Discuss the important features of the law of gravitation

Explanation

(i) Because of inverse dependence on square of distance the distance between two masses increases, the strength of the force tends to decrease.
(ii) Because Uranus is at larger distance from the Sun compared to the Earth, the planet Uranus experiences less gravitational force from the Sun than the Earth.

(iii) The gravitational forces between two particles always constitute an action-reaction pair. From this, it is known that gravitational force exerted by the Sun on the Earth is always toward the Sun. The reaction-force is exerted by the Earth on the Sun. The direction of reaction is toward Earth.
(iv) The torque experienced by the Earth due to the gravitational force of the Sun is given by,
`vec(tau)=vec(r)xxvec(F)`
`=vec(r)xx(-(GM_(S)M_(E))/(r^2)hat(r))`
`=0`
Since, `vec(r)=rvec(r),(vec(r)xxvec(r))=0`
So, `vec(tau)=(dvec(L))/(dt)=0`
It implies that angular momentum `vec(L)` is a constant vector. The angular momentum of Earth about the Sun is constant throughout the motion. It is true for all the planets.
(v) The expression `vec(F)=(GM_(1)M_(2))/(r^2)hat(r)` Here it was assumed that both Earth and Sun are treated as point massses.
(vi) This assumption is a good approximation because the distance between the two bodies is very much larger than their diameters.
(vii) The force of attraction between a hollow sphere of mass M with uniform density and point mass m kept outside the hollow sphere is calculated by replacing the hollow sphere of mass M as equivalent to a point mass M located at the centre of the hollow sphere. The force of attraction between the hollow sphere of mass M and point mass 'm' can be calculated by considering the hollow sphere also as another point mass. It is shown in the Figure below.
(viii) If we place another object of mass 'm' inside a hollow sphere of mass M as in Figure below, the force experienced by this mass 'm' will be zero.
(a)
(b)
(ix) The success of the law of gravitation is that it concludes that the mango that is falling down and the Moon orbiting the Earth are due to the same gravitational force.