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» <html><body><p></p>Solution :`<a href="https://interviewquestions.tuteehub.com/tag/implies-1037962" style="font-weight:bold;" target="_blank" title="Click to know more about IMPLIES">IMPLIES</a>` The necessary <a href="https://interviewquestions.tuteehub.com/tag/centripetal-415325" style="font-weight:bold;" target="_blank" title="Click to know more about CENTRIPETAL">CENTRIPETAL</a> force for satellite of mass m revolves around the earth is provided by <a href="https://interviewquestions.tuteehub.com/tag/gravitational-476409" style="font-weight:bold;" target="_blank" title="Click to know more about GRAVITATIONAL">GRAVITATIONAL</a> force. <br/> `:.`Centripetal force = Gravitational force,<br/> Subsituting this in equation (1), <br/> `:. (mv^<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)/R_e =mg ""...(1)` <br/> but `v= R_eomega` <br/> `:. v = R_e (2pi)/T"" [ :. omega =(2pi)/T]`<br/> `:.` Subsituting this in equation (1), <br/> `:. (R_e^2xx4pi^2)/(R_e.T^2)=g` <br/> `:. T^2= <a href="https://interviewquestions.tuteehub.com/tag/4pi-1882352" style="font-weight:bold;" target="_blank" title="Click to know more about 4PI">4PI</a> ^(2) R_e/g "" :. T = 2pi sqrt((R_e)/g)`</body></html>