The weight of an object is the force F on the object due to gravity, where F = mg. State how g (the acceleration due to gravity) varies with respect to the mass mb of the spherical body on which the object lies, and the radius of that body (assume all of the mass is at its center). (See Example 5.)

Data from Example 5

Newton’s universal law of gravitation can be stated as follows: “The force F of gravitation between two objects varies jointly as the masses m₁ and m₂ of the objects, and inversely as the square of the distance r between their centers.” We write this as

where G is the constant of proportionality.

F Gm m2 2 r force varies jointly as masses and inversely as the square of the distance