Answer: [tex]M_{total}=[/tex] 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.:
[tex]a^{3}=(M_{1}+M_{2})P^{2}[/tex]
where
a is semimajor axis in astronomical units (AU);
P is period measured in years;
[tex]M_{1}+M_{2}[/tex] 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:
[tex]P=\frac{594}{365}[/tex]
P = 1.63 years
Calculating total mass:
[tex]a^{3}=(M_{total})P^{2}[/tex]
[tex]M_{total}=\frac{a^{3}}{P^{2}}[/tex]
[tex]M_{total}=\frac{1.7^{3}}{1.63^{2}}[/tex]
[tex]M_{total}=[/tex] 1.85
The total mass of the two-object system is 1.85 mass units.
