Dear John,
I looked into your interesting assertion about
the Equation of Time. You say:
On the average, it is only off [mean time]
by about seven minutes...
It isn't really appropriate to use the term
average here because we are not dealing with
random variables or errors. We are just looking
at a conversion scheme for going from one time
system to another. That didn't stop me taking
a look and, essentially, agreeing with your
figure!
Three pedantic points first:
1. The average of the Equation of Time is,
of course, zero.
2. The average absolute value is just
over seven minutes and this is your
figure.
3. The RMS value [Root Mean Square]
is probably more useful and that is
about 8.75 minutes which is more
than I expected intuitively.
Here are some intriguing figures in which
the left-hand column shows minutes and the
right-hand column show the percentage of the
time that the absolute value of the Equation
of Time is less than the associated number
of minutes:
mins %age
1 7.7
2 16.2
3 25.2
4 37.0
5 42.5
6 49.6
7 58.4
8 61.4
9 64.4
10 67.9
11 71.2
12 73.4
13 79.5
14 86.3
15 92.1
16 95.6
17 100.0
For example, is you pick a day of the year at
random, there is a 25.2% chance that your local
sun time is within 3 minutes of your local mean
time.
Expressed the other way we have:
10% 1m 13s
25% 2m 58s
50% 6m 02s
75% 11m 58s
90% 14m 14s
95% 15m 52s
100% 16m 26s
I was surprised that the 75% figure was so
high, close to 12 minutes.
Maybe my calculations are wrong!
All the best
Frank
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