Abstract
The present study concerns the application of an analytical theory of the stellar three- - bodies problem to the triple stellar system ξ UMa, whose components move along short-period orbits with periods of 2 years and 60 years. For this purpose the solution of the simplified canonical system of differential equations obtained in terms of hyperelliptic integrals by Hamilton-Jacobi method was used. The precision of the solution was increased by addition of short-periodic terms computed from the formulae of the transformation by von Zeipel’s method.
The orbital elements of the system ξ UMa computed from the analytical theory were compared with those obtained by numerical integration. These two sets of elements agree quite well. Therefore, the analytical theory can be used for computation of the long-term orbital evolution of triple stellar systems similar to ξ UMa.
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© 2001 Springer Science+Business Media Dordrecht
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Solovaya, N.A., Pittich, E.M. (2001). Application of the Nonrestricted Three-Bodies Problem to the Stellar System ξ UMa. In: Dvorak, R., Henrard, J. (eds) New Developments in the Dynamics of Planetary Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2414-2_20
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DOI: https://doi.org/10.1007/978-94-017-2414-2_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5702-0
Online ISBN: 978-94-017-2414-2
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