Law of Gravitational Attraction

The law of gravitational attraction was proposed by Sir Isaac Newton in order to understand planetary motion around the planets. In this article we shall discuss the statement of the law.

Introduction to Law of Gravitational Attraction

“Everybody in the 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 distance between them”

Mathematically, we can state this as:

                        F = G Mm/r^2

Where F is the magnitude of the attracted force between two bodies of masses M and m, separated by a distance r.

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Law of Gravitational Attraction

For the gravitational force between an extended object (like the earth) and a point mass, is not directly applicable.  Each point marks in the extended object will exert a force on the given point mass and these force will not all be in the same direction. We have to add up these force vectorially  for all the point masses in the extended object to get the total force.  This is easily done using calculus.  For two special cases, a simple law results when you do that:

1. The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is just as if the entire mass of the shell is concentrated at the centre of the shell. Qualitatively can be understood as follows:

Gravitational forces caused by the various regions of the shell have component alone the line joining the point mass to the centre as well as along a direction perpendicular to this line.  The component  perpendicular  to this line cancel out when summing over all regions of the shell leaving only a resultant force along the line joining the point to the centre.

2. The force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it is zero.  Qualitatively, we can again understand this result.  Various regions of the spherical shell attract the point mass it in various directions. These forces cancel each other completely.

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The Law of gravitational Attraction : Summary


The law of gravitation is strictly true for point masses.  If the bodies are far apart, i.e. the distance between them is much greater than their sizes, then to a good approximation one may take r in to be the distance between there centers of mass. The gravitational force is a conservative force.