Are there two mean Suns? In the book I'm reading, the authors appear to refer to a mean Sun on the ecliptic moving in a circular orbit with constant angular velocity and with the same orbital period as the true Sun. This mean Sun is used to calculate the position of the Sun in its apparent orbit around the Earth. And then they refer to another (?) mean Sun on the celestial equator, again moving with constant angular velocity. This mean Sun is used to define mean solar time. I'm confused.
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1Yes. See the end of my answer here: https://astronomy.stackexchange.com/a/48253/16685 – PM 2Ring Oct 11 '22 at 07:21
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When computing an orbit you use the "mean anomaly", you could call that a "mean sun", or "mean [whatever object]", but it's usually referred to as the mean anomaly to avoid confusion. The book isn't wrong, it's just that's not the terminology used by most people, the author is probably doing it that way to simplify the terminology. But "mean sun" pretty much always refers to mean solar time. – Greg Miller Oct 11 '22 at 12:20