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Gravitation — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsGravitation3 Marks
Question
Consider earth satellites in circular orbits. A geostationary satellite must be at a height of about 36000km from the earth's surface. Will any satellite moving at this height be a geostationary satellite? Will any satellite moving at this height have a time period of 24 hours?
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Answer

$\text{T}=\Big(\frac{\text{g}\text{R}^2\text{T}^2}{4\pi^2}\Big)^{\frac{1}{3}}-\text{R}$

$\text{T}=\frac{4\pi^2(\text{h}+\text{R})^3}{\text{g}\text{R}^2}$

$=\frac{4\times3.14^2\times(36000+6400)^3\times10^9}{9.8\times(6400\times10^3)^2}$

$=24.097\text{Hr}$

Which implies that it is a geostationary sattelite with time period = 24Hrs.

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