Gravity Near the Earth's Surface

Recall Newton's formula for Universal Gravitation for finding the force of attraction between two masses:

Near the surface of the Earth, m1 is the mass of the Earth (mE), m2 is the mass of an object (mo), and r is the adius of the Earth (rE). From the force diagram below, for an object on the Earth's surface, we can set this force equal to the weight of the object, or mog, where g is the acceleration due to gravity: 9.8 m/s2.  Thus, from Newton's formula above,

Henry Cavendish used an apparatus to determine the value of G. His experiment used two masses suspended from a thin thread and he measured the movement of the thread when a large mass was brought near those two masses. (Click here for more information on Cavendish's experiment.) From this, the value of G could be determined as

6.67 x 10-11 N.m2/kg2

He also found that by knowing this number and placing it back into Newton's formula, he could determine the
mass of the Earth. Thus Cavendish is known as "the man who weighed the Earth."

The value of g can be different at various locations due to localized densities in the Earth as well as the fact that the Earth is not a perfect sphere. Devices called Gravimeters can measure anomalies to 1 part in 109. Actual anomalies vary from 1 part in 106 to 1 part in 107. Nothing you or I would notice.

To learn more about Newton's Law of Universal Gravitation, click on