A satellite is to be placed in equatorial geostationary orbit around earth for communication.
(a) Calculate height of such a satellite.
(b) Find out the minimum number of satellites that are needed to cover entire earth so that at least one satellites is visible from any point on the equator.
`[M = 6 xx 10^(24) kg, R = 6400 km, T = 24 h, G = 6.67 xx 10^(-11) SI units]`

Explanation

Here, `G = 6.67 xx 10^(-11) SI` units, `M = 6 xx 10^(24) kg`,
`R = 6400 km = 6.4 xx 10^(6)m, T = 24 h = 24 xx 60 xx 60 s`
(a) `h = [(GMT^(2))/(4 pi^(2))]^(1//3) - R`
`= [((6.67 xx 10^(-11)) xx (6 xx 10^(24)) xx (24 xx 60 xx 60)^(2))/(4 xx (3.142)^(2))]^(1//3) - 6.4 xx 10^(6)`
`= 4.23 xx 10^(7) - 6.4 xx 10^(6) = 3.59 xx 10^(7) m`
(b) From Fig.
`cos theta = (R )/(R + h) = (1)/(1+ (h)/(R ))`
Now `(h)/(R ) = (3.59 xx 10^(7))/(6.4 xx 10^(6)) = 5.61`
Hence, `cos theta = (1)/(1 + 5.61) = 0.1513 = cos 81^(@) 18'`
If `n` be the number of satellite that are needed to cover entire earth, then `n = (360^(@))/(2 theta) = (360^(@))/(81^(@)18' xx 2) = 2.31 ~~3`