The orbital velocity of an artificial sate

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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 of the earth's radius, the orbital velocity is

A

$\frac{3}{2}v$

B

$\sqrt {\frac{3}{2}} \,v$

C

$\sqrt {\frac{2}{3}} \,v$

D

$\frac{2}{3}\,v$

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 of the earth's radius, the orbital velocity is

$v = \sqrt {\frac{{GM}}{{R + h}}} $

For first satellite $h = 0$, ${v_1} = \sqrt {\frac{{GM}}{R}} $

For second satellite $h = \frac{R}{2}$, ${v_2} = \sqrt {\frac{{2GM}}{{3R}}} $

${v_2} = \sqrt {\frac{2}{3}} {v_1} = \sqrt {\frac{2}{3}} v$