Newton’s Law of Universal Gravitation states that:

Every particle attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Consider two particles of masses m1 and m2 separated by a distance r. Each will exert a force F on the other, given by

where F : gravitational force between the two particles. m1, m2: masses of the two particles.

r: distance between the two particles.

G: constant of universal gravitation.

m1

m2

F

F

r

m1

m2

F

F

r

Figure 1

The two forces form an action-reaction pair and have the following characteristics, * are equal in magnitude,

* are opposite in direction,

* act on different bodies

* are of the same type (gravitational force).

G is a universal constant called the gravitational constant (or constant of universal gravitation), which has been measured experimentally to be : G = 6.67 x 10-11 N m2 kg-2.

Important points to note about Newton’s Law of Gravitation

1.Newton’s Law of Gravitation is a universal law. It applies everywhere in the universe.

2.Attractive Nature of gravitational force: Note that the particles in this case are always attracted to each other.

3.The gravitational force is a field force that always exists between two point masses regardless of the medium that separates them. In fact, it would still exist if there were no medium between them.

4.Inverse-square law:

Newton’s Law of Gravitation is an example of an inverse-square law i.e. the force is inversely proportional to the square of the separation of the particles.

F

5.Even though the law is stated for point masses, the law could also be applied for the attraction exerted on an external object by a spherical object with radial symmetry, e.g.

(a) sphere of uniform density;

(b) spherical shell of uniform...

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