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,

**V**is the_{e}**Escape velocity**measure using**km/s.****V**is the_{o}**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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