On the integral solution of hyperbolic Kepler’s equation

Calvo, M. ; Elipe, A. (Universidad de Zaragoza) ; Rández, L. (Universidad de Zaragoza)

Resumen: In 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.

Idioma: Inglés

DOI: 10.1007/s10569-024-10184-5

Año: 2024

Publicado en: Celestial Mechanics and Dynamical Astronomy 136, 2 (2024), 13 [14 pp.]
ISSN: 0923-2958

Factor impacto JCR: 1.4 (2024)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 84 / 136 = 0.618 (2024) - Q3 - T2
Categ. JCR: ASTRONOMY & ASTROPHYSICS rank: 54 / 84 = 0.643 (2024) - Q3 - T2

Factor impacto SCIMAGO: 0.448 - Applied Mathematics (Q2) - Computational Mathematics (Q2) - Modeling and Simulation (Q2) - Mathematical Physics (Q3) - Space and Planetary Science (Q3) - Astronomy and Astrophysics (Q3)

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)