# Time period of revolution of a satellite around a planet of radius R is T. period of revolution around another planet, whose radius is 3R but having same density is?

1
by tabishabbasi786

2015-05-18T12:49:33+05:30

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Uniform circular motion:

We know that centripetal acceleration for a satellite of mass m  going around around a planet of mass M, in a circular orbit of radius R , with a uniform velocity v :

m v² / R  =  G M m / R²
=>  v = √ [GM/R]  = R ω

=> ω =  √[ GM / R³ ]
=>  T = 2π √[ R³/GM ]
= K √[ R³/M ]    ,  K is a constant

mass =     M = d 4π/3 * R³
=>    R³/M = 3/(4πd)

=>  T  =  K '  √ [ 1/d ]

So the time period of a satellite going around a planet is inversely proportional to the square root of the density of the planet.

Hence, the time period remains same....  as  T.

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