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Planetary Rotation

Suppose that the planet is rotating rigidly about the axis $ \theta=0$ at the angular velocity $ {\mit\Omega}$ (where $ {\mit\Omega}\gg \omega_1$ ). The planet's rotational angular velocity vector is thus

$\displaystyle \mbox{\boldmath$\Omega$}$$\displaystyle = {\mit\Omega}\,\cos\theta\,{\bf e}_r - {\mit\Omega}\,\sin\theta\,{\bf e}_\theta.$ (12.43)


$\displaystyle \phi = \varphi - {\mit\Omega}\,t.$ (12.44)

It follows that $ r$ , $ \theta $ , $ \phi$ are spherical coordinates in a frame of reference that co-rotates with the planet.

Richard Fitzpatrick 2016-03-31