Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_231

3/231 An earth satellite A is in a circular west-to-east equatorial orbit a distance 300 km above the surface of the earth as indicated. An observer B on the equator who sees the satellite directly overhead will see it directly overhead in the next orbit at position B' because of the rotation of the earth. The radial line to the satellite will have rotated through the angle \(2\pi + \Delta\theta\), and the observer will measure the apparent period \(\tau'\) as a value slightly greater than the true period \(\tau\). Calculate \(\tau'\) and \(\tau' - \tau\). Note: From the introductory section for Article 3/13 (page P-83), use \(g = 9.825 \text{ m/s}^2\) for the absolute gravitational acceleration at the surface and Earth radius \(R = 6371 \text{ km}\).