A satellite is put into a circular orbit with the intention that it hover over a certain spot on the
earth’s surface. However, the satellite’s orbital radius is erroneously made 1.0 km too large for this to happen. At what rate and in what direction does the point directly below the satellite move across the earth’s surface?
R = Radius of earth = 6400 km
r = radius of orbit of geostationary satellite = 42000 km
T = Time period of earth about its axis = 24 hr.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
V rel = 
= 
m/sec ≈ 1.66 cm/sec., to the east along equator
Sol. R = Radius of earth
r = radius of orbit of geostationary satellite
T = Time period of earth about its axis
T α r 3 / 2
ω α r – 3 / 2 
= 
× 
Δ ω = 
× 
× ω
V rel = ( ω 1 – ω 2 ) R = – Δω × R
= 
× 
× R × ω
V rel = 
× 
× R × 
= 
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