A satellite which is geostationary in a particular is taken to another orbit Its distance from...

Question:

A satellite which is geostationary in a particular is taken to another orbit Its distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is?

Geostationary Orbits:

If a satellite revolves around the earth with the same speed of earth's rotation, which is about 24 hours a day, it is very useful for communication purposes and is located at about 36,000 km above the earth's surface. This position does not depend on the mass of the satellite.

Answer and Explanation:

According to Kepler's 3rd law, the relationship between the orbital period T and the orbital radius R is expressed as

{eq}T^2\propto R^3 {/eq}

If R increases by 2R, the new orbital period T' is written as

{eq}T'=2^{3/2}T {/eq}

Here, T is 24 hours in the case of a geostationary satellite. So,

{eq}\begin{align} T'&=2^{3/2}T\\ &=2^{3/2}\times 24\\ &=\boxed{67.88\,\rm hours} \end{align} {/eq}


Learn more about this topic:

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Kepler's Three Laws of Planetary Motion

from Basics of Astronomy

Chapter 22 / Lesson 12
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