The nature of the orbit of a visual binary calculated from three fundamental positions and the area constant

Details The nature of the orbit of a visual binary calculated from three fundamental positions and the area constant The nature of the orbit of a visual binary calculated from three fundamental positions and the area constant

Jan 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981a%26a....94...45d&link_type=abstract

Astronomy and Astrophysics, vol. 94, no. 1, Jan. 1981, p. 45-51. In French.

Astronomy and Astrophysics

Astrophysics

5

Binary Stars, Orbital Mechanics, Stellar Motions, Elliptical Orbits, Roots Of Equations

Scientific paper

Conditions determining the existence of elliptical, hyperbolic, parabolic or mathematically trivial solutions for the orbit of a visual binary star calculated according to three fundamental positions and the apparent area constant are examined. The significance of the condition on a function of the area constant determining the occurrence of the elliptical solution is analyzed in terms of variables derived from the fundamental positions and area constant, and alternative conditions on the class of solutions possible are derived which depend on the orbital eccentricity. Conditions for the existence of trivial solutions are then obtained as a function of eccentricity and the relation of the focus occupied by the primary star to the triangle formed by the three fundamental positions, and illustrated graphically for the various possible conditions. The usefulness of the preliminary determination of the domain of existence of the possible solutions is emphasized.

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