Reading: Develop the model
Two masses exert forces on one another
Newton's ideal gravitational interaction has magnitude F=Gm₁m₂/r², where r is separation between the masses' centers, G is the universal gravitational constant, and m₁ and m₂ are masses in kilograms. Both bodies experience equal and opposite forces, consistent with Newton's third law. Their resulting accelerations can differ because their masses differ.
Inverse square is not inverse linear
If separation doubles while both masses remain fixed, the gravitational force becomes one quarter as large. If separation triples it becomes one ninth as large. This is because r appears squared in the denominator. The Gravity Field Explorer can compare a starting radius with a larger radius and graph the force and field strength ratios.
Field strength and test mass
For a spherical central body outside its surface, gravitational field magnitude is g(r)=GM/r². A small test mass has force F=mg(r). The field strength is independent of the test mass even though the force it experiences is proportional to test mass. Earth is approximately spherical for this first-pass model; closer to real Earth, geography and shape make the field more complicated.
Center distance is not altitude
For a satellite at altitude h above Earth's surface, radial distance r=R_E+h, not r=h. Surface gravity follows GM/R_E²; at altitude, g(h)=GM/(R_E+h)². The Earth's radius itself is approximately 6371 km. Simply inserting 400 km as r in the inverse-square formula produces an extremely misleading result.