The area of a circle is $\pi r^2$ if you increase $r$ the area will increase by the square so if this area was of energy and you increase the area it is dispersed you would expect its energy to weaken by the square. Is this the intuition behind gravity weakening be the square of the distance?

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    $\begingroup$ AFAIK, Gravity and electrostatic/dynamic forces that fall off as square of distance have been observed empirically, they have no theoretical reasoning behind them. So, in that sense there is no "explanation" for the behavior. $\endgroup$ – tpb261 Sep 11 '14 at 6:51
  • $\begingroup$ Also see How general relativity gets to an inverse-square law $\endgroup$ – John Rennie Sep 11 '14 at 7:19
  • $\begingroup$ There are plenty of models for non-Newtonian gravity. Except maybe by using Occam's razor, one can not make any theoretical argument for or against any of these models. The only judge is nature, by answering to our experiments. $\endgroup$ – CuriousOne Sep 11 '14 at 7:23
  • $\begingroup$ @tpb261 but to accept that it is just cos' is pathetic. To understand the world around us requires understanding that there is a reason behind they way things work. If theoretical physicists were to accept this ideology of the universe being an orderly one, we would have made far more progress than what we have. To be a great mind requires the pursuit of both knowledge and understanding. It sounds to me you only pursue the former. $\endgroup$ – Ray Kay Sep 13 '14 at 12:58
  • $\begingroup$ We "believe" that the "flux" remains same at different spherical surfaces, and since area of the surface increases the "flux density" which we define as field strength falls of as $\frac{1}{r^2}$. If you're more comfortable with these assumptions, then, be my guest. I can see about 3-4 assumptions in the linked answer, also. Finally, it's observation. We just model field strength as "flux density", giving it the property of being indestructible across spherical surfaces. Why? To explain observations. But, small minds, small thoughts. Be careful of what you speak/say. Not all'll be indifferent. $\endgroup$ – tpb261 Sep 15 '14 at 5:27