Question

A geo-stationary satellite is revolving around the earth. To make it escape from gravitational field of earth, is velocity must be increased

(a) 100%

(b) 41.4%

(c) 50%

(d) 59%

Answer 1

Correct option is (b) 41.4%

\(v_e = \sqrt 2v_o \)

\(=1.414v_o\)

Fractional increase in orbital velocity

\(= \left(\frac{\Delta v}{v}\right)\)

\(=\frac{v_e - v_0}{v_0}\)

\(= \frac{1.414 v_o - v_o}{v_o}\)

\(= 0.414\)

Increase in orbital velocity % = 41.4%