A satellite can be in a geostationary orbit a | vedclass

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

Question

(C) For a geostationary orbit,the angular velocity of the satellite must be equal to the angular velocity of the planet,$\omega_s = \omega_p$.From Kep

Vedclass · Accepted Answer

$r/(4^{1/3})$

Vedclass · Answer

(C) For a geostationary orbit,the angular velocity of the satellite must be equal to the angular velocity of the planet,$\omega_s = \omega_p$.From Kepler's third law,the orbital radius $r$ and angular velocity $\omega$ are related by $G M = \omega^2 r^3$,which implies $r^3 \propto \omega^{-2}$ or $r \propto \omega^{-2/3}$.Let the initial angular velocity be $\omega$ and the new angular velocity be $\omega' = 2\omega$.Let the initial radius be $r$ and the new radius be $r'$.Then,$\frac{r'}{r} = \left( \frac{\omega'}{\omega} \right)^{-2/3} = (2)^{-2/3} = \frac{1}{(2^2)^{1/3}} = \frac{1}{4^{1/3}}$.Therefore,$r' = \frac{r}{4^{1/3}}$.

$A$ satellite can be in a geostationary orbit around a planet at a distance $r$ from the centre of the planet. If the angular velocity of the planet about its axis doubles,a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

Similar Questions

$A$ geostationary satellite is revolving around the Earth. If the radius of the Earth is $R$ and the angular speed of the Earth about its own axis is $\omega$,then the radius of the orbit of the geostationary satellite is ($g =$ acceleration due to gravity).

Two stars of masses $M$ and $2M$ are at a distance $d$ apart and are revolving around their common center of mass. The angular velocity of the system of the two stars is ($G$ is the universal gravitational constant).

Which one of the following statements regarding an artificial satellite of the earth is incorrect?

$A$ satellite revolves around the earth in an elliptical orbit. Its speed

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

Vedclass Test Series

Exam Paper Generator

Online Exam Module