Why did Newton assume inverse square dependence on distance in his law of gravitation ?
Answers
Gravitation is the attraction between objects that have mass. Newton's law states: The gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance.
The inverse square law proposed by Newton suggests that the force of gravity acting between any two objects is inversely proportional to the square of the separation distance between the object's centers. Altering the separation distance (r) results in an alteration in the force of gravity acting between the objects.
First a minor correction. Newton initially considered acceleration due to gravity as following the inverses square law. He hypothesized that the acceleration of the Moon into Earth is nothing but a FACTOR of the acceleration of a falling apple unto the Earth. Once he showed that to be true, he extrapolated his theory to include Gravitational Force. He needed this UNSEEN FORCE at a DISTANCE to rationalize why the Moon was falling. If you wish to see by numbers; here are some numbers: the apple is at one Earth radius from the Earth’s center. It accelerates at 9.81 m/s/s. The Moon is at 60.3 Earth radii from the Earth’s center. Then the Moon’s acceleration is: (9.81/(60.3)^2 = 0.0027 m/s/s). Subsequent calculations by Astronomers showed that the Moon is indeed falling into Earth at that rate. To further illustrate my point and give you a satisfactory answer, the diagram below (courtesy of Wikipedia) shows the process of thought of Newton:
He considered the gravitational force (or its resulting acceleration due to gravity) to be an OUTWARD EMANATING field. Indeed, “g” is a MEASURE of the Gravitational Field Strength. He had to envision a 3-D emanation and the geometry of space that he envisioned gave him the evidence that he needed to conclude that gravity was an inverse square proportion as well.
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