Accurate and efficient orbital propagators are critical for space situational awareness because they drive uncertainty propagation which is necessary for tracking, conjunction analysis, and maneuver detection. We have developed an adaptive, implicit Runge-Kuttabased method for orbit propagation that is superior to existing explicit methods, even before the algorithm is potentially parallelized. Specifically, we demonstrate a significant reduction in the computational cost of propagating objects

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... in low-Earth orbit, geosynchronous orbit, and highly elliptic orbit. The new propagator is applicable to all regimes of space, and additional features include its ability to estimate and control the truncation error, exploit analytic and semi-analytic methods, and provide accurate ephemeris data via built-in interpolation. Finally, we point out the relationship between collocation-based implicit Runge-Kutta and Modified Chebyshev-Picard Iteration. used to warm-start the iterations arising on each time step of IRK, thereby reducing the computational cost. Second, we have developed an efficient error-control mechanism that allows for the propagation to be entirely adaptive a . Time-adaptivity is achieved through the use of an error estimator which makes use of the propagated solution in order to select the optimal time step for a given tolerance, thereby controlling the accumulation of local error, and minimizing the cost of propagation per time step. This feature, among others, distinguishes our work from that of Bai & Junkins, 11 Bradley et al., 5 and Beylkin & Sandberg, 6 who studied the use of fixed-step collocation-based methods for orbit propagation. By virtue of being adaptive, our implementation of IRK is not restricted to the propagation of nearlycircular orbits. Highly elliptic orbits can also be efficiently propagated. Fixed-step propagators, on the other hand, are forced to take extremely small time steps when propagating highly elliptic orbits in order to maintain high accuracy. Alternatively, the equations of motion can be transformed (e.g., using the Sundman transform) so that fixed steps can be taken in an orbital anomaly, rather than in time, in an effort to distribute the numerical error evenly across the steps. Unfortunately, this approach results in the need to solve an additional ordinary differential equation, 12 and hence both options incur increased computational costs. This paper focuses on the propagation of objects in low-Earth orbit (LEO), geosynchronous orbit (GEO), and highly elliptic orbit (HEO). The new propagator is found to be superior to existing propagators when medium to high accuracy is required. Specifically, we propagate objects in LEO, GEO, and HEO for multiple orbital periods. The performance is compared to that of DP8(7) and ABM, the latter being a method that is similar to GJ, albeit ABM has error control, whereas the standard implementation of GJ does not have error control. 7 In a serial computing environment, we demonstrate that the new propagator outperforms DP8(7) and ABM by 60% to 85% in LEO and in GEO, and by 30% to 55% in HEO. In a parallel computing environment, the new propagator outperforms DP8(7) and ABM by 92% to 99% in LEO and in GEO, and by 86% to 97% in HEO. Hence, the real impact of the new propagator is its ability to significantly reduce the computational cost of orbit propagation, even before the algorithm is potentially parallelized. The layout of this paper is the following. In Section II, we introduce implicit Runge-Kutta methods and describe the construction of collocation-based IRK methods. In Section III, we describe the implementation of adaptive IRK methods for efficient orbit propagation. In Section IV, we compare the performance of our adaptive collocation-based IRK propagator to that of DP8(7) and ABM. In Section V, we summarize our results.