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An artificial satellite revolves around ...

An artificial satellite revolves around the earth, remaining close to the surface of the earth, Show that its time period is `T = 2pi sqrt(R_e/g)`

Text Solution

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`implies` The necessary centripetal force for satellite of mass m revolves around the earth is provided by gravitational force.
`:.` Centripetal force = Gravitational force,
Subsituting this in equation (1),
`:. (mv^2)/R_e =mg " "...(1)`
but `v= R_eomega`
`:. v = R_e (2pi)/T" " [ :. omega =(2pi)/T]`
`:.` Subsituting this in equation (1),
`:. (R_e^2xx4pi^2)/(R_e.T^2)=g`
`:. T^2= 4pi ^(2) R_e/g " " :. T = 2pi sqrt((R_e)/g)`
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