A geosynchronous Earth satellite is one that remains above the same point on Ear

Question

A geosynchronous Earth satellite is one that remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth's rotation). Such orbits are useful for communication and weather observation. Calculate the radius of such an orbit.

_________m

A geosynchronous Earth satellite is one that remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth's rotation). Such orbits are useful for communication and weather observation. Calculate the radius of such an orbit. Mass of Earth = ME = 5.97 x 1024 kg. _________m

Explanation / Answer

Time period of satellite = Time period of earth = 24 hrs = 24 x 3600 sec

v = 2 x pi x r / T

satellite moves in circle in a radius of r with velocity v.

then , gravitational force = centripetal force

GMm / r^2 = mv^2 / r  

GM / r = v^2

puttting value of v

GM/r = (2 x pi x r / T )^2

6.67 x 10-11 x 5.97 x 10^24 / r   = (2 x pi x r / (24 x 3600) )^2 '

r = 4.22 x 10^7 m

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