Two stars in a faraway part of the Milky Way are orbiting each other as a binary star system. By careful measurement we find out that they are separated by 1.7 AU. We also determine that
their orbital period is 594 Earth-days. The total mass of the two-object system is

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.:

where

a is semimajor axis in astronomical units (AU);

P is period measured in years;

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 = 1.63 years

Calculating total mass:

1.85

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

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get