Calculating a planet's mass & gravitational pull

[Ack]

Hmm... I've often wondered about the error associated with using point source gravitational equations. Too lazy to look it up, so maybe someone here knows.

The equations posted here all assume that gravity comes from a point source at the core of a planet. This is fine when you are many, many planet diameters away from a planet. But when you get within some distance, the gravitation effects should be distributed across the planet's height, width, and thickness. The gravitational force that a body feels when within this distance is the vectored sum of all these components. Additionally, each layer of a planet has a different density and therefore differing gravitational contributions.

A second option is that during planet formation, the denser elements settle more towards the planet core. In effect, the bulk of the planet's mass resides in the core. This would make the point source error very small until you've pierced the surface and moved very close to the planet's core.