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 will be
A
32v
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B
√32v
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C
√23v
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D
23v
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Solution
The correct option is C √23v We know that v=√GMR+h where h is the height of the satellite, v is the orbital velocity of satellite, M is mass of Earth and R is radius of Earth.
When the satellite is orbiting just above the surface of the earth (h=0) v=√GMR
When the satellite is orbiting at an altitude of half of the earth’s radius i.e h=h2 ⇒vo=√GMR+R2⇒vo=√23GMR⇒vo=√23v