Question

Find the radius of the orbit of a geostationary satellite; such a satellite remains always over the same point of the equator of the Earth. Are there areas on the surface of the Earth that cannot be seen from any geostationary satellite? If so, what fraction of the total surface are?

Answer 1

let r be the radius of the orbit of the radius of the geostationary satellite.

mass of the Earth, Me = 5.98*10^24 kg

Time period of satellite, T = 24 hours

= 24*60*60 s

= 86400 s

now use, T = 2*pi*r^(3/2)/sqrt(G*Me)

T^2 = 4*pi^2*r^3/(G*Me)

r^3 = G*Me*T^2/(4*pi^2)

r = (G*Me*T^2/(4*pi^2))^(1/3)

= (6.67*10^-11*5.98*10^24*86400^2/(4*pi^2))^(1/3)

= 4.225*10^7 m (or) 42250 km <<<<<<<----------Answer

only half of the area(hemi spherical area) can be seen, the remaining half of the area cannot be seen from any geostationary satellite.

A_seen/A_total = 0.5 <<<<<<<-----------Answer