Prove that if the spectrograph slit is set along the equator of a rapidly rotating planet and our line of sight lies in the plane of this equator

Prove that if the spectrograph slit is set along the equator of a rapidly rotating planet and our line of sight lies in the plane of this equator, then the spectral lines have the form of straight lines inclined to the extent of the spectrum.

The angular velocity of rotation is constant, a v = wr. Therefore, the Doppler shift is proportional to the distance from the center of the disc.

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