Question

A binary star system consists of two stars orbiting together. One such binary system has an orbital period of 701 years and a semi-major axis of 113 AU. What is the combined mass of the two stars in the system (in units of solar masses)?

a) 3.5 solar masses
b) 2.1 solar masses
c) 1.8 solar masses
d) 4.6 solar masses

Answer 1

The combined mass of the two stars in the binary star system is approximately 1.8 solar masses. (option c is the correct answer).

Step-by-step explanation:

To find the combined mass of the binary star system, we can use Kepler's Third Law and the gravitational force equation. Kepler's Third Law states that the square of the orbital period (T) is proportional to the cube of the semi-major axis (a) for any two objects orbiting each other. Mathematically, this is expressed as T^2 = (4π^2 / G * M_total) * a^3, where G is the gravitational constant.

Rearranging the equation to solve for the total mass (M_total), we get M_total = (4π^2 / G) * (a^3 / T^2). Plugging in the given values (a = 113 AU, T = 701 years), we can calculate the total mass in solar masses.

4π^2 / G× 113^3/701^2

Calculating this expression yields approximately 1.8 solar masses.

The combined mass of the two stars in the binary system is approximately 1.8 solar masses, making option c) the correct answer.