Question

Two stars in a faraway part of the Milky Way are orbiting each other as a binary star system. By

Answer 1

Answer: $M_{total}=$ 1.85

Explanation: Estimate the total mass of a binary system is done by a reformulation of Kepler's Third Law, which states that the square of the period of a planet's orbit is proportional to the cube of its semimajor axis, i.e.:

$a^{3}=(M_{1}+M_{2})P^{2}$

where

a is semimajor axis in astronomical units (AU);

P is period measured in years;

$M_{1}+M_{2}$ is total mass of the two-stars system;

For the two stars faraway in the Milky Way:

1 year is equivalent of 365 days, so period in years:

$P=\frac{594}{365}$

P = 1.63 years

Calculating total mass:

$a^{3}=(M_{total})P^{2}$

$M_{total}=\frac{a^{3}}{P^{2}}$

$M_{total}=\frac{1.7^{3}}{1.63^{2}}$

$M_{total}=$ 1.85

The total mass of the two-object system is 1.85 mass units.