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Two satellites A and B go around the planet P in circular orbit having radius 4R and R. If the speed of the satellite A is 3v. Then find the speed of the

satellite B



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Orbital velocity of a planet of mass M at a distance R from its centre is given by 

v= \sqrt{ \frac{GM}{R} }

For A, radius = 4R, velocity = 3v
for B, radius = R, velocity = ?

  \frac{v_a}{v_b} = \sqrt{ \frac{GM}{R_a} }/\sqrt{ \frac{GM}{R_b} }\\ \\ \frac{v_a}{v_b} =  \sqrt{ \frac{R_b}{R_a} }=  \sqrt{\frac{R}{4R}}=\\ \\ \frac{3v}{v_b} = \frac{1}{2} \\ \\v_b=2 \times 3v=6v

Speed of satellite B is 6v.
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