The sun occupies a definite position with reference to the equator, and stands at a definite distance from the earth on each day of the year.Something about this seemed strange and I wanted to investigate it. Each year is 365.25 days long but our calendar is normally only has 365 days in it. So it seems to me like there should be some drift in the position and distance or precessing of the sun over time.
I started out by charting the position of the Sun at the First Point of Aries, the Vernal Equinox over a decade. But the Equinox drifts so I actually used noon on 20Mar of each year. Cartes du Ciel only gives the solar distance out to three decimal places and they are nearly always the same over a decade so I switched to Stellarium which gives the solar distance out to eight significant digits. I didn't find a way to turn off DST without reading a manual or using the help function so I decided to ignore it as irrelevant since I wanted to find the distance of the Sun at the same date and time on a series of years and that would not correspond to the actual Equinox anyway. I charted the first 10 years of the century and it looked like there was a 4-year periodicity but to be sure I wanted to see more cycles of it so extended the chart to cover 2001-2020. The periodicity was maintained throughout the period. Four years agrees with the Leap Year cycle so I looked up the years of Leap Year and found that they coincide with the years of maximum solar distance. It appears that the cycle is reset each time we reset the calendar by adding an extra day.
That set me to wondering what would happen to the distance if I plotted it at the actual instant of the Equinox. For this I used the dates and times published by the US Naval Observatory. I first graphed one 4-year period and the variability looked familiar so I added another Leap Year cycle to see if it carried through and it did. When making this chart I calculated the UT offset at 5 hours rather than the 4 that I think it should be for the whole chart but rather than go looking up when we last changed the dates of DST and seeing if it impacted the chart I left it in EST which means the time scale is the same throughout no matter how the clocks happen to have been set in a given year.
Next I wanted to see if there was any difference in where the Sun appeared in the sky so I looked up the R.A. and Dec. on each of my 20March noons. I looked at it in both the RA/Dec and Alt/Az systems and although I had to play with the RA labels to get it to plot because the Sun's position straddles the 2300/000 hour merician during a Leap Year cycle it gave the best plot.
In the context in which I was reading that statement I interpreted it to mean that the Sun would be in exactly the same position in the sky on a given date and time in perpetuity. Rereading Darwin's statement I don't now interpret it to mean that there is repeatability in the Sun's position. In the end I decided that although the Sun's position does change from year to year on a given date and time that change is below my capability to discern it and for practical purposes does not exist and that it is in the same position in the sky on the same date and time each year.
