The Mercury Messenger spacecraft was inserted into an orbit around the planet Mercury. After approximately two months in orbit it was decided to adjust the orbit period with a spacecraft burn exactly at periapsis. The pre-adjustment orbit had a minimum altitude of 325 km above the planet's surface, and a period of 11.80 hours (the maneuver increased the period to 12.00 hours). a) What was the eccentricity, e, and semi-major axis, a (km) of the initial orbit (period T= 11.80 hours)? b) The spacecraft entered Mercury's shadow at a true anomaly of 0= 155. How long after shadow entry did the maneuvering burn occur (you can assume here that the burn duration is infinitely short)? As part of this calculation give the values of the eccentric anomaly and the mean anomaly (radians) and the mean motion (inverse seconds) for the true anomaly of 0 = 155.