For a satellite orbiting in an orbit, close to the surface of earth, to escape, what is the percentage increase in the kinetic energy required?

Question

For a satellite orbiting in an orbit, close to the surface of earth, to escape, what is the percentage increase in the kinetic energy required? (A) 41 % (B) 61 % (C) 81 % (D) 98 %

Tardigrade Admin · Accepted Answer

Orbital velocity for close to earth orbits =√g R. Escape velocity required =√2 g R. % Increase required =(ve-v0/v0) × 100 =(√g R(√2-1)/√g R) × 100=41 %

Q. For a satellite orbiting in an orbit, close to the surface of earth, to escape, what is the percentage increase in the kinetic energy required?

$41%$

$61%$

$81%$

$98%$

Orbital velocity for close to earth orbits $= g R$ .
Escape velocity required $= 2 g R$ .
$%$ Increase required $= \frac{v _{e} - v _{0}}{v _{0}} \times 100$
$= \frac{g R ( 2 - 1 )}{g R} \times 100 = 41%$