# Relation Between Escape Velocity And Orbital Velocity

Escape velocity is the minimum velocity required to overcome the gravitational potential of a massive body and escape to infinity. Orbital velocity is the velocity with which an object revolves around a massive body. The relation between escape velocity and orbital velocity are proportional.

## Relation Escape Velocity And Orbital Velocity Formula

In astrophysics, the relation between escape velocity and orbital velocity can be mathematically written as-

 $V_{o}=\frac{V_{e}}{\sqrt{2}}$ Or $V_{e}=\sqrt{2} V_{o}$

Where,

• Ve is the Escape velocity measure using km/s.
• Vo is the Orbital velocity measures using km/s.

We know that $Escape\;velocity=\sqrt{2}\times Orbital\;velocity$ which implies, the escape velocity is directly proportional to orbital velocity. That means for any massive body-

• If orbital velocity increases, the escape velocity will also increase and vise-versa.
• If orbital velocity decreases, the escape velocity will also decrease and vise-versa.

### Escape Velocity And Orbital Velocity

Deriving the relation between escape velocity and orbital velocity equation is very important to understand the concept. For any, massive body or planet.

• Escape velocity is given by – $V_{e}=\sqrt{2gR}$ ———-(1)
• Orbital velocity is given by – $V_{o}=\sqrt{gR}$ ———–(2)

Where,

g is the acceleration due to gravity.

R is the radius of the planet.

From equation (1) we can write that-

$V_{e}=\sqrt{2}\sqrt{gR}$

Substituting $V_{o}=\sqrt{gR}$ we get-

$V_{e}=\sqrt{2}V_{o}$

The above equation can be rearranged for orbital velocity as-

$V_{o}=\frac{V_{e}}{\sqrt{2}}$

Hope you understood the relation between escape velocity and orbital velocity for any object for any massive body or planet.

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