It's worth remembering that all these things were well understood long ago. Ptolemy wrote a whole chapter about the changing length of the solar day in the Almagest nearly 2000 years ago….
On the inequality in the solar days ……it seems appropriate to add a brief discussion of the subject of the inequality of the solar day. A grasp of this topic is a necessary prerequisite, since the mean motions which we tabulate for each body are all arranged on the simple system of equal increments, as if all solar days were of equal length. However, it can be seen that this is not so. The revolution of the universe takes place uniformly about the poles of the equator. The more prominent ways of marking that revolution are by its return to the horizon, or to the meridian. Thus one revolution of the universe is, clearly, the return of a given point on the equator from some place on either the horizon or the meridian to the same place; and a solar day, simply defined, is the return of the sun from some point either on the horizon or on the meridian to the same point. On this definition, a mean solar day is the period comprising the passage of the 360 time-degrees of one revolution of the equator plus approximately 0;59 time-degrees, which is the amount of the mean motion of the sun during that period; and an anomalistic solar day is the period comprising the passage of the 360 time-degrees of one revolution of the equator plus that stretch of the equator which rises with, or crosses the meridian with, the anomalistic motion of the sun in that period. This additional stretch of the equator, beyond the 360 time-degrees, which crosses the horizon or meridian cannot be a constant, for two reasons: firstly, because of the sun’s apparent anomaly; and secondly, because equal sections of the ecliptic do not cross either the horizon or the meridian in equal times. Neither of these effects causes a perceptible difference between the mean and the anomalistic return for a single solar day, but the accumulated difference over a number of solar days is quite noticeable……” Almagest III 9, translated by G.J. Toomer What is given above, describes - if you read it carefully - the two components of the equation of time. (0:59 time degree above = 59/60 of a degree) Kevin On 14 Sep 2011, at 22:44, Tom Laidlaw wrote: > This article has an extra 71 sec, but it does not say exactly which day. On > the other side it has a deffciency of 75 sec. > > "Apparent solar time, sometimes called true solar time, is determined by the > daily apparent motion of the observed Sun. It is based on the interval > between two successive returns of the Sun to the local meridian. The length > of a solar day varies throughout the year, and the accumulated effect of > these variations (equation of time) produces seasonal deviations of up to 16 > minutes. Why, you may ask: Earth’s orbit is elliptical and the Earth’s axial > tilt. Consequently, apparent solar days are shorter in March (26–27) and > September (12–13) than they are in June (18–19) or December (20–21). In 2010, > the greatest Universal Time(UT1) interval between apparent midnights (at > Greenwich) is 86,471 seconds and the shortest interval is 86,325 seconds." > > Ref. http://www.universetoday.com/14700/how-long-is-a-day-on-earth/ > > Tom > > > > From: [email protected] [mailto:[email protected]] On > Behalf Of Tom Laidlaw > Sent: Wednesday, September 14, 2011 2:25 PM > To: 'Marcelo'; 'Frank Evans' > Cc: 'Sundial' > Subject: RE: longest day > > According to a wi9kipedia article the longest Apparent Solar Day is Dec. 22 > at 24 hrs. 29.9 sec. > http://en.wikipedia.org/wiki/Solar_time#Apparent_solar_time > Does it have a name? How about Longest Apparant Solar Day > > Tom Laidlaw > > From: [email protected] [mailto:[email protected]] On > Behalf Of Marcelo > Sent: Wednesday, September 14, 2011 12:49 PM > To: Frank Evans > Cc: Sundial > Subject: Re: longest day > > I used to think that the longest day was the summer solstice. Methinks that > you refer to some effect from the Equation of Time. And I don't know if there > is a name for it. > > 2011/9/14 Frank Evans <[email protected]> > Greetings, fellow dialists, > I tried to astonish my grandson by telling him that this was the longest day > of the year. (I think this is correct; today is 24 hours and 22 seconds > long.) He replied by asking if there was a name for this day. He said he > couldn't find anything on the interwebs. > > I am being outplayed by a grandson! Any help with a name, please? > Frank 55N 1W > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial >
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