# 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.

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}