Question

what is the orbital velocity for close to earth orbits?

what is the %increase in velocity required for such a settalite to escape?

Answer 1

Let mass of the satellite be m

R = radius of earth

M = mass of earth

For close earth satellite

mv²/R= GMm/R²

=> mv²= GMm/R

=> v²= GM/R

=> v = √(GM/R)

Thus orbital velocity = √(GM/R)

Now to move it away to infinity it must be given the escape velocity v_c

v_c = √(2GM/R)

Thus the velocity needs to be increased will be

v-v_c = √(2GM/R) - √(GM/R)

=> ∆v = (√2-1) √(GM/R)

=>∆v/v = 1.414 – 1 = 0.414

=> ∆v/v×100 = 41.4%

Thus velocity of the satellite must be increased by 41.4%