Gravitational Force

Gravity is universal: every mass attracts every other with a force F = GMm/r², along the line joining their centers. Divide that force by the test mass and you get the gravitational field g = GM/r², the acceleration gravity would give. The value you memorized for the ground, about 10 N/kg, is only the field at Earth's surface. Move twice as far from the center and it drops to a quarter. The field even has a story inside a spherically symmetric body: inside a solid sphere of uniform density only the mass closer to the center than you pulls, so the field grows with distance from the center; inside a thin hollow shell it cancels to nothing at all.

Three slips recur here. Treating g as a fixed constant, carrying 10 N/kg into orbit or onto another planet instead of recomputing g = GM/r². Inverting the shell theorem, so the inside rule (a point in a thin shell feels zero net force) trades places with the outside rule (the whole mass acts as if at the center). And mishandling the solid sphere, where only the mass within the radius counts, so the force grows in proportion to r instead of falling off as 1/r². Each is the same mistake in disguise: g = GM/r² is a rule about distance and enclosed mass, not a value to memorize.