Abstract
The convergence of Lagrange series is studied on a part of the elliptical orbit for values of eccentricity exceeding the Laplace limit. The regions in the vicinity of the two apses of the orbit are identified in which the Lagrange series converge absolutely and uniformly for the values of the eccentricity greater than the Laplace limit. The obtained results are of practical interest for astronomy when studying motions of stellar bodies in orbits with high eccentricity. In particular, these series may be used to calculate the orbits of comets or asteroids with high eccentricity as they pass through the neighborhood of perihelion or to calculate the orbits of artificial satellites with high eccentricity “hanging” in the vicinity of apogee. In stellar dynamics, these series may be used in cases of close binary stars, many of which move in orbits with an eccentricity greater than the Laplace limit.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
