Legend

 ac = centripetal acceleration v = velocity r = radius Fc = centripetal force m = mass Fg = force of gravity G = universal constant

Terrestrial Gravity

 The universal law of gravitation describes the relationship between the motion and earth and the satellites around it. the moon, etc.  But for objects near earth's surface, use Fg = mg.   Though these two equations for gravity look different, they still agree with each other, under the condition that g is the non-spinning, absolute acceleration due to gravity.  This represents the "true" weight of an object due only to its gravitational interaction with the Earth and therefore identical to:Fg = mg = Gm1m2/r2 g = Gmearth/r2 mearth = mass of earth = 5.97 X 1024 kg r = distance from center of earth to object (m) This shows that acceleration due to gravity, g, is not a constant (even though we assumed it was until now), it depends on the distance between the earth and the object.  In the vicinity of the planet, the acceleration due to gravity is the same for all bodies independent of their masses.  By substituting for m2 and r, we can calculate the acceleration due to gravity for any celestial body.
 Gravitation Kepler's Laws