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)

An artificial satellite revolves around the earth, remaining close to

1.	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)
Answer» Solution :`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)`