By Plummer H. C. 1875

ISBN-10: 1163790745

ISBN-13: 9781163790748

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It is the ratio of the radii r2/rl whose determination would provide a sensitive photometric clue to the mass-ratio of a contact system. This underlines the importance of photometric determination of the ratios of the radii of contact binary systems; but owing to purely geometrical difficulties this important task of light curve analysis is, unfortunately, not yet well in hand. Suppose next that a contact binary system, consisting of two components at their Roche limits, is viewed by a distant observer from an arbitrary direction.

84) and 13 v {1 + r 3(1- v 2) + ~r3(1- v 2)(2 - 3v 2) + ... 85) m3 v {1 + r 3(1- v 2) + ~r6(1- v 2)(2 - 3v 2) + ... 87) n2 - {1- r3 v 2 - ~r6v2(1_ v 2) + ... 77) with equal ease. c: Double-Star Problem The general theory outlined in Section IL1A led us to expect that the Roche coordinates associated with the rotational problem admit of a solution in the closed form; and the contents of Section IL1B did not disappoint these expectations. 1A that the tidal problem should admit of a similar solution if we change over from the Z-axis for the X -axis (and the direction cosine v for A) as one of symmetry of the respective configuration.

25)-this latter system is clearly integrable to furnish a triply-orthogonal set of curvilinear Roche coordinates in the rotational case. 57) 44 CHAPTER III. 51). 25) can again be integrated to furnish a triply-orthogonal system of curvilinear coordinates. However, when terms arising from both rotation and tides are present in the expressions for ~ and its derivatives, all three coefficients A,13 and C will not vanish. 44) we find (cf. 51) of integrability; and, accordingly, numerical integrations (cf.

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An Introductory Treatise On Dynamical Astronomy by Plummer H. C. 1875

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