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


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.


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


  1. Abt, H. A. 1986, Astrophys. J., 304, 688.ADSCrossRefGoogle Scholar
  2. Abt, H. A. 1988a, Astrophys. Space. Sci. , 142, 111.ADSCrossRefGoogle Scholar
  3. Abt, H. A. 1988b, Astrophys. J., 331, 922.ADSCrossRefGoogle Scholar
  4. Bartkevicius, A. 2008, Baltic Astron., 17, 209.ADSGoogle Scholar
  5. Broucke, R., Cefola, P. 1972, Celestial Mech., 7, 388.ADSCrossRefGoogle Scholar
  6. Giannuzzi, M. A. 1989, Astrophys. Space. Sci., 161, 241.ADSCrossRefGoogle Scholar
  7. Halbwachs, J. L. 1983, Astron. Astrophys., 128, 399.ADSGoogle Scholar
  8. Halbwachs, J. L. 1986, Astron. Astrophys., 168, 161.ADSGoogle Scholar
  9. Hartkopf, W. I., Mason, B. D., Worley, C. E. 2001, Sixth Catalog of Orbits of Viual Binary Stars,
  10. Kuiper, G. P. 1935, Publ. Astron. Soc. Pacific., 47(15), 12.ADSGoogle Scholar
  11. Öpik, E. 1924, Publ. Obs. Astro. Univ. Tartu., 25, 6.Google Scholar
  12. Press, W. H., Teukolsky, S. A., Vetterling, W. H., Flannery, B. P. 1992, Numerical Recipes (Cambridge Univ. Press).Google Scholar
  13. Reed, B. C. 1984, J. R. Astron. Soc. Can., 78(2), 83.ADSGoogle Scholar
  14. Sharaf, M. A., Abou-Elazm, M. S, Nouh, M. I. 2000, Astr. Nach. 1, 321.Google Scholar

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

Personalised recommendations