The ratio of kinetic energy of a body orbiting near the earth's surface and the kinetic energy of the same body escaping then what is earth's gravitational field
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For any orbit we must have the centripetal force equal to the gravitational force. So this gives:
2=2
where in this case is Earth’s mass, the satellite mass, the satellite speed, and the satellite distance from the Earth’s centre. Hence the kinetic energy of the satellite is:
=122=22=22=2
Now the kinetic energy needed to escape gravity is that needed to cancel the satellite’s gravitational potential energy with respect to Earth which is;
=−
Hence we can see that the satellite requires a kinetic energy of 2, ie: twice its existing orbital kinetic energy
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