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Calculating the Orbit of a Double Star with Visual, Speckle, and Radial Velocity Data

The mathematical technique known as semidefinite programming (SDP) is used with 260 visual and speckle and 129 double-line radial velocities to determine the orbit of the system 24 Aquarii. The fractional mass and the parallax of the system are also determined. SDP calculates a unique ellipse that satisfies the observations and represents a global minimum of the adjustment criterion. SDP also permits great flexibility; the visual and speckle observations are reduced with the robust L1 criterion, whereas least squares are used for the radial velocities. The period of the system is determined as 48.28 yr, the fractional mass as 0.433, and the parallax as 0.019″.