Orbits Containing Arcs of Minimum Altitude Variation

This thesis identifies the mean orbital elements which produce arcs of minimum altitude variation over an oblate planet with an axi-symmetric gravitational field. Such orbits are useful for surveillance or scientific study missions using optics with fixed focal lengths. Both Earth and Mars are considered and the optimum eccentricity is found as a function of argument of periapsis and inclination for two values of semi-major axis for each planet. The results are curve fit to develop a single equation which identifies the eccentricity needed to produce an arc of minimum altitude variation given the argument of periapsis, inclination, semi-major axis, ellipticity of the planet, equatorial radius, and the zonal J2. Once arcs with minimum altitude variations are identified, the properties of the arcs are considered. The mid-latitude, altitude, duration, and latitude range of the arcs are found as a function of argument of periapsis and inclination for various planet and semi-major axis combinations. The secular change in mean orbital elements will determine the most stable orbits. Secular changes in orbital elements due to the geopotential, drag, and third body effects are considered. The velocity impulse needed to return the satellite to the original orbit from the perturbed orbit is found and used to determine stability. Identifying orbits which require minimum station keeping fuel allows planners to select orbits permitting longer useful operational life.