Legend

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

Gravitation

Even the planets are subject to Newton's laws of motion, and their circular orbits can also be characterized by the equations for uniform circular motion.  However, the force acting here is special; where does this mysterious force of gravity which keeps the planets in their order come from?  There are no obvious or visible pushes or pulls like most forces.  The short answer is Newton's law of universal gravitation.  Which applies no only to planets, but to all objects:

 F = Gm1m2/r2 G = universal constant = 6.67 X 10-11 Nm2/kg2 m1, m2 = masses of particles or objects (kg) r =  distance between their centers (m)

From Newton's second law (F = ma), we know that a body of mass m is proportional to the force.  And the force of gravity acting between two bodies should be inversely proportional to the distance between their centers.  G, here, has the units of Nm2/kg2, and the force is properly in Newtons.   the numerical value of this Universal Gravitational Constant has to be determined experimentally.

The above equation suggest to the following:
Every particle is attracted to every other particle by a force that,
i) is proportional to their masses
ii) is inversely proportional to the square of the distance between them
iii) acts in a straight line between them

 Circular Motion Terrestrial Gravity