Themechanicsofspace?ightisan olddiscipline.Itstopicoriginallywasthemotion of planets, moons and other celestial bodies in gravitational ?elds. Keplers (1571 - 1630) observations and measurements have led to probably the ?rst mathematical description of planets motion. Newton (1642 - 1727) gave then, with the devel- ment of his principles of mechanics, the physical explanation of these motions. Since then man has started in the second half of the 20th centuryto capture ph- ically the Space in the sense that he did develop arti?cial celestial bodies, which he brought into Earths orbits, like satellites or space stations, or which he did send to planets or moons of our planetary system, like probes, or by which p- ple were brought to the moon and back, like capsules. Further he developed an advanced space transportation system, the U.S. Space Shuttle Orbiter, which is the only winged space vehicle ever in operation. In the last two and a half decades there were several activities in the world in order to succeed the U.S. Orbiter, like the HERMES project in Europe, the HOPE project in Japan, the X-33, X-34 and X-37 studies and demonstrators in the United States and the joint U.S. - European project X-38. However, all these projects were cancelled. The motion of these vehicles can be described by Newtons equation of motion.

Coordinate Transformations.- Transformations between Often Used Coordinate Systems.- Keplers Laws of Planetary Motion and Newtons Celestial Mechanics.- The Two-Body Problem.- General Equations for Planetary Flight.- A Resumé of the Aerothermodynamics of Space Flight Vehicles.- Three and Six Degree of Freedom Trajectory Simulations.- Numerical Applications of the General Equations for Planetary Flight.- The Earth Atmosphere.- Solution of Problems.- Our Planetary System.- FORTRAN Codes.- MATLAB Codes.- Constants, Relations, Units and Conversions.