Double star orbits with semi-definite programming and alternativesR. L. Branham Jr.
Ianigla-CCT, Mendoza, C.C. 330, Mendoza, Argentina
Received 19 February 2009 / Accepted 7 September 2009
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.
Key words: binaries: visual -- methods: numerical
© ESO 2009