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Newton's Law of Gravitation

Newton’s law of gravitation states that everybody in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The direction of the force is along the line joining the particles.
Vector form According to Newton’s law of gravitation,
Fig. 1
46767.png = unit vector from A to B
46761.png = unit vector from B to A,
46755.png = gravitational force exerted on body A by body B
46749.png = gravitational force exerted on body B by body A
Here negative sign indicates that the direction of 46743.png is opposite to that of 46737.png.
Similarly, 46731.png
46718.png[∵ 46712.png]
Therefore, it is clear that 46706.png46700.png, which is Newton’s third law of motion.
Here G is the constant of proportionality which is called universal gravitational constant.


Important Points
  • The value of G is 6.67 × 10–11 N-m2 kg2in SI and 6.67 × 10–8 dyne-cm2/g2 in CGS system.
  • Dimensional formula = [M–1L3T –2].
  • The value of G does not depend upon the nature and size of the bodies.
  • It also does not depend upon the nature of the medium between the two bodies.

Properties of gravitational force

  • It is always attractive in nature while electric and magnetic forces can be attractive or repulsive.
  • It is independent of the medium between the particles while electric and magnetic forces depend on the nature of the medium between the particles.
  • It holds good over a wide range of distances. It is found true for interplanetary to inter-atomic distances.
  • It is a central force, i.e., acts along the line joining the centers of two interacting bodies.
  • It is a two-body interaction, i.e., gravitational force between two particles is independent of the presence or absence of other particles; so the principle of superposition is valid, i.e., force on a particle due to a number of particles is the resultant of forces due to individual particles, i.e., 46669.png While nuclear force is many body interaction
  • It is the weakest force in nature, as Fnuclear Felectromagnetic > Fgravitational.
  • The ratio of gravitational force to electrostatic force between two electrons is of the order of 10–43.
  • It is a conservative force, i.e., work done by it is path-independent or work done in moving a particle round a closed path under the action of gravitational force is zero.
  • It is an action reaction pair, i.e., the force with which one body (say Earth) attracts the second body (say moon) is equal to the force with which Moon attracts the Earth. This is in accordance with Newton’s third law of motion.

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