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ORBITS AND ORBITAL VELOCITY
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. |