## Another example of a 1/r2 law

### Gravity: Another Example of a 1/r^{2} 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.

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} Nm^{2}/kg^{2}), m_{1} is the
mass of the first object in kilograms, m_{2} 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 × 10^{8}
m from the surface of the earth.

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