Do you understand that the formula is true only if the Earth is a sphere?

Not true

Please provide any evidence that you have that Newton's Law of Gravitation is true if the Earth is not a sphere. Thanks.

Newtons law of gravitation is a general mathematical description of the gravitational force between two point masses with known masses and with known positions with respect to each other. If you want to calculate the gravitational field of a sphere, you simply add up the gravitational force contributions of all the point masses in the sphere, with respect to some point in space. Get that? I wish I could write maths here, but its not possible...

Lets say you stand on a spherical planet. Each mass element, each particle inside the planet exerts a gravitational force on your body. The total force acting on your body is simply the sum of contributions from all particles inside the planet. Anyway, the same goes for a plane slab, or for a pyramid or a cube or for any shape you prefer. You don't need a sphere, the physics is the same...

A sphere has one nice property though! One can proof that (because of the spherical symmetry of a sphere) the gravitational field of a sphere, outside the sphere, is the same as the gravitational field of a single particle (with an equal mass as that of the sphere) that would be located at the center of the sphere. In this way, the gravitational field of a sphere as a whole is described by the same well known expression for Newtons gravitation of a point mass. This is not true for general shapes...

Still Newtonian gravity works fine for any geometry or shape...

http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation