Titre du document

The Roche Coordinates in three dimensions and their application to problems of double-star astronomy

Lien vers le document
Nom du Corpus

AstroConcepts

Auteur(s)
  • Zden?k Kopal
Affiliation(s)
  • Boeing Scientific Research Laboratories, Seattle, Wash., USA
  • Department of Astronomy, University of Manchester, England
Résumé

In a preceding paper (Kopal, 1969; in what follows referred to as Paper I) we introduced a new system of curvilinear coordinates-hereafter referred to as Roche Coordinates — in which spheres of constant radius in spherical polars have been replaced by surfaces of constant potential of a rotating gravitational dipole; while the angular coordinates are orthogonal to the equipotentials. In Paper I we established an explicit form of such a transformation, and related the Roche coordinates with polar coordinates (with which they coalesce in the immediate neighbourhood of each one of the two finite mass-points) in the plane case. The aim of the present investigation will be to generalize the definition of the Roche coordinates to three dimensions. The opening Section 1 of this paper will contain a general outline of the proposed three-dimensional transformation; and in Section 2 details of this transformation will be explicitly worked out correctly to quantities of first order in superficial distortion — an approximation which should prove adequate in regions surrounding the two finite masses; while in Section 3 we shall evaluate (to this degree of accuracy) the metric coefficients of the respective transformation, and its direction cosines, in both polar and curvilinear coordinates. Section 4 will then contain a formulation of the fundamental equations of hydrodynamics in terms of the three-dimensional Roche coordinates; and their advantages for a treatment of certain classes of dynamical problems encountered in doublestar astronomy will be illustrated in the concluding Section 5 by an investigation of the vibrational stability of the Roche model. We shall show that this model is capable of performing free radial oscillations which remain barotropic only if its equilibrium form is spherical (i.e., in the absence of any external mass in the neighbourhood); but not if it is distorted to any extent by rotation or tides.

Langue(s) du document
Anglais
Année de publication
1970
Revue

Astrophysics and Space Science

Éditeur
Springer (journals)
Type de publication
journal
Type de document
research-article
Présence de XML structuré
Non
Version de PDF
1.3
Score de qualité du texte
10
Nom du concept
  • Roche equipotentials
Catégories Science-Metrix
  • 1 - natural sciences ; 2 - physics & astronomy ; 3 - astronomy & astrophysics
Catégories Inist
  • 1 - sciences appliquees, technologies et medecines ; 2 - sciences exactes et technologie ; 3 - terre, ocean, espace ; 4 - geophysique externe
Catégories Scopus
  • 1 - Physical Sciences ; 2 - Earth and Planetary Sciences ; 3 - Space and Planetary Science
  • 1 - Physical Sciences ; 2 - Physics and Astronomy ; 3 - Astronomy and Astrophysics
Catégories WoS
  • 1 - science ; 2 - astronomy & astrophysics
Identifiant ISTEX
B6479E87129904AEAF9E568E048D8FF24FD2D614
ark:/67375/1BB-KNV79052-H
Powered by Lodex 9.4.5