On the Maximum Separation of Visual Binaries.

In this paper, an efficient algorithm is established for computing the maximum (minimum) angular separation ρ( ρ), 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.). Numerical studies are included and some important results are as follows: (1) there is no dependence between ρ and the spectral type and (2) a minor modification of Giannuzzi's () formula for the upper limits of ρ functions of spectral type of the primary. [ABSTRACT FROM AUTHOR]