# Calculate the masses of two binary stars

#### leonne

1. The problem statement, all variables and given/known data
One of the most massive binary star systems known is called WR-20a and is located
in the Large Magellanic Cloud (a small companion galaxy to the Milky Way). This
system is nearly edge on, and the stars are moving in circular orbits with observed
speeds of 362.2 km s^-1 and 366.4 km s^-1 in an orbital period of just 3.686 days!

Calculate the masses of these two stars
What is the distance between the two stars?

2. Relevant equations
Vn=(2pie*an)/p ,p^2=(4pie^2 /G(m1+m2)) A^3
A=a1+a2
3. The attempt at a solution
I am thinking of using vn=... and solving for a using keplers 3rd law to find I can find the center of mass of the two star but not sure how i would find the mass of the individual star, or am i using the wrong formulas?

for the other part would i use @=r/d were r =(a(1-e))/1+ecos e would be 1 because its a circular orbit right?
But not sure what @ would be the angular distance or i use some other formula?

Last edited:

#### Quinzio

I would say they have circular orbits, I'm not sure. Let's assume so.

You've got the instant speed of the stars, then the period of revolution (3.686d).
We can easily found their circumference, and their radii.

Given that, by calculating the ratio of the centrifugal forces, you should have a ratio of the masses.
Gravitational force must compensate centrifugal force, and this will give a product of the 2 masses.
Then you should have all to find the two masses.

#### leonne

ok thxs ill try it out, ill post if i get it or not. yea saw a ratio like v1/v2=m2/m1

#### leonne

ok so here is what i figured out , using centrifugal forces formula i got m=(4v^2 *R)/G

R=a(1-e^2)/1+ecos@ Its a circular orbit so the e is 0 not 1 like i said in first post so a=r
then i do the same thing for the other star

thxs for the tip

#### leonne

um wait would R=a(1-e^2)/1+ecos@ be distance between the two star? looking picture of a binary orbit and showed like R being the distance between the 2 stars

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving