Eclipsing binary problem im really frustrated

[Soylentgreen]

Eclipsing binary problem! I am really frustrated!

I have been looking at this problem for a while and i am really getting frustrated. I asked my astronomy teacher, but we are both stumped. This isn't graded, but i really need to learn how to do it for science olympiad.

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!

 

[Chronos]

It looks like qustion 1 should be the apparent magnitude of star Q, not R. It also appears, based on the answer, that Q4 also is in reference to star Q. The first step is to deduce the absolute magnitude of R. This is easy. Since the luminosity of R is 5x solar, you merely subtract log[5] from the sun's absolute magnitude [4.8]. I get 4.1. Since you also know the apparent magnitude of R [11.6], the distance to R is also easily derived from the difference between absolute and apparent magnitudes [luminosity falls off with the square of the distance]. The absolute magnitude of star Q can then be rougly calculated [starting with the assumption it is roughly the same distance as R]. Knowing the mass of R and periodicity of the orbit you can apply Kepler's law to roughly figure to separation between the two stars. It does, however, require you to make certain assumptions about star Q, since virtually no information is provided other than luminosity. I would be inclined to assume both stars had similar mass-luminosity ratios, in which case the answer to question 2 looks like it is in the right ballpark.

 

[Soylentgreen]

cool. thanks for your help dude

 

[Kurdt]

I'd get a new astronomy teacher. As chronos pointed out the question is mainly to do with the equations concerning magnitudes and Kepler's laws.