8.12 These next few problems are based on the Messenger spacecraft launched from Earth on August 3, 2004. After gravity-assist maneuvers around the Earth, Venus, and Mercury, Messenger went into orbit around Mercury on March 18, 2011. The radius and mass of Mercury are 2,440 and 3.30 1023, respectively. The orbit is designed to be highly elliptical, with the altitude of closest approach (periapsis) of 200.0 , and the altitude of farthest distance (apoapsis) of 15,193. Please note these are altitudes above the surface of Mercury, not the distances from the planet's center. Calculate the period of the Messenger orbit. Ignore the influence of the gravitational attraction of the sun on the spacecraft's orbit. 8.13 Using the information from 8.12, calculate the spacecraft's velocity at periapsis and at apoapsis. 8.15 Using the information from 8.12, calculate the eccentricity of the Messenger's orbit about Mercury.