Talk:Equation of time/Archive 2

Archive 1

Archive 2

Effect of obliquity on length of solar day

In the section Obliquity of the ecliptic, I query the statement If this effect operated alone, then days would be up to 24 hours and 20.3 seconds long (measured solar noon to solar noon) near the solstices, and as much as 20.3 seconds shorter than 24 hours near the equinoxes.

How was ±20.3 seconds calculated? Let me guess ...

The most detailed calculations that I performed resulted in -19.56426 seconds at the equinoxes, +21.33290 seconds at the solstices. Values for 365 days (1 to 365) were calculated, with day zero being the March 20 equinox. The value of obliquity used was 23.43696°. Minor point: If a factor mean solar days per sidereal day = 365.24219 / (1 + 365.24219) is to be applied, then the range is -19.51084 to +21.27465 seconds.

I compared 3 sequences: DAY [multiples of 2π/365.24219], ALPHA (lambda = DAY), LAMBDA (alpha = DAY). Alpha is Right Ascension and Lambda is Ecliptic Longitude. The differences of (ALPHA (DAY) - DAY) give almost identical results (±0.06s) throughout the sequence, with range -19.51524 to +21.26943 seconds. But the differences of (DAY - LAMBDA (DAY)) give a range of -21.26973 to +19.51502 seconds.

So that the differences of ((ALPHA (DAY) - LAMBDA (DAY)) / 2) give a range of -20.39249 to 20.39223 seconds. And applying a factor of mean solar days per sidereal day, we have ±20.3 seconds.

Would others agree that the statement should be If this effect operated alone, then days would be up to 24 hours and 21.3 seconds long (measured solar noon to solar noon) near the solstices, and as much as 19.6 seconds shorter than 24 hours near the equinoxes.? — Preceding unsigned comment added by Time Fan (talk • contribs) 08:15, 22 January 2018 (UTC) --Time Fan (talk) 14:28, 23 January 2018 (UTC)

The author is proposing an original calculation to determine the change in the length of the solar day resulting from the obliquity of the ecliptic, and is documenting that there is a disagreement about the result of such calculation. This sounds suspiciously like Original Research.

In fact, much of the section on Major components of the equation lacks citations. If we can't find a citation for this discussion of the components of the length of day, the discussion will have to be removed from the article as Original Research.--SteveMcCluskey (talk) 09:14, 22 January 2018 (UTC)

I recognize your name from a copy of Astronomies and Cultures in Early Medieval Europe, and take on board your comments about Original Research. I have documented my methods and values, mainly for comparison with those of experts. The section Major components of the equation is helpful, even without citations, and my question seems answerable: How was ±20.3 seconds calculated, and is it perhaps not quite correct? Obviously I found the section stimulating enough to write a fresh series of programs. — Preceding unsigned comment added by Time Fan (talk • contribs) 10:27, 22 January 2018 (UTC) --Time Fan (talk) 10:33, 22 January 2018 (UTC)

The quantity you are talking about is related to the slope of the equation of time. If there were no eccentricity, the EOT would be a perfect sinusoid, and the steepest slopes would be equal in the positive and negative direction. --Lasunncty (talk) 21:28, 25 January 2018 (UTC)

Apparent length-of-day due to obliquity: Like user Lasunncty, I expected the result to be symmetric. However, calculations suggested otherwise. Intervals of radians per mean solar day along the ecliptic gave the symmetric result -9.863764 to +9.863340 minutes for the Equation of Time (with negative sign meaning the apparent solar time is ahead of mean solar time). So that looks correct. Now, the differences of this sequence may be interpreted as the desired results. Would you agree? Range: -19.51524 to +21.26943 seconds. At day zero (March 20 equinox), EoT is zero. Something easy to check: first 6 elapsed days: EoT [minutes] = (-0.3252141 -0.6500896 -0.9742879 -1.2974712 -1.6193020 -1.9394438), and EoT differences [seconds] = (-19.51285 -19.49253 -19.45190 -19.39100 -19.30985 -19.20851). Time Fan (talk) 02:16, 26 January 2018 (UTC)

I'm guessing one reason you are not getting exactly symmetric results is that you are dividing the EOT into 365 discrete days. In reality it is a continuous function, so the true minima and maxima may fall in between some of your discrete days. --Lasunncty (talk) 18:15, 26 January 2018 (UTC)

This discussion focuses on disagreements between individual editor's calculations. The way to resolve this (in Wikipedia at least) is to consult authoritative sources (e.g. classic works on spherical astronomy, discussions of the construction of sundials, etc.) and find what they have to say about the factors contributing to the equation of time. Adding to published discussions with our own calculations will always be original research and therefore is not acceptable in Wikipedia. --SteveMcCluskey (talk) 20:17, 26 January 2018 (UTC)

