# Two body orbital system question

1. Jan 25, 2007

### ^_^physicist

1. The problem statement, all variables and given/known data
The observed period of the binary system Cygnus X-1, presumed to be a bright star and a black hole, is equal to 5.6 days. If the mass of the visable (the star) is 20*Mass of the Sun, and the black hole has a mass 16*Mass of the Sun, show taht the semimajor axis of the orbit of the black hole relative to the visable star is roughly 1/5 the distance from the Earth to the sun.

2. Relevant equations
Period (using AU) relationship to semimajor axis of a system

T = [m,sub 1 + m, sub 2]^(-1/2)*a^3/2, where 'a' is the semi-major axis and both values of 'm' are given in units of mass of the sun.

Reduced mass: (m,sub 1)*(m,sub 2)/((m, sub 1)+(m, sub 2))

Postion vector of particle 1 relative to particle 2

R= (r(from center of mass), sub 1)*(1+ ratio of masses)

3. The attempt at a solution

I am not entirly sure where to go with this, however, I did calculate some values so far:

u= 8.888*Mass of Sun
a= .020384 AU, note that the value of this semi-major axis is for the binary system as a whole, not relative to either one of the points.

Any ideas where to go with all of this?

(I am still working at it, but a hint would be nice)

2. Jan 26, 2007

### Kurdt

Staff Emeritus
Binary stars obey Kepler's laws.

3. Jan 27, 2007

### ^_^physicist

I will be retracting my question....

After stareing at the question for a good 3 hours, my brain kicked in and noticed that I had done a simple math mistake (seriously, I moved the decimal place over 1 too many). I guess thats what I get when I do homework late at night.

sorry of the stupid question.