Question

what is the formula for time period of satellite

Answer 1

Time Period = $\frac {Circumference\ of\ the\ orbit}{Orbital\ Velocity}$

Explanation:

• Time Period can be defined as the time taken by satellite to go once around the earth.

Therefore, T = $\frac {Circumference\ of\ the\ orbit}{Orbital\ Velocity}$

⇒ T = $\frac{2\pi r}{v}$ =${2\pi r}\sqrt\frac{r}{GM}$ (As r = R + H)

⇒T = $2\pi \sqrt \frac{r^3}{GM}$ = $2\pi \sqrt \frac{r^3}{gR^2}$

(As GM = $gR^2$)

⇒$2\pi \sqrt \frac{(R + h)^3}{gR^2}$ = $2\pi \sqrt \frac{R}{g}\times(1 + \frac{h}{R})^\frac{3}{2}$ (As r = R + h)