(April 5, 2015 at 11:06 am)robvalue Wrote: What's with the d squared? I remember my A level physics teacher had us guess what power the d would be in the gravitational equation. For some reason I guessed 2. Freaky.
Spherical geometry and flux is the main reason. Masses are a point source of gravity. In physics, we often consider forces as a field (giving a net effect, rather than calculating the effect from each source) the action of which is represented by field lines. Sources are drawn with field lines pointing radially outward. The number of field lines is proportional to the strength of the source. The flux of the source, which is effectively the number of field lines per unit area, must remain constant across any sphere centred at the source and since the surface area of a sphere is proportional to the radius squared, the flux must be inversely proportional to the radius squared.
If more of us valued food and cheer and song above hoarded gold, it would be a merrier world. - J.R.R Tolkien
