13.3.1—Derive, from Newton’s law of gravitation and the definition of gravitational

Equating gravitational force GMm/r² with weight mg gives g=GM/r² for a point mass or spherical source outside its surface.

The test mass cancels, so g depends on source mass M and centre distance r, not on the mass being tested.

Doubling distance from a planet’s centre quarters g; changing the test object’s mass does not change g.

g is a field strength, not a universal constant; G is constant while g varies with location.