A satellite is to revolve round the earth in a circle of radius 8000 km. With what speed should this satellite be projected into orbit? What will be the time period ? Take g at the surface = 9.8 m/s2 and radius of the earth = 6400km.
7.08 km/s, 118 minutes
Suppose, the speed of the satellite is v.The acceleration of the satellite is v2r, where r is the radius of the orbit.The force on the satellite is GMmr2 with usual symbols.Using Newton's second law,
GMmr2=mv2r
or, v2=GMr=gR2r=(9.8m/s2)(6400km)2(8000km)
giving v = 7.08 km/s.
The time period is 2πrv=2π(8000km)(7.08km/s)≈118minutes.