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Relation between escape velocity and orbital velocity formula

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What is  Escape velocity?

“The velocity required by a body to escape from the earth’s gravitational field.”It is our daily life experience that an object projected upward comes back to the ground after rising to a certain height. This is due to the force of gravity acting downward. With increased initial velocity, the object rises to the greater height before coming back. If we go on increasing the initial velocity of the object,a stage comes when it will not return to the ground. It will escape out of the influence of gravity. The initial velocity of an object with which it goes out of the earth’s gravitational field is known as E.V.

Escape velocity formula

The E.V corresponds to the initial kinetic energy gained by the body,which carries it to an infinite distance from the surface of earth.formula of escape velocity

We know that the work done in lifting a body from earth’s surface to an infinite distance is equal to the increase in its potential energy:

FORMULA OF P.E

Where M and R are the mass and radius of the earth respectively.The body will escape out of the gravitational field if the initial kinetic energy of the body is equal to the increase in potential energy of the body in lifting it up to infinity.Then

value of escape velocity

Orbital velocity

When the object in the earths orbit ,its motion is known as orbital motion.The velocity by which the object moves in the earth’s orbit is called orbital velocity.It remains constant in the gravitational field.

The earth and some other planets revolve around the sun in closely circular paths.The artificial satellites launched by men also adopt nearly circular course around the earth.This type of motion is called orbital motion.Formula of this velocity is given as:

Consider a satellite going round the earth in circular path.The mass of the satellite is m and vº is the orbital speed.The mass of the Earth is M and rº represents the radius of orbit.A centripetal force is required to hold satellite in orbit which is given as:

 

orbital velocity formula

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