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Every particle in this universe attracts every other particle with a force that is proportional to the product of these masses and inversely proportional to the square of the distance between them.

According to Newton,

Force of gravitation, F µ product of masses

directly proportional to 1/square of the separation between them

Thus, F= G(m1m2/r² )

where m₁ and m₂ are the masses of the particles, r is the distance of separation between them and G in Universal Gravitational Constant.

Magnitude (and unit) of G : 6.67 * 10^–11 N m² / kg²

Dimension of G         : M^–1 L³ T².

Characteristics of the Gravitational Force:

(a)   Gravitational force is always attractive and directed along the line joining the particles.

(b)   It is independent of the nature of the medium surrounding the particles.

(c)   It holds good for long distances like inter-planetary distances and also for short distances like inter-atomic distances.

(d)   Interaction means that, both the particles experience forces of equal magnitude in opposite directions. If  F1, F2 are the forces exerted on particle 1 particle 2 and on particle 2 by particle 1 respectively, then F1= -F2. Since the forces F1  and F2  are exerted on different bodies, they are known as action-reaction pair.

(e)   It is a conservation force. Therefore, the work done by the gravitational force on a particle is independent of the path described by the particle. It depends upon the initial and final position of the particle. Therefore no work is done by the gravity if a particle moves in a closed path.

(f)    If a particle 1 is acted by n particles, say, the net force F1  exerted on it must be equal to the vector sum of the forces due to surrounding particles.

Þ F = ΣF

where  F1= force acted on the particle 1, by the i^th particle

Hence, gravitational force between any two particles does not depend upon the presence or absence of other particles (bodies).

Illustrations

1. Three identical particles each of mass mare placed at the vertices of an equilateral triangle of side a. Find the forcer exerted by this system on a particle P of mass m placed at the

(a)            the mid point of a side

(b)            centre of the triangle.

Sol. Using the superposition principle, the net gravitational force on P is

F = FA + FB+FC

(a)   As shown in the figure, when P is at the mid point of a side, FA and FB will be equal in magnitude but opposite in direction. Hence they will cancel each other. So the net force on the particle P will be the force due to the particle placed at C only.

(b)       At the centre of the triangle O, the forces FA, FB, Fc will be in magnitude and will subtend 120º with each other. Hence the resultant force on P at O is

F= FA + FB + FC = 0