A satellite orbits at height h from Earth's surface where h ll R (R = Earth's radius). The minimum increase in speed for the satellite to escape Earth's gravitational field is:

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EEJ MAIN Physics QUESTION #7005

Question 1

A satellite orbits at height $h$ from Earth's surface where $h \ll R$ ($R$ = Earth's radius). The minimum increase in speed for the satellite to escape Earth's gravitational field is:

$\sqrt{2gR}$
$\sqrt{gR}$
$\sqrt{\dfrac{gR}{2}}$
$\sqrt{gR}\,(\sqrt{2}-1)$✔️

Correct Answer Explanation

For $h \ll R$, orbital radius $\approx R$:

Orbital speed: $v_o = \sqrt{gR}$

Escape speed from surface (approximately same radius): $v_e = \sqrt{2gR}$

Minimum increase: $\Delta v = v_e - v_o = \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}(\sqrt{2}-1)$

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