Physics/astronomy eclipsing binary problem help

[Soylentgreen]

physics/astronomy eclipsing binary problem! help!

I have been looking at this problem for a while and i am really getting frustrated.

Here it is. I have an eclipsing binary system with a period of 1 year. Star Q has 800 solar luminosities, while the other star, star R, has 5 solar luminosities.
the radius of star R is 1,000,000 km, and it is .75 solar masses. Its apparent magnitude is 11.6.
It does not say whether or not the stars are main sequence.

a) what is the apparent magnitude of star R?
b) what is the separation of the two stars in km
c) what is the distance to the star system in parsecs.
d) what is the absolute magniude of star R.the answer for the above questions are as follows:
a) 5.8-6.3
b) 7-8x 10^9 km
c) 470-530 parsecs
d) 2.8-3.4

i have the answers but i don't know how to get to them and i have been trying for over an hour and a half. please help someone!

 

[denverdoc]

probably not the best place to post this problem.

 

[m2003]

Hello,

I understand that you are struggling with the eclipsing binary problem in physics and astronomy. Let me try to provide some guidance to help you solve this problem.

First, let's break down the information provided. We have an eclipsing binary system with a period of 1 year. This means that the two stars orbit each other once every year. We also know the luminosity of each star, with star Q being 800 solar luminosities and star R being 5 solar luminosities.

Next, we are given the radius of star R, which is 1,000,000 km, and its mass, which is 0.75 solar masses. We also know its apparent magnitude, which is 11.6. However, we are not given any information about the main sequence status of the stars.

To solve this problem, we need to use some equations from physics and astronomy. First, we can use the relationship between luminosity, apparent magnitude, and distance to calculate the distance to the star system. This equation is:

m - M = 5log(d/10)

Where:
m = apparent magnitude of the star
M = absolute magnitude of the star
d = distance to the star in parsecs

Since we know the apparent magnitude of star R (11.6) and we are trying to find the distance, we can rearrange the equation to solve for d:

d = 10^((m-M+5)/5)

Substituting the values we have for star R, we get:

d = 10^((11.6-M+5)/5)

We also know that the absolute magnitude of the star is related to its luminosity by the equation:

M = -2.5log(L/L_sun)

Where:
L = luminosity of the star
L_sun = luminosity of the Sun (3.828 x 10^26 watts)

Substituting the values for star R, we get:

M = -2.5log(5/3.828 x 10^26)

M = -2.5log(1.307 x 10^-26)

M = 2.5 x 26.883

M = 67.207

Now we can substitute this value for M in the equation for distance and solve for d:

d = 10^((11.6-67.207+5)/5)

d = 10^(-50.