in' it. Contrast this with the space of Newtonian physics (including gravity): absolute, fixed, flat, ....

NEOWatcher
2007-Mar-26, 08:28 PM
...
It works just fine in flat, Euclidean geometry, but could fail if the space you inhabit has a different geometry.....
My guess would be that works fine in any geometry, but the shape of the sphere changes along with the shape of the space.

Jerry
2007-Mar-27, 05:51 AM
Maxwell observed the similarity between the measured speed of light, and the calculated speed of an electromagnetic field, and concluded light and electromagnetic radiation (ER) are the same. (They are) The equations describing gravity and ER are very similar - gravity basically lacks the terms associated with bipolarity - the ends of magnets and electromagnetic poles. The jury is still out on whether these two fundamental forces are actually the same.

Maksutov
2007-Mar-27, 07:19 AM
Maxwell observed the similarity between the measured speed of light, and the calculated speed of an electromagnetic field, and concluded light and electromagnetic radiation (ER) are the same. (They are) The equations describing gravity and ER are very similar - gravity basically lacks the terms associated with bipolarity - the ends of magnets and electromagnetic poles. The jury is still out on whether these two fundamental forces are actually the same.ER is a force? I thought it was energy with a momentum component. After all, F=MA, i.e., there has to be mass involved. Now if you're talking about electricity, etc., that's different. In other words, the electromagnetic force.

But, on the other hand, one question is if gravity is in fact a force at all, or just a distortion of the continuum caused by the presence of mass. One observing a particle circling down into a funnel wouldn't call the funnel a force. The only thing that qualifies it as a force is that it apparently causes an acceleration.

Meanwhile, re the classic illustrated example, I sure hope there are anti-doughnuts on the other end of that black hole for anti-Homer to enjoy.

Nereid
2007-Mar-27, 12:02 PM
We know that Gravitational force works by an inverse square formula (double distance = 1/4 effect). The visual appearance of an object also follows the same rules. Is this coincidence, or is there a relationship?This interesting page, on distances, may clarify "visual appearance", an ambiguous term (does it refer to luminosity? or angular size? or something else).

This page (http://homepages.wmich.edu/%7Ekorista/cosmology.html), courtesy of BAUT's Spaceman Spiff, is a good source of resources for helping you understand the relationship between General Relativity and cosmology.