<p>A reference frame that has its Z axis fixed with respect to the Earth's rotation axis is not inertial. The Earth's rotation axis undergoes precession and nutation, and on a shorter term, undergoes polar motion as well.</p>

CC BY-SA 3.0
2018-03-16T04:07:14.617Z
What is the method then?
Tarlan Mammadzada
CC BY-SA 3.0
2018-03-16T15:53:38.857Z
@TarlanMammadzada -- You need to get ephemeris data to find the change in the axis of the earths rotation since the epoch of the ECI frame, and apply that change to the result of the calculation you describe in the question.
antlersoft
CC BY-SA 3.0
2018-03-16T02:27:56.230Z
2018-03-16T02:27:56.230Z
David Hammen
<p>How to perform the conversion of (r,v) vector from ECEF to ECI (J2000) coordinate frame?</p>

<p><strong>What I tried</strong></p>

<p>I multiplied the matrix ([cosA -sinA 0] [sinA cosA 0] [0 0 1]) by the state vector, where A is Greenwitch mean sidereal time.</p>

<p>This equation shows that the Z axis doesn't change. However, I have the ephemeris of a real satellite in both coordinate frames, and there Z axis differs! 
Where is the issue?</p>

<coordinate><frame-of-reference>
ECEF to ECI conversion
Tarlan Mammadzada
# ECEF to ECI conversion

(Asked by: username_0 on 2018-03-15)

How to perform the conversion of (r,v) vector from ECEF to ECI (J2000) coordinate frame?

**What I tried**

I multiplied the matrix ([cosA -sinA 0] [sinA cosA 0] [0 0 1]) by the state vector, where A is Greenwitch mean sidereal time.

This equation shows that the Z axis doesn't change. However, I have the ephemeris of a real satellite in both coordinate frames, and there Z axis differs!
Where is the issue?

**Tags:** coordinate, frame-of-reference

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## 1 answers

### Answer by username_1 on 2018-03-16. Score: 1 | Accepted answer

A reference frame that has its Z axis fixed with respect to the Earth's rotation axis is not inertial. The Earth's rotation axis undergoes precession and nutation, and on a shorter term, undergoes polar motion as well.

> **Comments:**
> **username_0**: What is the method then?  
> **username_2**: @TarlanMammadzada -- You need to get ephemeris data to find the change in the axis of the earths rotation since the epoch of the ECI frame, and apply that change to the result of the calculation you describe in the question.  

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