Escape Velocity
“Escape velocity is the minimum speed needed for an object to escape from the gravitational influence of a massive body.” It does not have a fixed direction. Hence, it would be more right to say it as escape speed rather than escape velocity.
Formula for escape velocity from the Earth’ surface
We know that when an object is thrown away from the Earth’s surface then its kinetic energy changes into its gravitational potential energy. And when the complete kinetic energy changes into the gravitational potential energy from that place the object returns back.
Escape velocity = Value of gravitational potential energy
It is clear that escape velocity does not depend upon the mass of the object.
∵ g = 9.8m/s2 and R = 6.4 × 106 m
∴ Escape velocity from the surface of the Earth
Escape velocity for any object at height h from the surface of the Earth at point
Keeping the values g= 9.8 m/s2 and R = 6.4 × 106 m in the above equation;
ve = \(\sqrt{9.8 \times 6.4 \times 10^{6}}\) = 7.92 km/s
In this situation the escape velocity will be equal to the orbital velocity of the satellite revolving close to the Earth.
Relation between Orbital Velocity and Escape Velocity
In the article we will study that the orbital velocity of the satellite revolving close to the Earth is,
v0 = \(\sqrt{g R}\) …………. (1)
Escape velocity of the body at the surface of the Earth
Hence, it is clear that if due to any reason the orbital velocity is done \(\sqrt{2}\) times, the satellite would escape from its orbit.
