Rotation of Earth

The Earth-rotation vector resolved in an ECI or ECEF frame is:

\[ \boldsymbol{\omega}^i_{ie} = \boldsymbol{\omega}^e_{ie} = \left[ \begin{array}{c} 0 \\ 0 \\ \omega_{ie} \end{array} \right]. \]

Resolving the Earth-rotation vector into local navigation frame axes yields to:

\[ \boldsymbol{\omega}^{n}_{ie} = \left[ \begin{array}{c} \omega_{ie} \text{cos}L_b \\ 0 \\ -\omega_{ie} \text{sin}L_b \end{array} \right]. \]

For navigation, a constant rotation rate is assumed and the WGS 84 value of the Earth's angular rate is \(\omega_{ie} = 7.292115 \times 10^{-5}\) rad/s, which is about 15 degrees per hour.