Expert: Philip A. Stahl - 11/3/2009

Question
Can you help with this problem?  A visual binary has a period of 100 years, and the semi-major axis of the relative orbit is 1."00.

If one of the stars is identical to the Sun and has an apparent visual magnitude of +8.0, what is the mass of the other star?

Thanks!

Answer
Hello,

This looks like a fairly basic HW problem, so I will just get you oriented to solving it yourself. If you need more help after my hints, you can get back to me.

First, if one of the stars is *identical* to the Sun, it means it must have the same absolute magnitude, M = +4.8.

You will also need the distance modulus in this problem, and you will find an illustrated example of it in the latter part of a previously addressed problem here:

http://en.allexperts.com/q/Astrophysics-3368/Gray-atmosphere-distance-modulus.ht...

Now, for a semi-major axis in astronomical units A, and for which a" denotes the angular separation, one has:

A = a"/p

The only thing remaining is to relate A to the period P, and the sum of masses of the system (M1 + M2) using Kepler's law relating the period squared to the semi-major axis cubed.

I believe you ought to be able to get it from here. If you want you may send the solution and I will tell you if you are on the right trail, have it correct...or not.