This question will show you why gravitational force is an inverse-square law.
After analysing a large amount of observational data made by Tycho Brahe in the late 16th century, Johannes Kepler published his third law of planetary orbits, ten years after his first two laws, in 1619. Isaac Newton proposed his law of gravitation 68 years later in 1687.
(1) State Kepler's third law.
(2) For a planet orbiting the Sun in a circular orbit at a speed v , and at an orbital radius R , state the centripetal acceleration of the planet.
(3) State the speed, v , of the planet in terms of its orbital radius, R , and its period of orbit, T .
(4) Hence, show that the acceleration of the planet can be expressed as
a=T24π2R3×R21.
(5) Now, using Kepler's third law, show that the gravitational force responsible for the planet's acceleration must be an inverse square relationship with the planet's orbital radius.