When does the earth act like a point mass?
Treating the earth as a point mass seems to be a rather doubtful idealisation!. But there are two reasons why it is (or may be) legitimate to do so.- As we move further away from the earth it begins to ‘look’ more and more like a ‘dot’ (the photographs of the earth, from a satellite and from the moon, make the point visually!). This suggests (and it is true) that the earth acts like a point mass if it is far enough away. You might like to think what ‘far enough’ means.
- Even if we are close to (standing on!) the earth it
acts like a point mass
to the extent that it is spherical
To show this we have to add up the forces -felt by a ‘test’ mass- due to all the ‘bits (point masses) that make up the earth.
The upward pull of a bit like A cancels the downward bit of a piece like B.
And though C pulls harder than if it were at the centre this is offest by the fact that D pulls less. The net result is the same as if we had a single point mass, at the centre.