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#1




Averaging and the Equation of Time
Here take notice, that the Sun or the Earth passeth the 12. Signes,
or makes an entire revolution in the Ecliptick in 365 days, 5 hours 49 min. or there about, and that those days, reckon'd from noon to noon, are of different lenghts; as is known to all that are vers'd in Astronomy. Now between the longest and the shortest of those days, a day may be taken of such a length, as 365 such days, 5. hours &c. (the same numbers as before) make up, or are equall to that revolution: And this is call'd the Equal or Mean day, according to which the Watches are to be set; and therefore the Hour or Minute shew'd by the Watches, though they be perfectly Iust and equal, must needs differ almost continually from those that are shew'd by the Sun, or are reckon'd according to its Motion. But this Difference is regular, and is otherwise call'd the Aequation.." Huygens That description of the Equation of Time has a large error in it that is immediately apparent, at least for those who value their intelligence. If people give up the pretense that they have the faintest idea what Newton was doing with his absolute/relative time(keeping), space and motions definitions they would understand more in a short while than their predecessors understood in 3 centuries. The Equation of Time fits inside the calendar system as it relies on the noon event to equalize the variations to a 24 hour average so there can be no fractional element left over as a single orbit. Unlike a rotation which equates to one day/night cycle anchored to noon , the year does not equate to one orbital circuit as March 1st to February 28th as one circuit and one year is also valid for March 1st to February 29th as one year. It was how Sir Isaac got his idea of the allencompassing inverse square law in equating the Earth around the Sun is the same time period as the Sun around the Earth (found in Huygen's description)  "That the fixed stars being at rest, the periodic times of the five primary planets, and (whether of the sun about the earth, or) of the earth about the sun, are in the sesquiplicate proportion of their mean distances from the sun...This proportion, first observed by Kepler, is now received by all astronomers; for the periodic times are the same, and the dimensions of the orbits are the same, whether the sun revolves about the earth, or the earth about the sun." Newton For the slow of mind  Huygen's description of the Equation of Time is wrong as is Sir Isaac's attempt to mimic it as absolute/relative time  "Absolute time, in astronomy, is distinguished from relative, by the equation of time. For the natural days are truly unequal, though they are commonly considered as equal and used for a measure of time; astronomers correct this inequality for their more accurate deducing of the celestial motions... The necessity of which equation, for determining the times of a phenomenon, is evinced as well from the experiments of the pendulum clock, as by eclipses of the satellites of Jupiter." Principia Want to really appreciate something really complicated and genuine outside the realm of the wider public and that is it !. 
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#2




Averaging and the Equation of Time
On Wednesday, April 18, 2018 at 8:56:23 PM UTC+1, Gerald Kelleher wrote:
The Equation of Time fits inside the calendar system as it relies on the noon event to equalize the variations to a 24 hour average so there can be no fractional element left over as a single orbit. As usual, it is hard to tell what you think you are talking about, but noon moves around quite a bit within the 24 hour day, as much as 16 minutes. 
#3




Averaging and the Equation of Time
On Thursday, April 19, 2018 at 7:02:07 AM UTC6, wrote:
As usual, it is hard to tell what you think you are talking about, but noon moves around quite a bit within the 24 hour day, as much as 16 minutes. He is well aware of that fact. He just objects to people who prefer (or attribute unwarranted significance to) the "sidereal day", which he refers to as "stellar circumpolar motion", to the natural noon cycle when describing the motions of the Earth  simply because it conforms better to mechanical clock time. Basically, he doesn't think that anyone needs to use arithmetic or mathematics in connection the Earth's motions; he never does that, he just relies on inspiration, intuition, and spiritual feelings when he does (what he calls) astronomy, and so he doesn't see why anyone else would have to do otherwise. John Savard 
#4




Averaging and the Equation of Time
What I wouldn't give for a disciplined observer instead of airheads scrawling on information that looks forwards and backwards in history.
https://www.timeanddate.com/sun/ireland/dublin A location exits the circle of illumination (sunrise) and reenters it (sunset) with noon anchored midway to these rotational events regardless of season. The anchor for daily rotation is noon so the combination of two rotations, one constant and the other variable in response to the Earth's orbital motion creates the natural variation which has been observed for many hundreds of years. The Equation of Time reduces the anchor observation of the total length of time across many fixed noon observations to a 24 hour average by adding or subtracting timekeeping minutes and seconds to maintain the anchor of the 24 hour day to natural noon. The Equatorial speed is 1669.8 KM per hour based on a rate of rotation of 15 degrees across all latitudes via the Lat/Long system. Instead of sending satellites to look for alien planets it is must better to get to know our own planet first. 
#5




Averaging and the Equation of Time

#6




Averaging and the Equation of Time
I wish there were people with some discipline who recognized that noon is a fixed event defined by the position of the observer to sunrise when their location turns through the circle of illumination and sunset when the observers turns back through the circle of illumination.
The anchoring of rotation to the noon cycle exposes the flaw in Huygen's reasoning that the Equation of Time is outside the calendar framework  Here take notice, that the Sun or the Earth passeth the 12. Signes, or makes an entire revolution in the Ecliptick in 365 days, 5 hours 49 min. or there about, and that those days, reckon'd from noon to noon, are of different lenghts; as is known to all that are vers'd in Astronomy. Now between the longest and the shortest of those days, a day may be taken of such a length, as 365 such days, 5. hours &c. (the same numbers as before) make up, or are equall to that revolution: And this is call'd the Equal or Mean day, according to which the Watches are to be set; and therefore the Hour or Minute shew'd by the Watches, though they be perfectly Iust and equal, must needs differ almost continually from those that are shew'd by the Sun, or are reckon'd according to its Motion. But this Difference is regular, and is otherwise call'd the Aequation.." Huygens The averaging process is the sum of all total lengths divided equally creates the 24 hour average including the rotation that is now February 29th. Men are supposed to recognize that while one 24 hour day correlates to one rotation, a year does not correspond to one orbital circuit of the Earth so from March 1st to February 29th for one yearly cycle is just as valid as from March 1st to February 28th. Timekeeping comes into close proximity to planetary dynamics but that is the reasonable conclusion that has yet to be accepted. 
#7




Averaging and the Equation of Time
On Thursday, April 19, 2018 at 9:53:00 PM UTC+1, Gerald Kelleher wrote:
A location exits the circle of illumination (sunrise) and reenters it (sunset) with noon anchored midway to these rotational events regardless of season. That is a spectacular amount of wrong in one sentence, even for you Gerald. 
#8




Averaging and the Equation of Time
https://www.youtube.com/watch?v=LPoj2lCNWbs
I get a kick out of that playful use of the noon event because it always happens at the exact time an observer is midway to the circle of illumination as a function of both their daily rotation (constant) and the slow rotation as a function of orbital motion (variable). The length of time changes (by the firing of the miniature canon) with each noon event so it has nothing to do with the seasonal changes in the length of the shadow (declination) but strictly a combination of two rotations that cause the time difference with each cycle. Don't mind that other threads descend into anarchy since this is where genuine astronomy and timekeeping innovations live. 
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