# Calculate the masses of two binary stars

• leonne
In summary, we discussed a binary star system called WR-20a which is located in the Large Magellanic Cloud and has two stars moving in circular orbits with observed speeds of 362.2 km s^-1 and 366.4 km s^-1 in an orbital period of 3.686 days. To calculate the masses of the two stars, we used the centrifugal forces formula and found a ratio of the masses using the ratio of the speeds. We also used the formula R=a(1-e^2)/1+ecos@ to determine the distance between the two stars in a circular orbit.
leonne

## Homework Statement

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?

## Homework Equations

Vn=(2pie*an)/p ,p^2=(4pie^2 /G(m1+m2)) A^3
A=a1+a2

## 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:
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.

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

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

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

## 1. How do you calculate the masses of two binary stars?

To calculate the masses of two binary stars, you need to first measure their orbital parameters, such as the period, semi-major axis, and eccentricity. Then, using Kepler's laws and Newton's law of universal gravitation, you can derive an equation to calculate the masses of the stars.

## 2. What is the significance of calculating the masses of binary stars?

Calculating the masses of binary stars is important because it can provide information about the stars' evolution, structure, and properties. It can also help us understand the dynamics of the binary system and its formation.

## 3. Can the masses of binary stars change over time?

Yes, the masses of binary stars can change over time due to various factors such as mass transfer, stellar winds, and gravitational interactions with other stars. This can affect the binary system's stability and evolution.

## 4. Are there any limitations or uncertainties in calculating the masses of binary stars?

Yes, there are limitations and uncertainties in calculating the masses of binary stars. These can include observational errors, uncertainties in the orbital parameters, and the complexity of the binary system. It is important to take these into account when interpreting the results.

## 5. What is the difference between equal-mass and unequal-mass binary stars?

Equal-mass binary stars have two stars with similar masses, whereas unequal-mass binary stars have a more massive primary star and a less massive secondary star. The masses of unequal-mass binary stars can affect the orbital parameters and dynamics of the system.

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