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To launch a communication satellite in a circular orbit 1000 km above the surface of the Earth, what orbital speed must be imparted to the satellite? Find the acceleration due to gravity at the orbit.
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Orbit radius (Ro) = Earth radius (Re= 6.37^6m) + 1.0^6m .. Ro = 7.37^6m
Grav field strength ∝ 1/R² .. .. field at surface gs = 9.80m/s², at Ro field = go
go/ge = (Re/Ro)² .. .. go = 9.80 x (6.37^6 / 7.37^6)² .. .. ►go = 7.32 m/s²
go = centripetal (radial) acceleration = V²/Re
go = V² / Re .. .. V = √(go.Re) .. .. √(7.32 x 6.37^6) .. .. ►V = 6.83^3 m/s