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Another example of a 1/r2 law

Gravity: Another Example of a 1/r2 Law

There are numerous examples in physics where the relationship between one physical variable and another physical variable follows an inverse square relationship. The force of gravitational attraction between two masses behaves in accordance with this relationship.

cartoon of two masses being gravitationally attracted

Two masses at a given distance place equal and opposite forces of attraction on one another. The magnitude of this force of attraction is given by:


where G is the universal gravitation constant (6.67 × 10-11 Nm2/kg2), m1 is the mass of the first object in kilograms, m2 is the mass of the second object in kilograms, and r is the distance between the centers of the two masses, in meters.

From this law and the relationship it embodies it can be seen that a doubling of the separation will cause the force of attraction between the masses to decrease to a value equal to 1/4 of the original force. A tripling of the original distance will result in a force which is 1/9 the original force, and so forth and so on. The graph below represents the force of gravitational attraction on a 70 kg person as she move from the surface of the earth towards a distance of 3 × 108 m from the surface of the earth.

Graph of Gravitational Force vs. Distance

Graph of the force of gravity as a function of distance from mass


A service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA/GSFC

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