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# What is Escape Velocity?-Definition, And Formula

August 22, 2022

Escape Velocity is the speed at which something escapes Earth’s gravitational pull. In space, escape velocity is the minimum velocity necessary to leave the planet. On Earth, escape velocity is the speed at which a rocket would need to travel to reach orbit.

## What is Escape Velocity?

The minimum speed needed for a free, non-propelled object to escape from the influence of a primary body is called the celestial mechanics, escape velocity, or escape speed. It is often stated as an ideal speed, ignoring atmospheric friction.

Escape speed is more accurately described as a speed than a velocity because it is independent of direction, and it increases with the mass of the primary body and decreases with the distance from the primary body. The escape speed is dependent on how far the object has traveled, and its calculation at a given distance takes into account that without new acceleration, it will slow down as it travels, but it will never stop.

## Escape Velocity Formula

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 a 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 escape velocity.

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

Initial K.E. = 1/2mv2esp

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

increased P.E=0-(-GMm/R)=GMm/R

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 absolute potential energy. then

1/2mv2esp=GMm/R

Vesp=âˆš2GM/R

As g=GM/R2

so Vesp=âˆš2gR

the approximate value of escape velocity is 11km-1.

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