Question

A satellite is revolving in a circular orbit at a height ' $h$ ' from the earth's surface (radius of earth $R;h<<R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to: (Neglect the effect of atmosphere.)

• A. $\sqrt{\frac{gR}{2}}$
• B. $\sqrt{gR}(\sqrt{2}-1)$
• C. $\sqrt{2gR}$
• D. $\sqrt{gR}$

Answer 1

The correct option is B $\sqrt{gR}(\sqrt{2}-1)$

Formula used:
$v_0=\sqrt{Rg},v_e=\sqrt{2Rg}$

Orbital velocity of a satellite revolving in a circular orbit at a height $(h<<R)$,

$v_0=\sqrt{Rg}$

and the velocity required to escape is

$v_e=\sqrt{2Rg}$

So, increase in velocity,
$\Delta v=v_e-v_0$
$=(\sqrt{2}-1)\sqrt{Rg}$

Final Answer: Option(d)