Question

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

Answer 1

Answer:
`M_(total)=` 1.85

Step-by-step 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=(594)/(365)`

P = 1.63 years

Calculating total mass:

`a^(3)=(M_(total))P^(2)`

`M_(total)=(a^(3))/(P^(2))`

`M_(total)=(1.7^(3))/(1.63^(2))`

`M_(total)=` 1.85

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