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Astronomy and Cosmology
Astronomy and Astrophysics
The Semi-Major Axis of Binary Stars
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[QUOTE="Ken G, post: 5641883, member: 116697"] Since the center of mass of the whole system won't move, the orbits of the two stars independently (with two semi-major axes) are simply scaled-down versions of the "orbit" of the displacement between the stars (one semi-major axis that is the sum, not the average, of the other two). The scale factor is set by the mass ratio, where it is 1/2 if the two stars have the same mass, and 1 for the lower-mass star in the limit that the ratio goes to 0. So the scale factor for the individual orbit of star 1 is $m_2/(m_1+m_2)$, and its orbit is just a miniature copy of the orbit of the total displacement, shrunk by that factor (and of course, the two stars' independent orbits are in phase with each other but mirror reflected). [/QUOTE]
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Astronomy and Astrophysics
The Semi-Major Axis of Binary Stars
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