Orbital Velocity Formula

Orbital Velocity Formula

Orbital velocity is the velocity at which a body revolves around the other body. Objects that travel in 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 center 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,

Vorbit = √GM / R

$Vorbit\,&space;=\,&space;\sqrt{\frac{GM}{R}}$

It is given by

Where,

G = gravitational constant,

M = mass of the body at center,

Orbital Velocity Formula is applied to calculate the orbital velocity of the 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 earth so that the satellite revolves round the earth if radius of earth R = 6.5 × 106 m, mass of earth M = 5.5 × 1024 kg and Gravitational constant G = 6.67 × 10-11 m3/s2 kg.

Solution:

Given:

R = 6.5 × 106 m

M = 5.5 × 1024 kg

G = 6.6 × 10-11 m3/s2 kg

The Orbital velocity formula is given by

Vorbit = GM / R

= 6.67 ×10−11 × 5.5×1024 / 6.5 ×106

= 36.68 x 1013 / 6.5 x 106

= 7.5 km/s

Example 2:

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

Given: Radius of Jupiter R = 70.5 × 106 m,

Mass of jupiter M = 1.5 × 1027 Kg,

Gravitational constant G = 6.67 × 10-11 m3/s2 kg

Solution:

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

Vorbit = GM / R

= 6.673×10−11×1.5×1027 / 70.5×106

= 10.0095 x 1016 / 70.5 x 106

= 0.141 x 1010

3.754 x 109 m/s.

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