The gravitational potential associated with two objects of mass M and m is V = -
ID: 3188683 • Letter: T
Question
The gravitational potential associated with two objects of mass M and m is V = -G M m/r, where G is the gravitational constant. If one of the objects is at the orgin and the other object is at P(x, y, z), then r^2 = x^2+ y^2 + z^2 is the square of the distance between the objects. The gravitational field at a point is given by F = -(gradient)V, where (gradient)V is the gradient in three dimensions. Show that the force has a magnitude |F| = G M m/r^2. Explain why this relationship is called an inverse square law.*note (gradient) = upside down triangle
Explanation / Answer
Inverse Square Law, General: Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius r is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound or radiation obey the inverse square law. It is a subject of continuing debate with a source such as a skunk on top of a flag pole; will it's smell drop off according to the inverse square law
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