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Two satellites A and B revolve around the planet with radius of R and R/2 respectively.If the orbit velocity of planet B is C,then the orbit velocity of planet A is...C A.0.500 B.0.600 C.0.707 D.0.800 E.0.867

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Jon P. | Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors gradKnowledgeable Math, Science, SAT, ACT tu...
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I assume you meant:  "If the orbit velocity of SATELLITE B is C, then the orbit velocity of SATELLITE A is..."
 
According to Kepler's 3rd law (for circular orbits), the square of the orbital period is proportional to the cube of the radius of the orbit.
 
So the cube of the radius of A's orbit is 8 times the cube of B's radius.  Take the square root of that to get the ratio of the periods.  The square root of 8 is 2√2 = 2.828 (approximately). 
 
So it takes A 2.828 times as long to go around the planet as B.  But A's radius is twice B's, which means that the length of A's orbit is also twice B's.  So it takes A 2.828 times as long to travel 2 times the distance.  That means that A's speed is 2 / 2.828 = .707 times B's speed. 
 
So the answer is C, 0.707.