Sirius A and Sirius B constitute a binary star pair in which the stars orbit their common center of mass with a period of 49.9 years. The stars are 2.40 × 10¹² m apart. Assume that the two stars have equal masses and that they move in a circle about their common center of mass. What is the mass of each star? G = 6.67 x 10^-11 N·m²/kg². A) 5.41 × 10³⁰ kg B) 2.70 × 10³⁰ kg C) 7.55 × 10³⁰ kg D) 3.30 × 10³⁰ kg E) 1.65 × 10³⁰ kg

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Quizplus · Accepted Answer

Using Kepler's third law for binary systems, the mass of each star can be calculated as M = (4π²/G) * (a³/P²), where a is the semi-major axis (half the distance between the stars) and P is the period. Substituting the given values, the mass of each star is approximately 1.65 × 10³⁰ kg.

Sirius a and Sirius B Constitute a Binary Star Pair