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arXiv · 1309.2868

Mass estimates for visual binaries with incomplete orbits

L. B. Lucy
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Abstract

The problem of estimating the total mass of a visual binary when its orbit is incomplete is treated with Bayesian methods. The posterior mean of a mass estimator is approximated by a triple integral over orbital period, time of periastron and orbital eccentricity. This reduction to 3-D from the 7-D space defined by the conventional Campbell parameters is achieved by adopting the Thiele-Innes elements and exploiting the linearity with respect to the four Thiele-Innes constants. The formalism is tested on synthetic observational data covering a variable fraction of a model binary's orbit. The posterior mean of the mass estimator is numerically found to be unbiased when the data cover > 40% of the orbit.

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L. B. Lucy. 2014-02-18. Mass estimates for visual binaries with incomplete orbits. https://doi.org/10.1051/0004-6361%2F201322649

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