Question

The moon will escape the Earth for ever, if the minimum increase in its velocity is

• A. 200 %
• B. 41.4 %
• C. 50 %
• D. 100 %

Answer 1

The correct option is B 41.4 %

Suppose the distance between moon and earth is r.
Its current orbital velocity, therefore is $V_o=\sqrt{\frac{G{M}_e}{r}}$; and the velocity it requires to escape from this distance is $V_e=\sqrt{\frac{2G{M}_e}{r}}$,
This implies $V_e=\sqrt{2}{V}_o$.
therefore to escape the percentage increase in velocity will be:
$\frac{V_e-V_o}{V_o}\times 100=\frac{\sqrt{2}-1}{1}\times 100=41.4\%$