Caption: The Earth orbiting the Sun with the zodiac constellations displayed.

Features:

1. The red great circle is the ecliptic. The zodiac constellations straddle the ecliptic.

2. The blue great circle is the celestial equator.

3. When the Sun is in conjunction with a zodiac constellation, the Sun is said to be in that zodiac constellation. The calendar dates for the conjunctions are given in Wikipedia: Zodiac: Constellations.

4. The Sun as seen from the Earth is aligned with the vernal equinox since it is seen at the point where the ecliptic goes north of the celestial equator (which defines the vernal equinox). This means the time of the image is circa Mar21 which is the vernal equinox in the other meaning of the term vernal equinox.

5. As the Earth moves eastward (counterclockwise as viewed from the NCP) the whole midnight night sky moves eastward.

   From the Earth-at-rest (or geocentric) perspective that we often take in observations, the Sun also moves eastward at the same rate as the whole midnight night sky.

6. Thus there must be a continuous advance in solar times for rising, setting, and transiting behavior of relatively unmoving objects---relatively unmoving on the celestial sphere compared to the Sun.

7. The solar times for these events gets earlier and earlier every day until the events have cycled through the whole day.

8. For example, the relatively unmoving objects that transit the meridian at midnight are those opposite the Sun.

   The objects in the midnight transit category for one day, get replaced in that category by objects farther east on the celestial sphere on the next day because of the Earth's eastward motion.

   The former midnight transit objects are now west of the meridian at midnight. They now transit before midnight.

9. One can make the same argument, mutatis mutandis, for the rising time of relatively unmoving objects. They rise earlier every day.

   Thus, the relatively unmoving objects that rise with Sun one day, rise before the Sun on the next day.

10. Yours truly mnemonicks the daily advance of risings, settings, etc. by the mnemonic: "The stars rise earlier every day."

11. How much earlier? The time interval is just the difference between the sidereal day (≅ 24h-4m+4s) and solar day (mean value ≅ 24h). So earlier by about 4 minutes.

    One can be a bit more precise. The mean solar day ≅ 86400.002 s (J2000) (i.e., the mean time from solar noon to solar noon) and the mean sidereal day ≅ 86164.1 s. Thus, earlier by 86400.002 s - 86164.1 s = 235.9 s = 3m:55.9s ≅ 4 minutes.

12. After a year, almost all the events beyond the Solar System have cycled back to the solar times they had a year earlier. Solar System events are different since the Solar System astro-bodies move relatively rapidly on the celestial sphere. So they do NOT cycle back in general though the slowest moving ones do approximately: e.g., ex-planet Pluto.

13. The cycling back is almost exactly a year simply because the Earth, Sun, and the fixed stars have the same relative positions after a year, and so almost all the remote astro-body motion phenomena relative to the ground (risings, settings, etc.) should happen at about the same solar times.

    Some more understanding---maybe---is given from a simple calculation. Say we observe a particular rising at solar time Y on ordinal date X of some year. One common year (365 days) later, there must again be a rising at about solar time Y on ordinal date X. But this must be the rising 365+1 since last year at solar time Y on ordinal date X since the mean sidereal day is shorter than the mean solar day and the relative positions of the Earth Sun and the fixed stars have NOT repeated until now. So accumulated time difference for 366 rising periods must be one day less than for 366 days so that the 366th rising happens 365 days later. The calculation for the accumulated time difference is 366*(86400.002 s - 86164.1 s) = 86340 s = 1439 m = 23.98 h .

    Why is this accumulated value time difference NOT exactly 24 h? Several reasons. The main reason is that the sidereal year = 365.256363004 days (J2000), NOT 365 days. The sidereal year is nearly the exact repeat time for relative positions of the Earth Sun, and the fixed stars. However, that ∼ 0.25 days decimal fraction of the sidereal year means the rising times etc. CANNOT happen at the nearly exact repeat time, but are offset from it by ∼ 0.25 days. Now the sidereal year is closely approximated by the Julian year = 365.25 which is the average year of the leap year cycle of 4 years. If you average over a leap year cycle of 3 common years = 365 days and 1 leap year = 366 days, you get an average accumulated value time difference of 24.00 h which 24 h to 4 digits. Highly accurate/precise calculations would have to account for the axial precession and various other factors including astronomical perturbations.