Give expression for inverse square law by using Kepler's law
Answers
Explanation:
The inverse-square law follows from Kepler's laws. Kepler's second law (area is swept out by the position vector at a constant rate) is equivalent to the fact that the angular momentum (per unit mass) is a constant of motion: r2θ = l ≡ const.
Explanation:
Newton's inverse square law states that gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The Newton's inverse square law is deduced from Kepler's 'Third law' of planetary motion. Kepler saw that planets move around in an elliptical orbit.
Centripetal force on planet is calculated as :
F = rmv2 = rm(T2πR)2 = rT24π2mr2
F = r24π2mT2r3
But from Kepler's law, T2r3 is constant for planets
Therefore F = r24π2m i.e K = r2G
From this the square inverse nature of gravitational force was derived by Newton.