Here we describe two routines, ENRKE and ENP5KE, for solving KE with both high speed and optimal accuracy, circumventing the abovementioned limit by avoiding the use of derivatives for the critical values of the eccentricity e and mean anomaly M, namely e > 0.99 and M close to the periapsis within 0.0045 rad. Moreover, a recent work demonstrated that the current solvers face an accuracy limit that becomes particularly stringent for high eccentricity orbits.Īims.
The repetitive solution of Kepler’s equation (KE) is the slowest step for several highly demanding computational tasks in astrophysics. Olivieri 2 ,3Īpplied Physics Department, School of Aeronautic and Space Engineering, Universidade de Vigo,Į-mail: Science Department, School of Informatics (ESEI), Universidade de Vigo,Ĭontext.
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