Why does the standard Solar System proportionality ($P^2 imes a^3$) break down when applied to binary stars?
Answer
Both stars possess significant mass, and neither is stationary.
The simple proportionality works well for planets because the Sun’s mass overwhelmingly dominates, treating the Sun as stationary. In binaries, both stars have significant mass and orbit a common barycenter, requiring the inclusion of both masses in the constant.
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