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An example of an advantage of equatorial coordinates with respect to azimuthal coordinates is that
The equatorial coordinates are much easier to calculate as they only depend on measurement with respect to the horizon
The equatorial coordinates do not change when the sky rotates, and therefore the equatorial coordinates of a star do not change when observing the sky from different planets of the solar system
The equatorial coordinates of a star do not change when observing the sky at different latitudes on Earth
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