InterviewSolution
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InterviewSolution
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The orbital velocity of a satellite is given by the expression V = sqrt((GM)/(R + h)), here M is the mass of the Earth, R is the radius of the Earth and 'h' is the height of the satellite from the surface of the Earth. Explain the reasons why the geostationary satellite is not possible to set in orbit around the Earth at two different heights from the surface of the Earth. |
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Answer» Solution :Can there be two GEOSTATIONARY orbits? - No - The time period of geostationary satellite is 24 hrs (or) 86400 seconds. We know, `T = 2 pi sqrt((1)/(g))` where 1 = (R + h) (or) (Radius of the EARTH + height of geostationary ORBIT from the SURFACE of the Earth) g = acceleration due to gravity at the geostationary orbit. But, `g = (GM)/((R + h)^(2))` `T = 2pi sqrt(((R + h)/(GM))/((R + h)^(2)))=2pi sqrt((R + h)^(3)/(GM))` Here, G, M, R are constants `rArr T alpha (R + h)^(3//2)` So, for only one value of 'h', 'T' will be equal to 24 hours. We can have only one geostationary orbit. |
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