# Orbital Velocity Formula

Orbital velocity is the velocity at which a body revolves around the other body. Objects that travel in the uniform circular motion around the Earth are called to be in orbit. The velocity of this orbit depends on the distance between the object and the centre of the earth.

This velocity is usually given to the artificial satellites so that it revolves around any particular planet.

The orbital velocity formula is given by,

$$\begin{array}{l}V \ orbit = \sqrt{\frac{GM}{R}}\end{array}$$

It is given by

Where,

G = gravitational constant,

M = mass of the body at centre,

R = radius of the orbit.

Orbital Velocity Formula is applied to calculate the orbital velocity of any planet if mass M and radius R are known.

Orbital Velocity is expressed in meter per second (m/s).

Question 1:

Calculate the orbital velocity of the earth so that the satellite revolves around the earth if the radius of earth R = 6.5 Ã— 106Â m, the mass of earth M = 5.9722Ã—1024Â kg and Gravitational constant G = 6.67408 Ã— 10-11Â m3Â kg-1Â s-2

Solution:

Given:

R = 6.5 Ã— 106Â m

M =Â 5.9722Ã—1024Â kg

G =Â 6.67408 Ã— 10-11Â m3Â kg-1Â s-2

The Orbital velocity formula is given by

Vorbit = âˆšGM / R

Â Â Â Â Â Â Â = âˆš6.67408 Ã— 10-11Â Ã—5.9722Ã—1024Â /Â 6.5 Ã— 106

Â  Â  Â  Â = âˆš36.68 x 1013/ 6.5 x 106

Â Â Â Â  Â  = 7.5 x 109km/s

Example 2:

A satellite launch is made for the study of Jupiter. Determine its velocity so that its orbit around the Jupiter.

Given: Radius of Jupiter R = 70.5 Ã— 106 m,

Â Â Â Â Â  Mass of Jupiter M = 1.5 Ã— 1027Â Kg,

Â Â Â Â Â  Gravitational constant G =Â 6.67408 Ã— 10-11Â m3Â kg-1Â s-2

Solution:

When the given parameters are substituted in the orbital velocity formula, we get

Vorbit = âˆšGM / R

Â Â Â  = âˆš6.67408 Ã— 10-11 Ã— 1.5 Ã— 1027Â Â Â / 70.5Ã—106

Â Â Â  = âˆš10.0095 xÂ 1016Â Â /Â 70.5 x 106

Â Â Â  = âˆš0.141 xÂ 1010

Â  Â  Â = 3.754 x Â 104m/s.