Example: Assume that a satellite is revolving around Earth in a circular orbit almost close to the surface of Earth. What is the time period of revolution of satellite is (Radius of earth is 6400 km, g= 9.8 ms−2) ?
Solution: Time period of the satellite is given by T=2πgr Almost close to surface of Earth ⟹r=Re ∴ Time period T=2π9.86400×103 Time period T=5077 seconds
Time Period of satellites
Example: A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a spy satellite orbiting a few hundred kilometers above the earth's surface will approximately be ( Given: REarth=6400 km )
Solution: For a satellite of mass m moving with a velocity v in a circular orbit of radius r around the earth of mass M, we have rmv2=r2GmM or v=rGM Now v=T2πr. Thus T2πr=rGM or T∝r23 ∴T1T2=(r1r2)23.....(1) Given r2=6400km and r1=36000km. For a geostationary satellite T1=24h. Using these values in (1), we have get T2=24×(36064)23=1.8h.