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Journal of Astrophysics and Astronomy

, Volume 33, Issue 4, pp 375–386 | Cite as

On the Maximum Separation of Visual Binaries

  • M. I. Nouh
  • M. A. Sharaf
Article

Abstract

In this paper, an efficient algorithm is established for computing the maximum (minimum) angular separation ρ max(ρ min), the corresponding apparent position angles (\(\theta|_{\rho_{\rm max}}\), \(\theta|_{\rho_{\rm min}}\)) and the individual masses of visual binary systems. The algorithm uses Reed’s formulae (1984) for the masses, and a technique of one-dimensional unconstrained minimization, together with the solution of Kepler’s equation for \((\rho_{\rm max}, \theta|_{\rho_{\rm max}})\) and \((\rho_{\rm min}, \theta|_{\rho_{\rm min}})\). Iterative schemes of quadratic coverage up to any positive integer order are developed for the solution of Kepler’s equation. A sample of 110 systems is selected from the Sixth Catalog of Orbits (Hartkopf et al. 2001). Numerical studies are included and some important results are as follows: (1) there is no dependence between ρ max and the spectral type and (2) a minor modification of Giannuzzi’s (1989) formula for the upper limits of ρ max functions of spectral type of the primary.

Keywords

Stars: spectral types—binaries: visual—numerical: optimization 

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Copyright information

© Indian Academy of Sciences 2012

Authors and Affiliations

  1. 1.Department of Physics, College of ScienceNorthern Border UniversityArarSaudi Arabia
  2. 2.Department of Astronomy, Faculty of ScienceKing Abdul-Aziz UniversityJeddahSaudi Arabia

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