The next five problems are based on the Messenger spacecraft launched from Earth on August 3, 2002. After gravity-assist maneuvers around the earth, Venus.and Mercury, Messenger is scheduled (at the time of this writing) to go into orbit around Mercury on March 18,2011. The radius and mass of Mercury are 2,440 km and 3.3 × 1023 kg, respectively. The orbit is designed to be highly elliptical, with the altitude of closest approach (periapsis) of 200 km, and the altitude of farthest distance (apoapsis) of 15,193 km. (Note: These are altitudes above the surface of Mercury, not the distances from the center of the planet.) Calculate the period of the Messenger orbit. Ignore the influence of the gravitational attraction of the sun on the spacecraft orbit.
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