[Note: I’m not entirely convinced that my “average year” calculations are correct. I was looking for a way to get 364.75 and since it is tantalizingly close to 365.25 I was looking for a way to get there from that. It may be better to just use 365.25 – 0.5 … now need a Reason Why.]

I was playing around with the calculator and stumbled across this curious sum.

Let’s start with how long a year is. As you should know, it’s 365.25 days for a solar year. If however, we measure against the background stars, it’s about 364.25 days.

From Wikipedia: “Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes 56 seconds. ”

If we take those 3 minutes 56 seconds == 236 seconds, and work out the difference over a year (x 365), we get 86140 seconds, which is 23.927777 hours, effectively one day.

So if we take the average of a solar year and stellar year, we get (365.25 + 364.25)/2 which is 364.75 days, or more precisely, 364.7436921 days.

Now we do this sum.

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