The orbital velocity of a planet revolving cl | vedclass

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Question

(B) The orbital velocity $v$ of a satellite revolving at a distance $r$ from the center of the Earth is given by the formula $v = \sqrt{\frac{GM}{r}}$

Vedclass · Accepted Answer

$\sqrt{gR}$

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(B) The orbital velocity $v$ of a satellite revolving at a distance $r$ from the center of the Earth is given by the formula $v = \sqrt{\frac{GM}{r}}$.For a satellite revolving close to the Earth's surface,the orbital radius $r \approx R$,where $R$ is the radius of the Earth.Thus,$v = \sqrt{\frac{GM}{R}}$.We know that the acceleration due to gravity at the Earth's surface is $g = \frac{GM}{R^2}$,which implies $GM = gR^2$.Substituting $GM = gR^2$ into the orbital velocity formula:$v = \sqrt{\frac{gR^2}{R}} = \sqrt{gR}$.

The orbital velocity of a planet revolving close to the Earth's surface is:

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