Question

Derivation of escape velocity and orbital velocity

Answer 1

When an object is thrown vertically upwards, it reaches a certain height and comes back to the earth. But when it is given greater initial velocity, it reaches greater height before coming back.

An object can be thrown up with a certain minimum initial velocity so that, the object goes beyond the earth's gravitational field and escape from earth, this velocity is known as escape velocity of the earth. So, escape velocity is defined as the minimum initial velocity that will take a body away above the surface of a planet when it's projected vertically upwards.

On throwing the object upwards, work has to be done against the gravity. If a certain minimum velocity is given to an object, such that the work done against gravity from the planet's surface to infinity(outside gravitational field of planet) is equal to the kinetic energy of the object, then it will not return back to the planet.

Answer 2

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• 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.