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  • A satellite is seen after each 8 hours over equator at a place on the earth when its sense of rotation is opposite to the earth. The time interval after which it can be seen at the same place when

A satellite is seen after each 8 hours over equator at a place on the earth when its sense of rotation is opposite to the earth. The time interval after which it can be seen at the same place when the sense of rotation of earth & satellite is same will be :

Option: 1

8 hours


Option: 2

12 hours


Option: 3

24 hours


Option: 4

6 hours


Answers (1)

best_answer

 

Time period of Rotation of earth -

T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{R}{g}}

R\rightarrow Radius of earth

T\rightarrow Time period of  rotation of earth
 

- wherein

R=6400\times 10^{3}m

g=10\: m/s^{2}

T=1.40\; hr

\omega =\frac{1}{800}\frac{rad}{sec}

 

 

Given 8=\frac{2\pi}{\omega _{1}+\omega _{2}}=\frac{2\pi}{\frac{2\pi}{T_{1}}+\frac{2\pi}{T_{2}}}

T1 = 24 hours for earth.

            (\omega _{1}+\omega _{2} is the relative angular velocity for opposite direction)

\Rightarrow  T2 = 12 hours (T2 being the time period of satellite, it will remain same as the distance from the centre of the earth remains constant).

\Rightarrow 8=\frac{2\pi}{\omega _{1}-\omega _{2}}=\frac{2\pi}{\frac{2\pi}{T_{2}}-\frac{2\pi}{T_{1}}}=24 \; hours..(\omega _{1}-\omega _{2} is the relative angular velocity for same direction)

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Rishi

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