Question

a satellite is orbiting the earth with speed v₀.To make the satellite escape,what should be the minimum % increase in its velocity?

Answer 1

we know that

orbital velocity

v_o= √(g.r)

escape velocity

v_e = √(2g.r)

thus, the increase in velocity would be

dv = v_e - v_o = √(2g.r) - √(g.r)

or

dv = (√2 - √1).√(g.r)

so,

dv = 0.414√(g.r)

now,

the percentage increse would be

% dv = [(v_e - v_o) / v_o ] x 100

= (dv / v_o) x 100

or

= [0.414√(g.r) / √(g.r)] x 100

so, we get

% dv = 0.414 x 100 = 41.4%