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motion: TOC for Knowledge Concepts, Exercises, and Solutions

Newton's insight that an orbit is an eternal free fall has the following important 
consequence: since an object is weightless during free fall, an object in orbit is 
weightless - it feels a zero gravitational force.

Mathematically, this means that the centripetal acceleration of the orbital motion 
is equal to the gravitational acceleration the orbiting body would ordinarily 
feel. In equations:

 a = GM/r2 = v2/r     Cancelling like terms in these ratios gives

     GM/r = v2        Taking the square root gives the equation

    v = sqrt(GM/r)   This is the expression for orbital velocity - the speed 
                     at which an orbiting object is always moving.

The escape velocity is a multiplicative factor greater than the orbital velocity:

    v = sqrt(2GM/r)   (escape velocity = sqrt(2) * orbital velocity)

If an object achieves escape velocity, it leaves its orbit and
is no longer gravitationally bound to the object it was orbiting.