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Originally Posted by oriel36
Hey, if you believe that the combined rotations of the Earth,the axial and annual orbital cannot be seperated (this is what the EoT does) ,good for you,in fact you will be following in the footsteps of your mentor Albert .
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(emphasis mine)
Check your sources, oriel36. The Equation of Time does not do what you think it does - all it does is average the effects of orbital obliquity and eccentricity over a year. It doesn't relate the lengths of the sidereal and solar days - it relates the individual and average solar day. The length of an individual day is what you call the "natural, unequal day" and depends on where the Earth is in its orbit. The average solar day is simply this span of time averaged over a year. We on this forum normally talk only about the averaged timespan; few of us ever determine positions by measuring the sun's height, but if we ever did, yes, the EoT would be very important.
However, when I'm looking at stars, tthe individual solar day is of no interest; I'm more interested in position relative to the other stars. So the relation of interest is that between the averaged solar day ("clock time") and sidereal time. The EoT does not enter into this at all.