Determine the sum of the masses of the Capella binary if the semi-major axis of its orbit is 0.85 AU. i.e.

bystudin | September 16, 2020 | Education

Determine the sum of the masses of the Capella binary if the semi-major axis of its orbit is 0.85 AU. i.e., and the circulation period is 0.285 years.

Period P = 2 * pi * sqrt (a ^ 3 / (G * (M1 + M2)))
M1 + M2 = a ^ 3 / (P / (2 * pi)) ^ 2 / G = (0.85 * 149500000000) ^ 3 / (0.285 * 86400 * 365.25 / (2 * 3.1416)) ^ 2 / (6.674 * 10 ^ -11) =
2.052014e + 33 / 2.048971e + 12 / 6.674e-11 ~ 1.5 * 10 ^ 31 kg

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