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a geo stationary satellite is orbiting the earth ata height of 6R above the surface of the earth,R being the radius of the earth.The time period of another satellite at a height of 2.5R above the surface of earth is.???

a geo stationary satellite is orbiting the earth ata height of 6R above the surface of the earth,R being the radius of the earth.The time period of another satellite at a height of 2.5R above the surface of earth is.???

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1 Answers

Vasantha Kumari
askIITians Faculty 38 Points
10 years ago
Here, the time period of satellite that orbits the earth is
T2 = 4 (pi)2r3 / GM2
where M is the earths mass. Hence, the ratio of time periods of the two satellites.
T1/T2 = (r1 / r2)3/2 or
T2=T1(r2/ r1)3/2 ...(1)
In the case of geostationary satellite T1 = 1 day which is equal to 24 hrs.
r1 = 6R + R = 7R
For the second satellite r2=2.5R + R = 3.5 R
substituting in eqn (1)
T2= 24(3.5R/ 7R)3/2 = 6v2
The time period of the other satellite is 6v2.

Thanks & Regards,

Vasantha Sivaraj,

askIITians faculty

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