# Calculating the angular momentum of stars from Gaia archive (Gaia DR3)

I am trying to calculate the angular momentum for a subset of stars from Gaia DR3. I have scanned the available fields in their database and could only find out the below fields that specifies the position of the stars,

• ra, dec: In barycentric coordinates
• l, b: Galactic longitude and latitude respectively
• ecl_lon, ecl_lat: Ecliptic longitude and latitude respectively

Similarly, we have the following fields that specifies velocities of the stars,

• pmra, pmdec: Proper motions along ra and dec respectively.

From elementary mechanics, angular momentum,

$$L_{ang} = mv\times r$$ and if I am interested in the specific angular momentum, I divide the angular momentum by $$m$$ giving me a the expression $$L_{ang} = v\times r$$ where $$r$$ is the distance of the object (stars in my case) from the center of mass (LSR and galactic center in my case).

I must calculate the angular momentum in both the LSR frame (Local Standard of Rest frame) and Galactocentric coordinates. I have the below questions,

1. Any idea how do I map the available data in Gaia to the expressions from mechanics?
2. Assume that my reasoning is not right, is there an alternative way to calculate the angular momentum of the stars from the available stars?
• Just to be sure I understand: you want to calculate the angular momentum of stars around the galactic center, not how fast the stars are spinning around their own center, correct? Since angular momentum would require knowing the mass (which you may be able to estimate from other fields), did you mean the angular speed times the distance or something? Jul 23, 2022 at 16:36
• Transform the velocities and positions into vectors in a galactocentric coordinate system. Jul 23, 2022 at 18:35
• @barrycarter You are right. I am not concerned about the mass because that is irrelevant. The quantity I am interested in is the angular momentum divided by the mass. Jul 24, 2022 at 6:03
• @ProfRob: I should have been explicit in my question. Yes I understand, I need transformations. The problem is I do not know what transformations to use. Do you have a reference or a worked out example perhaps? This would help me get understand the transformation. Jul 24, 2022 at 6:05
• You'd need the distance as well, which you can get from parallax values. We don't have an accurate idea of how far we are from the center of the galaxy, but you could estimate. After all that, you could just create a coordinate system and work through the math. Feel free to chat me for more help/details. Jul 24, 2022 at 10:29