The Mars Global Surveyor spacecraft was successfully inserted into an elliptical orbit around Mars on 9/12/97 with an orbital period of 45.0 hours. After two phases of aerobraking separated by a science-phasing-orbit interval, the orbital period was reduced to 11.6 hours on 3/27/98 and to 1.97 hours on 2/4/99, Aerobraking, through an uncertain Martian atmosphere, was responsible for circularization of the MGS orbit, Its correct termination led to a sun synchronous orbit with a local mean solar time near 2:03 am at the descending equator crossing. This paper describes the second phase of aerobraking and: a) the estimation of an atmospheric density model for every drag pass or periapsis passage by analyzing doppler tracking data, b) the generation of short-term, that is over one to several orbits, accurate atmospheric density predictions, c) maintaining the spacecraft's orbit within upper and lower bounds of atmospheric density or dynamic pressure during each periapsis passage, and d) the prediction of accurate periapsis passage times (Tp) over one to fifteen orbits. Finally, we summarize the post-aerobraking maneuvers and the state of the frozen, sun-synchronous, polar, MGS mapping orbit and its evolution.