Solar orbit

2017

The sun spends more less time near the sun around the winter solstice than during the summer solstice. The sun may also be further away during that time because eclipses are more likely to be annular in summer than in winter. (but this is a small effect). It is not clear that Hyparchus could have noticed this as there are only about one central eclipse near Greece in a hundred years, so it is hard to get statistics. Ie, the sun goes through the sky faster in winter than in summer.

Note from the times, the sun seems to go fastest in the winter to spring, than in the fall to winter-- not by much. This suggests that the sun is going fastests just after Christmas. (It actually happened at around Jan 6, but they could not have measured that. That is also when the sun is largest in the sky. It's diameter is about 3% larger (in diameter) then than in mid-summer. Again this would have been impossible for them to measure.).

Mean Sun

The mean sun is the location of the sun IF it travelled at a constant angular rate through the sky, not going faster in winter than in summer. The mean sun lags and leads the real sun along the eciptic by about 5 min of time at maximum lead/lag (just over one degree along the ecliptic) If one measures time by a sundial, the relation of the sundial time to the clock time is that the clock time is assumed to tick equally throught the year. The sun however is a bit slow and a bit faster. Thus if one looks at the position in the sky of the sun at exactly noon (always standard time) one finds that it is ahead or behind due south (assuming, like Vancouver lying on 120 parallel, that the mean sun noon is the same as noon on the clocks) at various times of the year. Part of this is due to the behaviour of the true sun with respect to the mean sun in its motion along the ecliptic. The other is due to the tilt of the earth's axis. At solstice and equinox the tilt effect is zero, but at other dates, it can have an effect of up to plus or minus 10 minutes in time. The problem is that that the direction of the highest point in the sky of the sun is not along the due-south-north axis at times other than the solstices and equinoxes.

Note that we now demand that all seconds be the same (the same fraction of he siderial rotation of the earth around its axis). It used to be that noon was defined as the time when the sun was highest in the sky, and it was defined that there were always 12 hours of daylight and 12 of nighttime. Ie, hours and thus minutes and seconds were of different lengths day or night, and were of different lengths throughout the year. It was only when mechanical clocks became readily available that time was redefined so that seconds were equal.