1237 AAS 08-180 QUASI CONSTANT-TIME ORBIT PROPAGATION WITHOUT SOLVING KEPLER’S EQUATION 1 Jeremy Davis, 2 Christian Bruccoleri 3 and Daniele Mortari 4 Texas A&M University, College Station, TX 77843 Abstract Efficient methods for solving Kepler’s equation, a transcendental equa- tion relating orbital position as a function of time, have been studied for centuries and generated a vast literature. This paper proposes a shift in focus from the efficient solution of Kepler’s equation to the al- ternative that, when the position of the spacecraft at precise instants in time is not required, one may simply use a quasi constant-time prop- agation technique to obtain the spacecraft trajectory. This method is much faster than solving Kepler’s equation iteratively and provides, during the initial stages of mission analysis, a good solution from which deeper investigation of the orbit characteristics can proceed. INTRODUCTION Computing the spacecraft trajectory for a desired period of time is often necessary during mission analysis or, more generally, spacecraft orbit simulation. The classi- cal analytical approach for addressing this problem requires the solution of a tran- scendental nonlinear equation, Kepler’s equation (KE) 5 , by using iterative numerical methods. The concept presented in this paper represents a shift in focus from the issue of an efficient and accurate solution to Kepler’s equation towards a completely different approach in which such solution is not required at all, at least for some applications. 1 Paper AAS 08-185 of 2008 AAS/AIAA Space Flight Mechanics Meeting, Galveston, TX, January 27-31, 2008. 2 PhD Student, Department of Aerospace Engineering, Texas A&M University, 616A H.R. Bright Building, Tel. (979) 845-0729, jeremy.davis@tamu.edu 3 Research Scientist, StarVision Technologies Inc., 1700 Research Parkway, Suite 170, College Station, TX 77845, cbruccoleri@starvisiontech.com 4 Associate Professor, Department of Aerospace Engineering, Texas A&M University, 611C H.R. Bright Building, Tel. (979) 845-0734, Fax (979) 845-6051, mortari@tamu.edu 5 See next section for definitions