Milky Way Galaxy centerline in its RA and DEC

[Philosophaie]

The Milky Way Galaxy encircles the globe with its gas and debris.
The center of the galaxy is at "Sagittarius A" located at a distance of 35,900 ly @ Right Ascension = 266.417 deg and 29.00781 deg.
It propagates out from there and encompasses our solar system and beyond.
We are on the outer limits of the galaxy.
I know our galaxy is warped but there must be a centerline.
Is there a way of calculating this centerline in its Right Ascension and Declination components?

[Nitpicker]

We are not at the outer limits of the Milky Way and I'm not sure I'd call it warped. We are about halfway out from the centre.

There is a galactic coordinate system which has the Sun at the origin for our convenience, and (0°, 0°) defined as the direction towards Sgr A*. The line of 0° galactic longitude could be considered the axis of the Milky Way, as it appears in the sky to us. The line of 0° galactic latitude is known as the Galactic Equator.

I'm not sure which centreline you are interested in.

[Philosophaie]

I am referring to the center of mass or galactic ecliptic type (not with the sun) centerline of the galaxy.

[Nitpicker]

I am referring to the center of mass or galactic ecliptic type (not with the sun) centerline of the galaxy.

You are mixing up your terms a little, from my point of view. I don't know what you are asking. But in our sky, it could only be galactic latitude zero, or galactic longitude zero, as I've already described them. These are lines in galactic coords. They do not relate to single points in celestial (RA,DEC) coords.

[Philosophaie]

Do the Galactic Coordinates have the Sun on the Galactic Latitude=0 as the Sun and Earth Elliptic? I understand that RA and DEC are Sun based quantities and are just points of reference. I am just looking for a mathematical model in RA and DEC for how the Milky Way goes across the sky.

Here are the 4 corners of the Milky Way Galaxy with 0degrees at Sagittarius, 90degrees at Coma Berenices, 270degrees at Sculptor and 180degrees at Auriga
This is the galactic plane with sun at 0degrees facing the center, 90degrees is perpendicular to galactic center, 180degrees facing away from the galactic center.

north pole (+90° latitude) 12h 49m
(12h 51m.4)
+27°.4
(+27°.13)
Coma Berenices

south pole (-90° latitude) 0h 49m
(0h 51m.4)
-27°.4
(-27°.13)
Sculptor

galactic center (0° longitude) 17h 42m.4
(17h 45m.6)
-28°.92
(-28°.94)
Sagittarius

anti-center (180° longitude) 5h 42m.4
(5h 45m.6)
+28°.92
(+28°.94)
Auriga

[Nitpicker]

Do the Galactic Coordinates have the Sun on the Galactic Latitude=0 as the Sun and Earth Elliptic? I understand that RA and DEC are Sun based quantities and are just points of reference. I am just looking for a mathematical model in RA and DEC for how the Milky Way goes across the sky.

Here are the 4 corners of the Milky Way Galaxy with 0degrees at Sagittarius, 90degrees at Coma Berenices, 270degrees at Sculptor and 180degrees at Auriga
This is the galactic plane with sun at 0degrees facing the center, 90degrees is perpendicular to galactic center, 180degrees facing away from the galactic center.

north pole (+90° latitude) 12h 49m
(12h 51m.4)
+27°.4
(+27°.13)
Coma Berenices

south pole (-90° latitude) 0h 49m
(0h 51m.4)
-27°.4
(-27°.13)
Sculptor

galactic center (0° longitude) 17h 42m.4
(17h 45m.6)
-28°.92
(-28°.94)
Sagittarius

anti-center (180° longitude) 5h 42m.4
(5h 45m.6)
+28°.92
(+28°.94)
Auriga

Galactic coords have the Sun as the origin, with Sgr A* (centre of Milky Way) in the (0,0) lat/long direction. The galactic north-south pole you have listed above, passes through the Sun, not through the centre of the galaxy. But it is independent of the Sun-Earth ecliptic.

Celestial coords (which can be either geocentric or tropocentric) are not Sun based and are also independent of the Sun-Earth ecliptic. They are aligned with the rotational axis of the Earth, so are convenient in relation to Earth's daily rotation. The celestial equator is a projection of Earth's equatorial plane into space. The celestial plane is inclined to both the ecliptic plane and the galactic plane.

[Nitpicker]

When a sky map is projected orthographically in celestial coordinates (RA,DEC), the ecliptic and galactic planes appear as (different) sinusoidal curves on the map. Is this what you mean?