Stellar Data
"The goal is to transform data into information, and information into insight." ~ Carly Fiorina[7]
In order to even start looking for data, we need to think about what we need to know. Our model requires the distance from the galactic center and linear velocity about the galactic center. Since we are looking at the stars not from the galactic center, but relative to us, we need to know the position of the star and galactic center relative to us. We will also need our motion about the galactic center and the star's motion which will also be relative to us. The position of our sun relative to the galactic center, Ro, is a constant maintained by the International Astronomical Union, IAU, to be 8.5 kpc (about 27,700 lightyears)[1]. Likewise the IAU defines our motion about the galactic center, Vo, to be 220 km/s (about 490,000 mph). Therefore we need a catalog that has the motion of the star relative to us, Vr, the distance the star is away from us, r, and the direction to the star, l.
The stellar data we are going to use is from the paper Kinematic data for O-B5 stars by Dr. Rubin[4], which is easily obtained from the VizieR catalog service; catalog V/31A. This paper contains the information we need for 897 stars, which should give us a decent idea of what is going on.
Now all we need to do is relate Vr, r, and l to V and R. Looking at the sketches of our galaxy below
where r' is the distance to the right triangle drawn, Vop is the sun's velocity towards the star, Vot is the sun's tangential velocity to the star, Vp is the star's velocity directly away from the sun, and Vt is the star's tangential velocity from the sun. Using some geometry, sine and cosine properties, and vector identities, we can easily derive
and
Now that we have these two equations and our mass equation, we can simply plug in the the numbers for each star and analyze our results.