Question

how to calculate the time period of a satellite to complete one revolution around earth's surface?

Answer 1

Answer on Question#37769 - Physics - Astronomy

How to calculate the time period of a satellite to complete one revolution around earth's surface?

Solution

The orbit of satellite is stationary. From hence we get that the gravitational force $\frac{GMm}{r^2}$ is equal to centrifugal force $m\omega^2 r$ . Here $G = 6.67 \cdot 10^{-11} \frac{m^3}{kg \cdot s^2}$ is gravitational constant, $M$ is mass of Earth, $r$ is radius of satellite's orbits, $\omega = \frac{2\pi}{T}$ is angular speed of satellite on orbit, $T$ is period of one revolution around Earth, $m$ is mass of satellite.

$$\frac {G M m}{r ^ {2}} = m \omega^ {2} r$$ $$\frac {G M}{r ^ {2}} = \omega^ {2} r$$ $$\omega = \sqrt {\frac {G M}{r ^ {3}}} \Rightarrow$$ $$T = 2 \pi \sqrt {\frac {r ^ {3}}{G M}}$$

Answer:

$$T = 2 \pi \sqrt {\frac {r ^ {3}}{G M}}$$