THE TRUE AND APPARENT ELLIPTICAL ORBITS OF A VISUAL BINARY STAR

Abstract

Observation of binary star orbits reveals only the apparent orbit of these two celestial

bodies which differs from the true orbit. Due to the inclination of the plane of the true orbit one

can only observe its projection onto the plane of sky. Computing the true orbit from the apparent

orbit is based on constructing the auxiliary ellipse. This process is well known (Kallrath 2009) but

requires arduous numerical computations. In this paper a simpler approach to obtain the auxiliary

ellipse is presented and its derivation is provided. This approach finds out that the coefficients of

the auxiliary ellipse are very simple functions of those of the apparent ellipse.

Keywords

• celestial mechanics,binary stars,auxiliary ellipse,true orbit

References

1. Atkinson, R. d'E. , "A New Method for Deriving the True Orbit of a Visual Binary",Astronomical Society of the Pacific, Vol. 78, No. 463, p.242.
2. Argyle, Bob (editor), Observing and Measuring Visual Double Stars, Springer LLC 2004.
3. Hilditch, R.W., An Introduction to Close Binary Stars, Cambridge, University Press 2001.
4. Kallrath, J. and Milone, E., Eclipsing Binary Stars: Modeling and Analysis, Springer LLC 2009.
5. Mullaney, James, Double and Multiple Stars and How to Observe Them, Springer 2005.
6. Tatum, J.B., Celestial Mechanics, Chapter 17, "Visual Binary Stars", Updated 2016,"astrowww.phys.uvic.ca/~tatum/celmechs.html".
7. Smart, W.M., Text-Book on Spherical Astronomy, Cambridge, University Press 1949.