The orbital speed of an artificial satellite | vedclass

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(C) The orbital speed $v$ of a satellite at a distance $r$ from the center of the Earth is given by $v = \sqrt{\frac{GM}{r}}$.For a satellite very clo

Vedclass · Accepted Answer

$0.5$

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(C) The orbital speed $v$ of a satellite at a distance $r$ from the center of the Earth is given by $v = \sqrt{\frac{GM}{r}}$.For a satellite very close to the surface,the distance from the center is $r_1 = R$,so $V_o = \sqrt{\frac{GM}{R}}$.For a satellite at a height $h = 3R$,the distance from the center is $r_2 = R + h = R + 3R = 4R$.The new orbital speed $v'$ is given by $v' = \sqrt{\frac{GM}{4R}} = \frac{1}{2} \sqrt{\frac{GM}{R}}$.Substituting $V_o$ into the equation,we get $v' = \frac{1}{2} V_o = 0.5\,V_o$.

The orbital speed of an artificial satellite very close to the surface of the Earth is $V_o$. What is the orbital speed of another artificial satellite at a height equal to three times the radius of the Earth (in $,V_o$)?

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