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Chapter 4: RESTRICTED THREE-BODY PROBLEM


CHAPTER IV


RESTRICTED THREE-BODY PROBLEM

The spectrum of KU Cygni displays extremely strong double emission lines of H$\alpha$. Following the model proposed by Joy (1942), the observance of H$\alpha$ spectral feature suggest the existence of a gaseous ring around the star eclipsed at primary minimum. Otto Stuve and his colleagues (Struve 1948, 1949, Struve & Huang 1957) postulated that the emission lines observed in many Algol systems originated from gaseous streams between the two components or perhaps even a gaseous envelope encircling both components. They noted that the motion of these streams and envelopes are very different than the orbital motion of the components. For this reason, the radial velocity curves of these systems are skewed and do not agree with corresponding light curve information, indicative of circular orbits. Kuiper (1941) was the first to use the ``Roche Model'' to describe the geometry of mass transfer from one component to the other. The driving force of mass transfer between stars was later understood with the advent of stellar evolution theories. The trajectory of the mass-transfer stream can be modeled using restricted three-body calculations or hydrodynamic models. With the Roche model in tow, and the trajectory calculations in hand, a description of the formation of an accretion disk systems can be formulated. The following sections briefly describe the calculations of Roche equipotential surfaces for a given mass ratio, as well as the equations to calculate particle trajectories in the restricted three-body problem.



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Next: Zero-Velocity Curves Up: Chapter Sections Previous: Trailed Spectrogram of KU   Contents
Quyen Nguyen 2004-09-11