 #1
Buzz Bloom
Gold Member
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 365
Summary:

I have recently become curious about the calculation of the GMT time of the March equinox (and also for September, but to a lesser extent since it is now March). I found the following source.
http://www.astropixels.com/ephemeris/soleq2001.html
Out of curiosity I calculated (from the cited source using a spreadsheet) the time in minutes between consecutive March equinoxes, and I noticed a pattern of irregularities. (See graph in the post body.)
Main Question or Discussion Point
Unfortunately, the only source I could find on the internet is the one I cited in the summary. This source has the date and GMT time for the two annual equinoxes and the two solstices for a hundred years: 20012100.
The 99 time difference values, A_{i}, shown in the graph below were calculated as described later.
As I considered the possible causes of this irregularity, I came up with the following candidates.
1. The EarthMoon barycenter.
2. The circular rotation of the Earth's axis.
3. The general relativity precession of Earth's elliptical orbit.
4. The gravitational influence of other planets. In particular the most likely are Venus and Jupiter.
Of these four, only the first seemed reasonably plausible to me. However, the radius of the barycenter is 4670 km. The Earth's orbital velocity around the sun is approximately 29.79 km/s. This implies that the barycenter effect is limited to a variation in the time between consecutive March equinoxes within an approximate range of +/ 3 minutes. The chart shows a variation range of approximately +/ 13 minutes.
The following is a summary of my calculations.
t_{0} = midnight (00:00) March 19 for a nonleapyear, and
t_{0} = midnight (00:00) March 20 for a leap year.
t_{y} = the equinox day in March for year y together with the equinox GMT time of day
M_{y} = t_{y}  t_{0} (in minuites)
i = y  2001
If y is not a leap year then
D_{i} = i^{th} DELTA time (in minutes) = M_{y+1}  M_{y}
If y is a leap year then
Di = i^{th} DELTA time (in minutes) = 24 x 60 + My+1  My
A = Average[i=1..99](D_{i})
A_{i} = D_{i}  A
The chart of A_{i} values shows the variability of the D_{i} times relative to the average D_{i} time.
If anyone knows of a reliable reference that discusses the causes if the variability of time between consecutive equinoxes, I would very much appreciate it. I searched the internet but failed to find any. If anyone finds an error in my calculations, i would also appreciate that information, as well as any other comments.
I have not included a picture of my spreadsheet, but I will post it if anyone requests it.
The 99 time difference values, A_{i}, shown in the graph below were calculated as described later.
As I considered the possible causes of this irregularity, I came up with the following candidates.
1. The EarthMoon barycenter.
2. The circular rotation of the Earth's axis.
3. The general relativity precession of Earth's elliptical orbit.
4. The gravitational influence of other planets. In particular the most likely are Venus and Jupiter.
Of these four, only the first seemed reasonably plausible to me. However, the radius of the barycenter is 4670 km. The Earth's orbital velocity around the sun is approximately 29.79 km/s. This implies that the barycenter effect is limited to a variation in the time between consecutive March equinoxes within an approximate range of +/ 3 minutes. The chart shows a variation range of approximately +/ 13 minutes.
The following is a summary of my calculations.
t_{0} = midnight (00:00) March 19 for a nonleapyear, and
t_{0} = midnight (00:00) March 20 for a leap year.
t_{y} = the equinox day in March for year y together with the equinox GMT time of day
M_{y} = t_{y}  t_{0} (in minuites)
i = y  2001
If y is not a leap year then
D_{i} = i^{th} DELTA time (in minutes) = M_{y+1}  M_{y}
If y is a leap year then
Di = i^{th} DELTA time (in minutes) = 24 x 60 + My+1  My
A = Average[i=1..99](D_{i})
A_{i} = D_{i}  A
The chart of A_{i} values shows the variability of the D_{i} times relative to the average D_{i} time.
If anyone knows of a reliable reference that discusses the causes if the variability of time between consecutive equinoxes, I would very much appreciate it. I searched the internet but failed to find any. If anyone finds an error in my calculations, i would also appreciate that information, as well as any other comments.
I have not included a picture of my spreadsheet, but I will post it if anyone requests it.
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