How to find the distance from a star to the center of the Milky Way Galaxy?

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SUMMARY

The distance from the Galactic Center to the Sun is approximately 8.2 kiloparsecs. To calculate the distance of a star from the Galactic Center, one must use the star's Galactic Latitude, its distance from the Sun, and the known distance from the Sun to the Galactic Center. The calculation involves forming a triangle with the Sun, the star, and the Galactic Center, where the lengths of two sides and the included angle can be determined using data from sources like the Gaia database and online calculators. The law of cosines is then applied to find the distance from the star to the Galactic Center.

PREREQUISITES
  • Understanding of Galactic Latitude and Distance measurements in parsecs
  • Familiarity with trigonometry, specifically the law of cosines
  • Knowledge of star coordinates: Right Ascension (RA) and Declination (Dec)
  • Access to astronomical databases such as Gaia and Exoplanet Archive
NEXT STEPS
  • Research how to use the Gaia database for stellar distance and position data
  • Learn about the law of cosines and its application in astronomical calculations
  • Explore online calculators for angle calculations in celestial geometry
  • Study the geometry of triangles in the context of astronomical distances
USEFUL FOR

Astronomers, astrophysicists, and students studying celestial mechanics or stellar distances will benefit from this discussion.

Michael_L
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TL;DR
How to find a distance of a star to the center of the Milky Way Galaxy? Given the astronomical data of a star in the catalogues, how to calculate it's radial separation from the center?
The distance of the sun to the Galactic Center is about 7.4–8.7 kiloparsecs.
If I use the known data of stars in various stellar catalogues, how can I calculate (approximately) a distance of a given star from the Center? What kind of data I need to look for? can it be calculated from Right ascension and Declination?
 
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Michael_L said:
can it be calculated from Right ascension and Declination?

No. That gives you a line and the star can be anywhere on that line. The points on that line are of varying distance to the center.
 
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Vanadium 50 said:
No. That gives you a line and the star can be anywhere on that line. The points on that line are of varying distance to the center.

Ok, I see. So what do I have to do to calculate it? The info I have can be found here:
https://exoplanetarchive.ipac.calte...erview/nph-DisplayOverview?objname=TRAPPIST-1
I got some idea:
"Distance (pc)" is calculated from the Sun, and not from the center. But if I have: Galactic Latitude (deg), Distance (pc) and the distance from the Sun to the center, so the distance from the center to a star can be calculated. Right?
We have a triangle with one known angle and two vertices.
 
Michael_L said:
Summary:: How to find a distance of a star to the center of the Milky Way Galaxy? Given the astronomical data of a star in the catalogues, how to calculate it's radial separation from the center?

The distance of the sun to the Galactic Center is about 7.4–8.7 kiloparsecs.
If I use the known data of stars in various stellar catalogues, how can I calculate (approximately) a distance of a given star from the Center? What kind of data I need to look for? can it be calculated from Right ascension and Declination?
Hi Mike:

I suggest you start by taking a look at
The first paragraph says
The Galactic Center (or Galactic Centre) is the rotational center of the Milky Way galaxy... It is 8.2 ± 0.4 kiloparsecs (26,700 ± 1,300 ly) away from Earth in the direction of the constellations Sagittarius, Ophiuchus, and Scorpius where the Milky Way appears brightest.​
You need to calculate the shape of a triangle with the sun at corner A, the star of interest at corner B, and the galactic center at corner C. The length AC is above, and the length AB should be available from on-line facts about the star. The angle BAC can be calculated from given positions is the sky for B and C. From that you can calculate the distance BC.

Good luck.

Regards,
Buzz
 
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Buzz Bloom said:
You need to calculate the shape of a triangle with the sun at corner A, the star of interest at corner B, and the galactic center at corner C. The length AC is above, and the length AB should be available from on-line facts about the star. The angle BAC can be calculated from given positions is the sky for B and C. From that you can calculate the distance BC.
I think it could be down to simple trigonometry. If you have the two distances and the included angle than the third side of the triangle can be calculated. This presupposes you know the angle to within the accuracy you need for your calculation. The angle could be found from similar sources as the two distances (or a galactic map and a protractor) Did you want to get the angle from actual observation?)
 
The ABC angle is the real challenge here. It is not an easy transformation form observed angles (alpha and delta) to galactocentric angle.
 
The Gaia project data contains everything you need to know. All the stars you could want to know about are on the (freely available ) ESA database. Their positions are all available - but you will need to dig down below the level of their lovely pictures. No geometrical activity needed, I think.
Give it a try
 
Hi, do anybody know probably there is some online calculator which calculate distance? smile3.png
 
Michael_L said:
The ABC angle is the real challenge here. It is not an easy transformation form observed angles (alpha and delta) to galactocentric angle.
There are calculators to do this ABC angle calculation for you, like this one. The Galactic center is at Sagittarius A*, so is at RA=17h45m40s, Dec=-29d0m28s. As has been said, the distance to the Galactic center is 8.2 kpc. Then you need the RA and Dec of the star you are interested in, and use the above starAngleCalc to get the angle ABC.* Then you just need the distance to the star you care about, which as @sophiecentaur said you can get from the Gaia database. Then you just use the law of cosines to get the distance of your star from the Galactic center.

*Edit. This will actually give you the angle BAC as defined in Post #4.
 
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