# 7.2.3 Earth’s Gravitational Field

From outer space, the Earth looks round. On Earth, however, the Earth looks flat. Similarly, on a cosmic scale, the Earth’s gravitational field is radial and non-uniform in strength. But on a terrestrial scale, it is vertically downward and uniform in strength.

Modeling the Earth as a uniform sphere of radius  ${{R}_{E}}=6370\text{ km}$ and mass $M=5.97\times {{10}^{{24}}}\text{ kg}$, we can calculate the theoretical value of g on the surface of the Earth to be

$\displaystyle g=\frac{{GM}}{{{{R}_{E}}^{2}}}=\frac{{(6.67\times {{{10}}^{{-11}}})(5.97\times {{{10}}^{{24}}})}}{{{{{(6370\times {{{10}}^{3}})}}^{2}}}}=9.81\text{ N k}{{\text{g}}^{{-1}}}$.

9.81 m s-2 is of course the published value for the acceleration of free fall. This is no coincidence because gravitational field strength is also the gravitational acceleration. An object free-falling on Earth’s surface must thus, in theory, accelerate at $g=9.81\text{ m }{{\text{s}}^{{-2}}}$. In practice, however, 9.81 m s-2 is only the average value of g. The main reasons for g to vary are:

1) Non-uniform density

The Earth is not uniform in composition. An oil field would cause the local g to be lower, but a mineral ore would cause the local g to be higher.