Universal gravitation and field strength

Newton’s law gives F=r2GMm​ between point masses, or outside spherical masses. Use centre-to-centre separation, not altitude. The pair forces have equal magnitude and opposite directions, although the two accelerations can differ. Doubling one mass doubles the force; doubling separation reduces it to a quarter.

Gravitational field is force per unit test mass: g=mF​=r2GM​, in Nkg−1 or equivalently ms−2. It does not depend on test mass. An altitude h above radius R means r=R+h. Fields add as vectors; between unequal masses, the zero-field point lies nearer the smaller mass.

Watch out: Gravity extends beyond the atmosphere and supplies orbital acceleration; apparent weightlessness is associated with shared free fall.