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

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$\sqrt{2/3} v$

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(C) The orbital velocity of a satellite at a distance $r$ from the center of the Earth is given by $v = \sqrt{\frac{GM}{r}}$.For a satellite just above the Earth's surface,the orbital radius is $r_1 = R$,so $v = \sqrt{\frac{GM}{R}}$.For a satellite at an altitude $h = R/2$ above the surface,the orbital radius is $r_2 = R + R/2 = \frac{3R}{2}$.The new orbital velocity $v'$ is given by $v' = \sqrt{\frac{GM}{r_2}} = \sqrt{\frac{GM}{3R/2}} = \sqrt{\frac{2GM}{3R}}$.Comparing the two velocities: $\frac{v'}{v} = \frac{\sqrt{\frac{2GM}{3R}}}{\sqrt{\frac{GM}{R}}} = \sqrt{\frac{2}{3}}$.Therefore,$v' = \sqrt{2/3} v$.

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half the earth's radius above the surface,the orbital velocity is:

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