Noted again, SteveMcCluskey! I eventually found some references to ±20 seconds (specifically for the obliquity effect) in web-pages, but the calculation seemed very coarse, and I could not establish their sources. See Equation of time (Academic Kids) and Wikipedia Equation_of_time diff=4887949 oldid=3162351. When considering apparent length-of-day, I suppose that people are almost always interested in the combined effects of eccentricity and obliquity, making it difficult to find an excellent reference for obliquity considered separately. But I will keep searching. Incidentally, with 9999 steps per year, the (synthetically derived) range was -19.51802 to +21.27345 seconds; I cannot see how user Lasunncty's guess about 'continuity and symmetry' affects matters. Time Fan (talk) 23:22, 26 January 2018 (UTC) Time Fan (talk) 23:32, 26 January 2018 (UTC) Time Fan (talk) 23:42, 26 January 2018 (UTC)

I agree that our own calculations cannot be used as a source, but it can help us understand what is going on. Time Fan, I just want to ask, since you set EOT=0 at the spring equinox, does it again =0 at the fall equinox? And if you run it for multiple years, does it give the same results each year? --Lasunncty (talk) 16:05, 27 January 2018 (UTC)

Regarding my calculations: Yes, by interpolation the EoT component due to obliquity is again zero at the September equinox. Rest assured that I am inspecting all days (graphically and numerically): especially the behaviour at peaks, troughs, and crossings. User Lasunncty also asked what happens "if you run it for multiple years": An additional experiment extended for 456 days, with day zero placed a half-day after the March equinox. Essentially the same results. Time Fan (talk) 19:53, 27 January 2018 (UTC) Addendum: When using 9999 steps per year, for one year, the EoT obliquity component ranged from -9.863815 to +9.863815 minutes. This might allay user Lasunncty's concerns about 'continuity and symmetry'. Time Fan (talk) 09:08, 30 January 2018 (UTC)

This conversation is very confusing. Time Fan, in your simulation are you talking about the EOT or only the tilt contribution to it? Also please sign your comments with the menu provided.--Gciriani (talk) 19:21, 27 January 2018 (UTC)

EoT component due to obliquity (now clarified above). Time Fan (talk) 19:57, 27 January 2018 (UTC)

To be more precise: EoT component due to obliquity, as conceived when contriving to move the sun along the ecliptic at a constant rate (2π / 365.24219 radians per mean solar day). Time Fan (talk) 20:56, 29 January 2018 (UTC)

Clever Babylonians

The irregular daily movement of the Sun was known by the Babylonians.

How the hell did they do that! Don’t you need clocks (that are more accurate than a sundial) to do it?

MBG02 (talk) 02:42, 13 November 2018 (UTC)

We have quite a lot on Babylonian (Mesopotanian) astronomy and existing sources. MUL.APIN Tablet 2 the Enuma Anu Enlil for instance. They were responsible for the base 60 system used to in Longitude and Latitude. Measuring the movement of planets against the sphere of stars was of great interest to them. They used a heliocentric model that was expanded by the Hellenistic astronomers. Here you have the clue to your question- the night sky is your clock. --ClemRutter (talk) 09:44, 13 November 2018 (UTC)

External links

Best page on the topic regarding visualization, interactive:

• Worldwide Suntime Calculator in a OSM map

--Leiamada (talk) 20:19, 17 February 2019 (UTC)

Variable undefined.

The variable t_p is not defined. Is is January first, earth's aphelion date, an equinox or solstice date, or something else entirely?

Tvb 1 (talk) 00:52, 19 August 2019 (UTC)tvb_1

It's the perihelion date. I added it into the article. --Lasunncty (talk) 06:48, 19 August 2019 (UTC)

Obliquity vs eccentricity

Should the "Eccentricity of the Earth's orbit" and "Obliquity of the ecliptic" sub-sections of "Major components of the equation" be flipped? It appears that the obliquity is a larger factor than the eccentricity. I'd do the flip now but wanted to first confirm that Earth's obliquity is the larger factor for the equation of time. --Marc Kupper|talk 17:08, 22 December 2019 (UTC)

I see no objection but stand to be corrected! It will be more than a simple flip as the second sub-section refers back to the first. There are also couple of failed verifications to fix first. ClemRutter (talk) 18:46, 22 December 2019 (UTC)

Obliquity vs EOT

The explanation here is too fuzzy. EOT is the offset between the mean sun and the true sun, and referencing and using those two definitions will be more simple I think:

"Assume the mean sun and the true sun travel on identical circles with axis tilted 23.5 degrees with respect to each other. Both travel with identical, constant linear and angular velocities, and make once full circle in a year. While the mean sun angular displacement along its circle is equal each and every ("mean sun") day of the year, the daily angular displacement of the projection of the true sun onto the circle of the mean sun is not. During equinox periods the angular velocity of the projection of the true sun onto the circle of the mean sun is smaller than the angular velocity of the mean sun, and is larger during solstice periods."Kerguelen Avon (talk) 10:55, 31 March 2020 (UTC)

Need a comment about hemispheres.

I assume that these values hold at least roughly good in the southern hemisphere as well as the northern? They're not reversed? There needs to be a statement on this. Koro Neil (talk) 20:04, 18 December 2020 (UTC)

Correct, these values pertain to the Earth as a whole, not just specific locations. --Lasunncty (talk) 11:22, 19 December 2020 (UTC)