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

$A$ man inside an artificial satellite feels weightlessness because the force of attraction due to the Earth is

$A$ planet moving along an elliptical orbit is closest to the sun at a distance $r_1$ and farthest away at a distance of $r_2$. If $v_1$ and $v_2$ are the linear velocities at these points respectively,then the ratio $\frac{v_1}{v_2}$ is

Why does a satellite not have an escape velocity?

At which height from the surface of the Earth does a polar satellite revolve around the Earth?

An earth satellite of mass $m$ revolves in a circular orbit at a height $h$ from the surface of the earth. $R$ is the radius of the earth and $g$ is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module