000133402 001__ 133402 000133402 005__ 20250923084424.0 000133402 0247_ $$2doi$$a10.1007/s10569-024-10184-5 000133402 0248_ $$2sideral$$a138074 000133402 037__ $$aART-2024-138074 000133402 041__ $$aeng 000133402 100__ $$0(orcid)0000-0002-3312-5710$$aCalvo, M. 000133402 245__ $$aOn the integral solution of hyperbolic Kepler’s equation 000133402 260__ $$c2024 000133402 5060_ $$aAccess copy available to the general public$$fUnrestricted 000133402 5203_ $$aIn a recent paper of Philcox, Goodman and Slepian, the solution of the elliptic Kepler’s equation is given as a quotient of two contour integrals along a Jordan curve that contains in its interior the unique real solution of the elliptic Kepler’s equation and does not include other complex zeroes. In this paper, we show that a similar explicit integral solution can be given for the hyperbolic Kepler’s equation. With this purpose, we carry out a study of the complex zeros of the hyperbolic Kepler’s equation in order to define suitable Jordan contours in the integrals. Even more, we show that appropriate elliptic Jordan contours can be defined for such integrals, which reduces the computing time. Moreover, using the ideas behind the fast Fourier transform (FFT) algorithm, these integrals can be approximated by the composite trapezoidal rule which gives an algorithm with spectral convergence as a function of the number of nodes. The results of some numerical experiments are presented to show that this implementation is a reliable and very accurate algorithm for solving the hyperbolic Kepler’s equation. 000133402 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000133402 590__ $$a1.4$$b2024 000133402 592__ $$a0.448$$b2024 000133402 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b84 / 136 = 0.618$$c2024$$dQ3$$eT2 000133402 593__ $$aApplied Mathematics$$c2024$$dQ2 000133402 591__ $$aASTRONOMY & ASTROPHYSICS$$b54 / 84 = 0.643$$c2024$$dQ3$$eT2 000133402 593__ $$aComputational Mathematics$$c2024$$dQ2 000133402 593__ $$aModeling and Simulation$$c2024$$dQ2 000133402 593__ $$aMathematical Physics$$c2024$$dQ3 000133402 593__ $$aSpace and Planetary Science$$c2024$$dQ3 000133402 593__ $$aAstronomy and Astrophysics$$c2024$$dQ3 000133402 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000133402 700__ $$0(orcid)0000-0001-5208-4494$$aElipe, A.$$uUniversidad de Zaragoza 000133402 700__ $$0(orcid)0000-0002-4238-3228$$aRández, L.$$uUniversidad de Zaragoza 000133402 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000133402 773__ $$g136, 2 (2024), 13 [14 pp.]$$pCelest. mech. dyn. astron.$$tCelestial Mechanics and Dynamical Astronomy$$x0923-2958 000133402 8564_ $$s614641$$uhttps://zaguan.unizar.es/record/133402/files/texto_completo.pdf$$yVersión publicada 000133402 8564_ $$s1161951$$uhttps://zaguan.unizar.es/record/133402/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000133402 909CO $$ooai:zaguan.unizar.es:133402$$particulos$$pdriver 000133402 951__ $$a2025-09-22-14:38:26 000133402 980__ $$aARTICLE