Discuss the important features of the law of gravitation

Explanation

Important features of gravitational force:
(i) As the distance between two masses increases, the strength of the force tends to decrease because of inverse dependence on `r^2` . Physically it implies that, (ii) Eg: 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.

(iii) 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. (iv) The torque experienced by the Earth due to the gravitational force of the Sum is zero given by
` vectau xx vecr xx vecF = vecr xx (- (GM_s M_E)/(r^2) hat r) = 0`
since `vecr = r hatr , ( hat r xx hat r) = 0`
So, `tau = (dvecL)/(dt) = 0`
It implies that angular momentum L is a constant vector. The angular momentum of the Earth about the Sun is constant throughout the motion. (v) Earth orbits around the Sun due to Suns gravitational force, it is assumed Earth and Sun to be point masses. This assumption is a good approximation because the distance between the two bodies is very much larger than their diameters. (vi) To calculate force of attraction between a hollow sphere of mass M with uniform density and point mass m kept outside the hollow sphere, we can replace the hollow sphere of mass M as equivalent to a point mass M located at the center of the hollow sphere. (vii) If another object of mass 'm' inside this hollow sphere as in figure, the force experienced by this mass ‘m' will be zero.