EDP Sciences
Free access
Volume 507, Number 2, November IV 2009
Page(s) 1107 - 1115
Section Astronomical instrumentation
DOI http://dx.doi.org/10.1051/0004-6361/200911875
Published online 15 September 2009
A&A 507, 1107-1115 (2009)
DOI: 10.1051/0004-6361/200911875

Double star orbits with semi-definite programming and alternatives

R. L. Branham Jr.

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

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