Calculate Mass of Eri B & C: Solar Mass Ratio

[mjolnir80]

Homework Statement

we are looking at two stars in the eridani system, eri B and eri C. the period of the system is 247.9 years. the system's measured trigonometric parallax is 0.201 arcseconds and the tru angular extent to the semimajor axis of the reduced mass is 6.89". the ratio of distances of eri b and c from the center of mass is a_b/a_c= 0.37. what is the mass of Eri B and C in terms of the mass of the sun?

Homework Equations

M_bR_b + M_cR_c / M_b+ M_c

The Attempt at a Solution

im kind of confused about how to start this off. i thought about using the distance of both the stars from the sun as the reference point for the formula but that doesn't really work. If anyone could give me a rough idea of what direction to go with this problem i would really appreciate it

 

[ideasrule]

I think the easiest way to start off is to use the modern version of Kepler's third law to find the system's reduced mass. You can then find the masses of the two components quite easily.

 

[mjolnir80]

ok so i got the reduced mass
now i know that the formula for reduced mass is m₁ + m₂ / m₁m₂ but i don't really know where to go from here
what I am having trouble understanding is where the parallax and ratio of distances comes in

 

[ideasrule]

How did you get the reduced mass without using the parallax? Kepler's third law is a relationship between mass, period, and semi-major axis. I don't see how you got mass without knowing the semi-major axis.

Supposing your reduced mass is correct, you know that from the definition of the center of mass, Mb*a_b=Mc*a_c. You also know the ratio between a_b and a_c.

P.S. reduced mass is m1*m2/(m1+m2), not (m1+m2)/m1m2

 

[mjolnir80]

thanks for the help
i used P^2/a^3 = 4 pi^2/ MG to get the mass