<p>The <a href="https://en.wikipedia.org/wiki/Galactic_coordinate_system" rel="nofollow noreferrer">galactic coordinate system</a> is centred on the sun with the xy plane in the plane of the galaxy and the x coordinate pointed towards the centre of the galaxy.</p>

<p>Since it is a heliocentric system the Euclidian distance is $\sqrt{x^2+y^2+z^2}$.</p>

CC BY-SA 4.0
2018-06-29T18:46:55.637Z
The Galactic coordinate system has two numbers, not three; it is an angular system, not a Cartesian system.
Peter Erwin
CC BY-SA 4.0
2018-06-29T19:55:38.203Z
UVW is how cartesian coordinates are usually referred to in the galactic frame. It is possible that the OP means "xyz relative to the centre of the galaxy", if so I'll delete this.
James K
CC BY-SA 4.0
2018-06-30T09:37:53.603Z
UVW refers to *velocities*, not positions.
Peter Erwin
CC BY-SA 4.0
2018-06-30T10:32:34.053Z
Having said that, yes, there are occasional uses of a "galactocentric" Cartesian system like what you describe, so in the absence of any more information from the  person asking the question, that's probably a reasonable answer.
Peter Erwin
CC BY-SA 4.0
2018-07-02T22:55:18.140Z
@Peter Erwin there is an alternative galactic coordinate system to the (l,b) one you mentioned above. It is a Cartesian coordinate system in which location coordinates are (X,Y,Z) and velocity vectors are (U,V,W) with the sun at (0,0,0). The X axis passes thru the sun with the positive direction being toward the center of the galaxy. The X,Y plane is the "plane" of the galaxy (not well defined and the sun is chosen arbitrarily to be "above" the plane). The Y axis is perpendicular to the X axis, positive in the direction of galactic rotation. The Z axis is perpendicular to the plane.
Jack R. Woods
CC BY-SA 4.0
2018-06-29T14:45:58.563Z
2018-06-29T14:45:58.563Z
James K
<p>How can I get heliocentric distance to a star when I have galactic x y and z coordinates known ?</p>

CC BY-SA 4.0
2018-06-29T18:46:22.660Z
Can you give an example of what you mean by "galactic x y and z coordinates"? The standard Galactic coordinate system (*l*, *b*) only has two numbers, which are angular directions on the sky, as seen from the Earth.
Peter Erwin
<positional-astronomy>
Heliocentric distance from galactic x y and z coordinates
Anjali
# Heliocentric distance from galactic x y and z coordinates

(Asked by: username_0 on 2018-06-29)

How can I get heliocentric distance to a star when I have galactic x y and z coordinates known ?

**Tags:** positional-astronomy
> **Comments:**
> **username_1**: Can you give an example of what you mean by "galactic x y and z coordinates"? The standard Galactic coordinate system (*l*, *b*) only has two numbers, which are angular directions on the sky, as seen from the Earth.  

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## 1 answers

### Answer by username_2 on 2018-06-29. Score: 2

The [galactic coordinate system](https://en.wikipedia.org/wiki/Galactic_coordinate_system) is centred on the sun with the xy plane in the plane of the galaxy and the x coordinate pointed towards the centre of the galaxy.

Since it is a heliocentric system the Euclidian distance is $\sqrt{x^2+y^2+z^2}$.

> **Comments:**
> **username_1**: The Galactic coordinate system has two numbers, not three; it is an angular system, not a Cartesian system.  
> **username_2**: UVW is how cartesian coordinates are usually referred to in the galactic frame. It is possible that the OP means "xyz relative to the centre of the galaxy", if so I'll delete this.  
> **username_1**: UVW refers to *velocities*, not positions.  
> **username_1**: Having said that, yes, there are occasional uses of a "galactocentric" Cartesian system like what you describe, so in the absence of any more information from the  person asking the question, that's probably a reasonable answer.  
> **username_3**: @Peter Erwin there is an alternative galactic coordinate system to the (l,b) one you mentioned above. It is a Cartesian coordinate system in which location coordinates are (X,Y,Z) and velocity vectors are (U,V,W) with the sun at (0,0,0). The X axis passes thru the sun with the positive direction being toward the center of the galaxy. The X,Y plane is the "plane" of the galaxy (not well defined and the sun is chosen arbitrarily to be "above" the plane). The Y axis is perpendicular to the X axis, positive in the direction of galactic rotation. The Z axis is perpendicular to the plane.  

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