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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