Final answer:
Using Kepler's third law of planetary motion and the given values of 2 AU for distance and 2 years for the orbital period, the total combined mass of the two stars in the binary system is calculated to be 1 Solar Mass.
Step-by-step explanation:
To determine the total combined mass of the two stars in a binary system, given that they are separated by a distance of 2 AU and have an orbital period of 2 years, we can use Kepler's third law of planetary motion.
The law is represented by the formula M₁ + M₂ = D³ / P², where D is the average distance between the two stars in astronomical units (AU), P is the period of their orbit in years, and M₁ + M₂ is the sum of the masses of the two stars in units of the Sun's mass.
In this scenario, D = 2 AU and P = 2 years. By plugging these values into the formula, we get M₁ + M₂ = 2³ / 2² = 4 / 4 = 1. Therefore, the total combined mass of the two stars is 1 Solar Mass.