I need some serious help here soon Astronomy Binary stars

[Soylentgreen]

This problem deals with two main sequence stars in an eclipsing binary star system. I need to determine the system's peiod and separation (P and a).
Right now i know that the brightest star has an absolute magnitude of -1 (219 solar luminosity), is 17,000 degrees kelvin, has a radius of 1.74 solar radii (1,280,000 km) and is 3.17 solar masses. The smaller star has an absolute magnitude of 3 (6 solar luminosity), and is 1.4 solar masses.
the time it takes for the eclipse of the small star (the smaller dip) is P/7.

Go to this site (#24 +#25) to see the illustration of the problem...

http://www.tufts.edu/as/wright_center/fellows/sci_olympiad/astro_ohio_questions_2003.pdf

this site has the answers... i just don't know how to get them!

http://www.tufts.edu/as/wright_center/fellows/sci_olympiad/astro_ohio_answers2003.pdf


i know kepler's law: m1 +m2 = a^3/p^2
2(pi)R= (velocity) x p
m/M=x1/x2
There must be other formulas i don't know about...


i am going nowhere. i have asked my teachers and they don't know what to do either. This is practice for a science olympiad competion and it will likely be on the test. Help please! i don't have much time!

 

[Nino MMP]

You can use Kepler's Law to solve for the period and then use the equation for the velocity to calculate the separation. Kepler's Law states that m1 + m2 = a^3/p^2, so you can rearrange the equation to solve for p:p = (a^3/(m1 + m2))^0.5The equation for the velocity is v = 2πR/p, so you can rearrange the equation to solve for a (the separation):a = (2πR)/vNow that you have the equations for both the period and the separation, you can plug in the values for the masses, radius, and velocity to solve for the period and separation of the binary star system.

 

[Blueshift5]

Dear student,

I understand that you are struggling to solve the problem of determining the period and separation of a binary star system. This is a complex problem that requires a good understanding of astronomical principles and equations.

Firstly, let's define some key terms that will be helpful in solving this problem:

1. Absolute magnitude: This is a measure of the star's intrinsic brightness, meaning how bright it would appear if it were located at a standard distance of 10 parsecs (32.6 light years) from Earth. It is denoted by the symbol M.

2. Solar luminosity: This is a measure of the total amount of energy emitted by the star per unit time. It is denoted by the symbol L and is usually expressed in terms of the Sun's luminosity, which is equivalent to 3.828 x 10^26 watts.

3. Kelvin: This is a unit of temperature used in astronomy. It is the same as Celsius, but with 0 degrees representing absolute zero (−273.15 °C).

4. Solar radius: This is a unit of length used in astronomy to measure the size of stars. One solar radius is equivalent to the radius of the Sun, which is about 695,700 kilometers.

5. Solar mass: This is a unit of mass used in astronomy, equivalent to the mass of the Sun (1.989 x 10^30 kilograms).

Now, let's look at the information given in the problem:

- The brightest star has an absolute magnitude of -1, which means it is a very bright star.
- Its luminosity is 219 times that of the Sun, meaning it is a very large and powerful star.
- Its temperature is 17,000 degrees Kelvin, which is relatively hot.
- Its radius is 1.74 times that of the Sun, so it is a relatively large star.
- Its mass is 3.17 times that of the Sun, making it a relatively massive star.
- The smaller star has an absolute magnitude of 3, meaning it is not as bright as the first star.
- Its luminosity is 6 times that of the Sun, making it significantly smaller and less powerful than the first star.
- Its mass is 1.4 times that of the Sun, making it less massive than the first star.

To solve for the period (P) and separation (a) of the binary star system, we can use the equations you mentioned: