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I have a set of dates, position angles ($\theta$) and angular separations ($\rho$) for visual binary star. For example:

1994.3132  57.0    0.097
1996.1783  73.4    0.051
2006.1938 182.0    0.126
2009.2597 192.9    0.152
etc.

What are algorithms to calculate orbital elements and to plot the orbit of the binary star?

Are there available codes (or programs) for this calculations? Python is preferable )

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If you google "calculate orbital elements binary star" you find these two as the first hits:

I am sure the following hits would also be helpful.

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The good software for orbit calculation is "Binary" (Binary Star Combined Solution Package) by CHARA team:

http://www.chara.gsu.edu/~gudehus/binary.html

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