Question

The time period of a earth sattelite in circular orbit orbit is idepedent of

Answer 1

The time period of an earth satellite in circular orbit is independent of ?

the correct answer is at the mass of the sattelite As we learnt in

For a satellite , Centripetal force = Gravitational force

\therefore \; \; mR\omega ^{2}=\frac{GmM_{e}}{R^{2}}\; \; \; \; \; \; where\; R=r_{e}+h

or\; \; \; \omega =\sqrt{\frac{GM_{e}}{R^{3}}}=\sqrt{\frac{GM_{e}}{(r_{e}+h)^{3}}}

\therefore \; \; \; T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{(r_{e}+h)^{3}}{GM_{e}}}

\therefore \; \; T\; is \; independent \; of \; mass\; (m)\; of\; satellite.

mw^2R = \frac{G_{e}m}{R^3} = \sqrt{\frac{Gm_{e}}{\left ( re+h \right )^3}}mw^2R = \frac{G_{e}m}{R^3} where R = R_{r} h

w = \sqrt{\frac{Gm_{e}}{r^3}} = \sqrt{\frac{Gm_{e}}{\left ( re+h \right )^3}}

T = \frac{2_{x}}{w} = 2\times \frac{\sqrt{\left ( r_{e} +h \right )}}{Gm_{e}}

therefore T is independent of mass of Satelite