Is the velocity of escape of a particle at rest on the surface of the earth the same as that of a particle just orbiting the earth? Explain.

The escape velocity of a particle of a particle from the surface of the earth is given by

The escape velocity of a particle of a particle from the surface of the earth is given by

When escape velocity is given to a particle on surface of earth, its total energy is

The escape velocity from the surface of the earth is (where R_(E) is the radius of the earth )

The escape velocity from the surface of the earth is (where R_(E) is the radius of the earth )

A particle is given a velocity (v_(e ))/(sqrt(3)) in a vertically upward direction from the surface of the earth, where v_(e ) is the escape velocity from the surface of the earth. Let the radius of the earth be R. The height of the particle above the surface of the earth at the instant it comes to rest is :

A particle is given a velocity (v_(e ))/(sqrt(3)) in a vertically upward direction from the surface of the earth, where v_(e ) is the escape velocity from the surface of the earth. Let the radius of the earth be R. The height of the particle above the surface of the earth at the instant it comes to rest is :