000168442 001__ 168442
000168442 005__ 20260205155159.0
000168442 0247_ $$2doi$$a10.1016/j.actaastro.2026.01.014
000168442 0248_ $$2sideral$$a147917
000168442 037__ $$aART-2026-147917
000168442 041__ $$aeng
000168442 100__ $$0(orcid)0000-0002-3312-5710$$aCalvo, Manuel$$uUniversidad de Zaragoza
000168442 245__ $$aPiecewise rational Padé and Hermite approximations for the elliptic Kepler equation
000168442 260__ $$c2026
000168442 5060_ $$aAccess copy available to the general public$$fUnrestricted
000168442 5203_ $$aAccurate and efficient solution of the Elliptic Kepler Equation (EKE) is fundamental in orbital mechanics and spacecraft trajectory analysis. In this work, we present a family of piecewise rational approximations for solving the EKE, (; ) ≡ − sin = , based on Padé and Hermite-type formulations. The proposed approaches replaces the transcendental term sin with Hermite and Piecewise Padé-Type (PPT) approximants, the later originally introduced by Brezinski, providing higher accuracy than the traditional Piecewise Padé (PP) method of Wu et al. without increasing computational cost. With these approximants, the resulting rational form reduces the EKE to a cubic equation that can be solved analytically, making it suitable for onboard implementations or large-scale orbit propagation tasks. Numerical experiments demonstrate that the PPT-based solution significantly improves accuracy for moderate and high eccentricities, including near-parabolic cases. Additionally, optimized parameter selection in general [3/2] rational representations yields further accuracy gains. These results show that the proposed piecewise rational method offers a reliable and computationally efficient alternative for precise orbital position determination across a wide range of eccentricities.
000168442 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-26R$$9info:eu-repo/grantAgreement/ES/DGA/E41-26R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-141385NB-I00$$9info:eu-repo/grantAgreement/ES/MICIU/PID2024-156002NB-I00
000168442 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
000168442 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000168442 700__ $$0(orcid)0000-0001-5208-4494$$aElipe, Antonio$$uUniversidad de Zaragoza
000168442 700__ $$0(orcid)0000-0002-4238-3228$$aRández, Luis$$uUniversidad de Zaragoza
000168442 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000168442 773__ $$g241 (2026), 199-206$$pActa astronaut.$$tActa Astronautica$$x0094-5765
000168442 8564_ $$s1442511$$uhttps://zaguan.unizar.es/record/168442/files/texto_completo.pdf$$yVersión publicada
000168442 8564_ $$s2232107$$uhttps://zaguan.unizar.es/record/168442/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000168442 909CO $$ooai:zaguan.unizar.es:168442$$particulos$$pdriver
000168442 951__ $$a2026-02-05-14:36:40
000168442 980__ $$aARTICLE