A geostationary satellite is taken to a new o | vedclass

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

Question

(C) The orbital time period for a satellite is given by $T = 2 \pi \sqrt{\frac{r^3}{GM_E}}$.From this relation,we can see that $T \propto r^{3/2}$.For

Vedclass · Accepted Answer

$48 \sqrt{2} 	ext{ hrs}$

Vedclass · Answer

(C) The orbital time period for a satellite is given by $T = 2 \pi \sqrt{\frac{r^3}{GM_E}}$.From this relation,we can see that $T \propto r^{3/2}$.For a geostationary satellite,the initial time period is $T_1 = 24 	ext{ hrs}$.Let the initial radius be $r_1$ and the new radius be $r_2 = 2r_1$.Using the proportionality $T \propto r^{3/2}$,we have the ratio:$\frac{T_2}{T_1} = \left( \frac{r_2}{r_1} ight)^{3/2}$.Substituting the given values:$\frac{T_2}{24} = \left( \frac{2r_1}{r_1} ight)^{3/2} = (2)^{3/2} = 2\sqrt{2}$.Therefore,$T_2 = 24 	imes 2\sqrt{2} = 48\sqrt{2} 	ext{ hrs}$.

$A$ geostationary satellite is taken to a new orbit such that its distance from the centre of the earth is doubled. Find the time period of this satellite in the new orbit.

Similar Questions

$A$ planet is moving in a circular orbit. It completes $2$ revolutions in $360$ days. What is its angular frequency?

What is the ratio of the time periods of a satellite $A$ of mass $m$ at a distance $r$ from the center of the Earth and a satellite $B$ of mass $2m$ at a distance $2r$ from the center of the Earth?

At which height can a satellite be in a geostationary orbit? To remain geostationary,obtain the equation for its height from the surface of the Earth.

$A$ small planet is revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force between the planet and the star were proportional to $R^{-5/2}$,then $T$ would be proportional to:

If $r$ denotes the distance between the sun and the earth,then the angular momentum of the earth around the sun is proportional to

Vedclass Test Series

Exam Paper Generator

Online Exam Module