Question

What is the relation between escape velocity and orbital velocity?

Answer 1

Escape velocity is the minimum speed needed for an object to "break free" from the gravitational attraction of a massive body. The escape velocity from Earth is about 40,270 km/h (25,020 mph). The velocity of this orbit depends on the distance from the object to the center of the Earth. The velocity has to be just right so that the distance to the center of the Earth is always the same.The orbital velocity formula contains a constant, G, which is called the "universal gravitational constant“.

Orbital velocity is given by, v = ($\sqrt{gR}$)
Escape velocity is given by, V = ($\sqrt{2gR}$)
On finding the ratio,
$\frac{v}{V}$ = $\frac{1}{\sqrt{2}}$
So, V = $\sqrt{2}$ $\times$ v