Question

what is the ratio of orbital velocity to escape velocity

Answer 1

Orbital velocity is the velocity of celestial body/satellite revolving around another celestial body in circular orbit. 
V$_{o}$ = $\sqrt{ \frac{GM}{R} }$ ---(i)

Escape velocity is the minimum initial velocity a body should be given to escape it from gravitational field.
V$_{escape}$ = $\sqrt{ \frac{2GM}{R} }$ ---- (ii)

Divide (i) and (ii)

$\frac{V_{o} }{V_{escape} } = \frac{1}{ \sqrt{2} }$




R = radius of circular orbit, M = mass of the celestial body about which satellite/body is performing circular motion. G = Universal gravitational constant