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{ (GM)/(R) }` ---(i)

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

Divide (i) and (ii)


`(V_(o) )/(V_(escape) ) = (1)/( √(2) )`




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