How many times is escape velocity (V_e), o

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How many times is escape velocity $({V_e})$, of orbital velocity $({V_0})$ for a satellite revolving near earth

A

$\sqrt 2 \, times$

B

$2\, times$

C

$3\, times$

D

$4\, times$

How many times is escape velocity $({V_e})$, of orbital velocity $({V_0})$ for a satellite revolving near earth

For a spherically symmetric massive body such as a star or planet, the escape velocity for that body, at a given distance is calculated by the formula$:$

$v_{e}=\sqrt{\frac{2 G M}{r}}$

For orbital velocity of a satellite in a circular orbit close to the earth's surface$:-$

$v_{0}=\sqrt{\frac{G m}{R}}$

Hence, $v_{e}=\sqrt{2} v_{0}$