What is the formula used to calculate the total mass ($M_1 + M_2$) of a binary system based on the refined Kepler's Third Law?
Answer
M_1 + M_2 = \frac{4\pi^2 a^3}{G P^2}
The relationship $P^2 = \frac{4\pi^2}{G(M_1 + M_2)} a^3$ is rearranged to solve directly for the sum of the masses, yielding $M_1 + M_2 = \frac{4\pi^2 a^3}{G P^2}$.
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