How can we determine the distance to the Galactic center?

[arcTomato]

Homework Statement

We can use "spectroscopic line shift of S2" and "its proper motion", but I don't have any idea what dose this sentences mean.
please show me details!!

Relevant Equations

spectroscopic line shift

Problem Statement: We can use "spectroscopic line shift of S2" and "its proper motion", but I don't have any idea what dose this sentences mean.
please show me details!
Relevant Equations: spectroscopic line shift

 

[phyzguy]

The "spectroscopic line shift" is the shift in spectral line frequency due to the Doppler effect. It tells you the velocity of the star S2 towards or away from us in absolute terms, meaning in km/sec. The "proper motion" is the apparent motion of the star on the sky, which you can see in the right hand plot you supplied. It is an angular motion, so has units like arcseconds/year. There are two unknowns, the distance to the star, and the inclination of the orbit to the line of sight. If you have both measurements as a function of time, you can solve for both unknowns. Does this help?

 

[arcTomato]

Hello!

There are two unknowns, the distance to the star, and the inclination of the orbit to the line of sight. If you have both measurements as a function of time, you can solve for both unknowns.

Please,Could you show me details how to solve??
I know the period , the velocity provided by "spectroscopic line shift" , and the apparent motion, right??
And, Is this Fig(c) the apparent orbit?