How can we determine the distance to the Galactic center?

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SUMMARY

The distance to the Galactic center can be determined using the "spectroscopic line shift of S2" and its "proper motion." The spectroscopic line shift provides the velocity of star S2 in km/sec, while proper motion indicates its angular motion in arcseconds/year. By measuring both parameters over time, one can solve for the two unknowns: the distance to the star and the inclination of its orbit relative to the line of sight. This method effectively combines dynamic measurements to yield precise astronomical distances.

PREREQUISITES
  • Understanding of Doppler effect and its application in astrophysics
  • Familiarity with angular measurements in arcseconds/year
  • Knowledge of orbital mechanics and inclination concepts
  • Basic proficiency in analyzing spectroscopic data
NEXT STEPS
  • Research the application of the Doppler effect in measuring stellar velocities
  • Learn about proper motion calculations and their significance in astronomy
  • Study orbital mechanics to understand inclination and its impact on distance measurements
  • Explore software tools for analyzing spectroscopic data and visualizing orbits
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Astronomers, astrophysics students, and researchers interested in stellar dynamics and distance measurement techniques in cosmology.

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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

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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?
 
Hello!
phyzguy said:
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?
 
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