# Geocentric Ecliptic to Perifocal Coordinate Transformation

I'm self-studying elementary orbital mechanics and am experimenting with transforming satellite position and velocity vectors between different coordinate systems. I know there are coordinate transformation matrices between Geocentric Ecliptic and Geocentric Equatorial coordinates (simple rotation around one axis), and between Geocentric Equatorial and Perifocal (P, Q, W) coordinates (utilizing inclination, longitude of the ascending node, and argument of periapsis data). But I can't seem to develop a single coordinate transformation matrix from Geocentric Ecliptic directly to Perifocal. Is there an Euler angle rotation sequence that accomplishes this?

## 1 Answer

After thinking about this problem further I finally figured out that making the coordinate transformation from ecliptic to perifocal is nearly the same as from geocentric to perifocal. The only difference is that you use an inclination value 23.4 degrees less, which is the angle between the ecliptic plane and the equatorial plane. Not sure why I didn't see in the first place.

• Don't forget to check your answer as accepted so they close the question. Commented Jun 3, 2019 at 23:21