Discuss the important features of the law of gravitation

Explanation

1.As the distance between two masses increase, the strength of the force tends to decrease because of inverse dependence on `r^(2)` . Physically it implies that the planet Uranus experiences less gravitational force from the Sun than the Earth since Uranus is at larger distance from the Sun compared to the Earth.
2. The gravitational forces between two particles always constitute an action-reaction pair. It implies that the gravitational force exerted by the Sun on the Earth is always towards the Sun. The reaction-force is exerted by the Earth on the Sun. The direction of this reaction force is towards Earth.
3.The torque experienced by the Earth due to the gravitational force of the Sun is given by`vec(tau) = vec(r) xx vec(F) = vec(r ) xx [- (GM_(S)M_(E))/(r^(2))] =0 `
Since `vec(r ) = r , hat(r) , (hat(r ) xx hat(r )) = 0 `
So `vec(tau) = (dvec(L))/(dt) = 0 ` It implies that angular momentum `vec(L)` is a constant vector.

4. The expression`vec(F) = (GM_(1)M_(2))/(r^(2)) hat(r)` has one inherent assumption that both`M_(1) and M_(2)` are treated as point masses. When you it is said that Earth orbits around the Sun due to Sun.s gravitational force, we assumed Earth and Sun to be point masses.
5. Ponit masses holds even for small distance.
6. There is also another interesting result. Consider a hollow sphere of mass M. If we place another object of mass .m. inside this hollow sphere the force experienced by this mass .m. will be zero.