NASA Insignia
Menu
Imagine the Universe!

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:

force=G*M1*m2/r^2

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

More Information Return to seeing more information about 1/R2 relationships.

More Information See a light curve for M31 and to try this technique to solve for its velocity.