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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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Circular orbit with uniform motion.

let the satellite with the orbiting radius 4 R  have a mass m1.
   its speed in the orbit = 3 v.

let the satellite with the orbit radius R have a mass m2.
   let its speed = v2.

let the mass of planet = M

The gravitational force of attraction is equal to the centripetal force acting on the satellite making it go around in a circle.

       centripetal force formula is = m V²/r          --- (1)

satellite 1:                 m1 * (3v)² / (4 R) =  G M m1 / (4 R)²        --- (2)
                         v² = G M / (36 R)          --- (3)

satellite 2:                m2 * v2² / R  =  G M m2 / R²        --- (4)
                                 v2² = G M / R          ---(5)
     from (3),    GM /R = 36 v²

     from (5),    v2² = 36 v²
                             v2 = 6 v
2 4 2
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