- #1

Unteroffizier

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__Problem:__

We have binary star system consisting of Star A and Star B. Astronomers have observed it for 11 years, during which it has moved from point A to point B. The major axis "a" = 4.5 degrees.

Relative magnitudes of A and B are 3.9 and 5.3 respectively. The system is being observed from a right angle (from the top, which means no transits, no magnitude shifts and no Doppler effect).

The orbits were converted into a simpler, Keppler-like system beforehand, where the motion of Star B is relative to Star A. Therefore, only Star B is in (relative) motion to simplify.

Find:

a) The orbital period of B star.

b) Absolute magnitude.

c) Distance from observatory.

__Relevant Equations__

Kepler's Second Law

Looping mass equation

Trigonometric functions (tg)

Area equation (ab*(arccos*h/a - h/a^2*sqrrt(a^2 - h^2)))

M = m + 5 - 5log (d)

__Solution Attempt__

I have not yet done the mathematics required to come up with valid results, but here is how I wish to continue. I only wish to know if I have the right idea, and if not, what I should change, so that I do not waste time, as I must focus on my mechanical engineering high school course as well.

a) Find absolute magnitude using "M=m+5-5log(d)" where m=ma+mb. I do not know if relative magnitudes of both stars add together to form one relative magnitude, or if ma = m.

**Need clarification**

b) Knowing absolute magnitude, find distance. If absolute magnitude = "n" at "d=10pc", then it should be simple mathematics to find "d."

c) Use tg of 4.5 and "d" to find physical length of apastron "a", the major axis.

d) Use distance between two points Star B traveled to calculate area in relation to 11 years and use Kep. 2. law to find "T" period.

e) Write excel program to continually calculate mass of stars, where Input 1 assumes that total system mass M = 2 solar masses, slowly gaining more precise results with every cycle. I do not have the equation cycle on hand, but I will find it eventually.

We are technically not meant to find the masses of the stars, but he gave us said equation, and told us to use it, and so I will.

Am I on the right track? Any fallacies?