Double star orbits with semi-definite programming and alternatives

Ianigla-CCT, Mendoza, C.C. 330, Mendoza, Argentina e-mail: richardbranham_1943@yahoo.com

Received: 19 February 2009
Accepted: 7 September 2009

Abstract

Many methods have been proposed to calculate the apparent orbit of a double star. Semi-definite programming (SDP) offers numerous advantages, but is mathematically and computationally demanding. Aitken suggested seventy years ago a simpler method that uses ordinary least squares to calculate the coefficients of a conic section to represent the apparent ellipse. But although simpler, this approach obfuscates what is being minimized geometrically, and the calculated ellipse appears inferior to that found from SDP. An alternative, proposed in various investigations, uses nonlinear least squares to minimize the square of the deviations in distance and position angle. This method can suffer from divergence or convergence, if it occurs, to a local rather than to a global minimum. All three methods are applied to three binary systems RST 4816, Wolf 424, and HR 466.