Question

Explain mathematically how did newton guess the inverse square rule

Answer 1

The inverse-square law, in physics, is any physical law stating that a specified physical quantity or intensity is inversely proportionalto the square of the distance from the source of that physical quantity. The fundamental cause for this can be understood as geometric dilution corresponding to point-source radiation into three-dimensional space (see diagram).

Radar energy expands during both the signal transmission and also on the reflected return, so the inverse square for both paths means that the radar will receive energy according to the inverse fourth power of the range.

In order to prevent dilution of energy while propagating a signal, certain methods can be used such as a waveguide, which acts like a canal does for water, or how a gun barrel restricts hot gas expansion to one dimensionin order to prevent loss of energy transfer to a bullet.