Question

Centauri A and Centauri B are binary stars with a separation of 3.45×1012m and an orbital period of 2.52×109s. Assuming the two stars are equally massive (which is approximately the case), determine their mass.

Answer 1

We can estimate the masses of binary star systems using Newton's reformulation of Kepler's third law. The equation to estimate the masses is D³ = (M₁ + M₂)P². Applying this equation to Centauri A and Centauri B, we find that each star has a mass of 1.6 times the mass of the Sun.

Step-by-step explanation:

We can estimate the masses of binary star systems using Newton's reformulation of Kepler's third law. According to Kepler's third law, the period (P) with which two objects in mutual revolution go around each other is related to the semimajor axis (D) of the orbit of one with respect to the other.

The equation to estimate the masses of binary star systems is: D³ = (M₁ + M₂)P². In this case, the separation between Centauri A and Centauri B is given as 3.45×10¹² m and the orbital period is given as 2.52×10⁹ s.

Using the given values, we can plug them into the equation and solve for the sum of the masses (M₁ + M₂), which in this case is equal to 3.2 times the mass of the Sun. Since the stars are assumed to be equally massive, each star would have a mass of half of the sum of masses, or 1.6 times the mass of the Sun.