Determining Mass of Binary Star Systems Using Center of Mass Method

[HasuChObe]

Hi, I'm new to these forums. Gonna give the homework help section a spin =] Here's my question:

(a) About half of the visible "stars" are actually binary star systems, two stars that orbit each other with no other objects nearby. Consider the motion of the center of mass of a binary star system. For a particular binary star system, telescopic observations repeated over many years show that one of the stars (whose unknown mass we'll call M1) has a circular orbit with radius R1 = 5x10^11 m, while the other star (whose unknown mass we'll call M2) has a circular orbit of radius R2 = 9x10^11 m about the same point. Make a sketch of the orbits, and show the positions of the two stars on these orbits at some instant. Label the two stars as to which is which, and label their orbital radii. Indicate on your sketch the location of the center of mass of the system. (Do this on paper; you will not be asked to turn it in. )(c) This double star system is observed to complete one revolution in 49 years. What are the masses of the two stars? (For comparison, the distance from Sun to Earth is about 1.5x10^11 m, and the mass of the Sun is about 2x10^30 kg.) This method is often used to determine the masses of stars. The mass of a star largely determines many of the other properties of a star, which is why astrophysicists need a method for measuring the mass.

M1 and M2 are unknown. The period for one revolution is 49 years. The radius of the circular orbit of M1 is 5x10^11. The radius of the circular orbit of M2 is 9x10^11. How do I find M1 and M2 given this information?
Supposed to use center of mass to figure this one out =/ All help is appreciated.

 

[RandallB]

Use what is given in the problem (1.5x10^11 m) as a circular radius of Earth's orbit.
Then using what you’ve learned and know about our local solar system to figure the circular orbit of the Sun (ignoring other planets of course) and other details; Center of Mass, periods, diagram, etc.

From doing that you should able to understand the formulas well enough to determine how to figure the given problem.
Let us know what you get

 

[HasuChObe]

-____-;; I don't know how to use the period. The chapter I'm on actually focuses on energy. More help needed!

 

[Adtudmaa]

m1= ((r1+r2)^2 *(r2) (2 pi)^2) / G T^2

m2 = ((r1+r2)^2 *(r1) (2 pi)^2) / G T^2