Analysis of a perturbation solution of the main problem in artificial satellite theory
Krambeck, Scott D.
Danielson, Donald A.
Howard, Richard M.
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The development of a universal solution of the main problem in artificial satellite theory has only recently been accomplished with the aid of high powered computers. The solution to this long standing problem is an analytical expression that is similar in form to the two-body solution. An analysis is presented in which the solution is compared with the two-body solution, a proven numerical solution, and actual measured satellite data. The solution is shown to be significantly more accurate than the two-body solution. The theoretical accuracy of the solution is confirmed. The solution compares extremely well with a proven numerical solution for at least 41 orbits with a relative error on the order of J2theta. The solution compares extremely well with measured satellite data for satellites in near Earth orbits. For a satellite in orbit at an altitude of approximately 1000 kilometers, the solution reduces the error of the two-body solution by about 95%. For satellites in orbit at semisynchronous and geosynchronous altitudes, the solution reduces the error of the two-body solution by at least 50%. The solution is free of singularities and is valid for all eccentricities and inclinations.
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