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# Cartesian Coordinates in the Milky Way (M45)

### #1 dwyer2bp

dwyer2bp

Sputnik

• topic starter
• Posts: 43
• Joined: 04 Apr 2019

Posted 20 February 2020 - 11:43 AM

Hi Everyone,

I am trying to make some 3D plots of star clusters and wanted to see if anyone could sanity check my method for calculating (x, y, z) coordinates from Galactic coordinates, the Sun being (x=0, y=0, z=0). I am using a few of the brightest stars in M45 as my test objects. Let's use the star Alcyone as an example. Below is the Galactic Coordinates (from the SIMBAD database I believe):

ly = light years

Alcyone: Eta (25) Tauri

• Distance: 403 (+/- 50) ly
• Longitude (°, min, sec): (166, 40, 6.2)
• Latitude    (°, min, sec): (-23, 27, 19.1)

Converted into Spherical coordinate system, where (°, min, sec) is plainly converted to degrees:

• r = 403 ly
• b = angle latitude    = -23.46°
• l  = angle longitude = 166.67°

I thought I could convert this to Cartesian, in units of light-years (ly):

• x = r * cos(l) * cos(b)
• y = r * sin(l)  * cos(b)
• z = r * sin(b)

Using this, Alcyone's coordinates in ly become: (-359.7376898696, 85.2479782529, -160.4075331494)

Now for a test. I've done this for the brightest 11 stars in M45 and plot them in Octave (which is like Matlab only free). Here is a video illustrating what this looks like, along with a few screen-caps below:

Does any of this seem unreasonable?

Thanks

Brian

### #2 StupendousMan

StupendousMan

Mariner 2

• Posts: 211
• Joined: 21 Aug 2005

Posted 20 February 2020 - 01:31 PM

This is all very reasonable.  Carry on!

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