What is the time period of a satellite orbiti | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The time period $T$ of a satellite at a height $h$ above the Earth's surface is given by the formula:$T = 2\pi \sqrt {\frac{{(R + h)^3}}{{GM}}}$Gi

Vedclass · Accepted Answer

$4\sqrt 2 \pi \sqrt {\frac{R}{g}} $

Vedclass · Answer

(B) The time period $T$ of a satellite at a height $h$ above the Earth's surface is given by the formula:$T = 2\pi \sqrt {\frac{{(R + h)^3}}{{GM}}}$Given that the height $h = R$,we substitute this into the equation:$T = 2\pi \sqrt {\frac{{(R + R)^3}}{{GM}}}$Since the acceleration due to gravity at the surface is $g = \frac{GM}{R^2}$,we can write $GM = gR^2$:$T = 2\pi \sqrt {\frac{{(2R)^3}}{{gR^2}}}$$T = 2\pi \sqrt {\frac{{8R^3}}{{gR^2}}}$$T = 2\pi \sqrt {\frac{{8R}}{g}}$$T = 2\pi \cdot 2\sqrt{2} \sqrt {\frac{R}{g}}$$T = 4\sqrt{2} \pi \sqrt {\frac{R}{g}}$

What is the time period of a satellite orbiting at a height $R$ above the Earth's surface?

Similar Questions

What are the directions of rotation of a polar satellite and the Earth?

The orbital period of a geostationary satellite is (in $\,h$)

An artificial satellite is placed into a circular orbit around the Earth at such a height that it always remains above a definite place on the surface of the Earth. Its height from the surface of the Earth is ........... $km$.

$A$ satellite is orbiting just above the surface of a planet of density $\rho$ with a periodic time $T$. The quantity $T^2 \rho$ is equal to ($G=$ universal gravitational constant).

Vedclass Test Series

Exam Paper Generator

Online Exam Module