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Due to Earth's axial tilt, the Sun's annual motion is along the ecliptic that is tilted to Earth's celestial equator.

When the Sun crosses the equator at both equinoxes or solstices, the Sun's daily shift is at an angle to the equator, so we have to do the projection of this shift onto the equator.

We like our clocks to run at a constant rate, so we cannot set them to follow the actual sunâ€”instead they will follow a nonexistent object called the "mean sun" that moves along the celestial equator at a constant rate that matches the real sun's average rate over the year.

Question is : why introducing a mean sun moving along the equator instead of a mean sun moving along the ecliptic ? Moving along the ecliptic needs to do a projection.

With a mean sun moving along the ecliptic, no need for projection, only one effect remains in the computation of the equation of time : Earth's elliptical orbit.

In this way, it would be easier, no ?

Thanks

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# Mean sun moving along equator

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