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Over a year, the ratio of daylight changes, e.g. in Montreal there is more daylight in the summer than in the winter.

I want to know if, given a bad data sample, e.g. five years, one might notice a trend of increasing or decreasing daylight ratios.

Here's why I ask. I'm doing research on the Dead Sea scrolls, and some of the fragments contain ratios that a scholar has argued represent daylight. What I'd like to know is a trend that the community of Qumran might have noticed in their dataset. They had a theory that darkness was increasing. I doubt their data was exhaustive, but I wonder if around Jerusalem there might have been a period of decreasing daylight ratios over a period of a few years roughly around 100 B.C.E.

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  • $\begingroup$ Astronomically, we believe the daylight ratios have remained about constant. The Earth's rotation is slowing down, and the Earth precesses, but neither of these would change the daylight ratio significantly, and certainly no more in 100 BCE than now. Of course, that's astronomically speaking. Something like that may have happened, but astronomers assume the daylight ratio has been fairly constant. $\endgroup$ – barrycarter Dec 2 '16 at 5:31
  • $\begingroup$ Thanks. You make it clear that there is no such pattern, but do you know if, with the amateurish data that this ancient community would've had, they might have been led to infer a trend of increasing darkness? $\endgroup$ – Modal Dec 2 '16 at 5:36
  • $\begingroup$ Unless you're including darkness from clouds and storms, the only thing I can think of is that they had bad horology (timekeeping). I'm not sure how accurate their clocks were back then. en.wikipedia.org/wiki/History_of_timekeeping_devices explains that water pressure caused inaccurate timekeeping until the Greeks addressed the issue in about 100 BCE. Perhaps that's it? $\endgroup$ – barrycarter Dec 2 '16 at 5:42
  • $\begingroup$ Interesting point about horology. The bias would have to make nights look increasing longer from year to year. As per the page you linked, a bias with the water clocks is that they make nights look shorter than they really are because the water flows more slowly when it's cold. However, this bias doesn't create a year-to-year trend. There might be a bias in how they map the ratios from one year to the next. Perhaps they aligned the arrays incorrectly, and ended up comparing Jan with Feb, Feb with Mar, etc. I would need a more precise explanation as to how this might come to be. $\endgroup$ – Modal Dec 2 '16 at 6:26
  • $\begingroup$ I was just guessing... but perhaps there was a short-term weather trend that led to unusually cold (or unusually warm) winters or something? Generally, when looking for historical facts in religious works, it's good to find corroborating facts in secular works or works of another religion. For all we know, the "darkness" may have been metaphorical. $\endgroup$ – barrycarter Dec 2 '16 at 15:13
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I don't think it's possible to have a change in the ratio of day to night when averaged on a yearly basis. To do so would require either a nonlinear change in the Earth's rotation or a significant shift in the polar axis tilt within a year.
If the rotation were simply slowing down over time, the year-averaged ratio would be the same every year (only the number of days in a year would change). Similarly, the only way a polar tilt could cause a change would be if the change in angle occurred at some (sinusoidal) rate not an integral ratio of the orbital period (year).
Either of those putative mechanisms can only change the per-year ratio by producing a day/night ratio in "summer" that is not the inverse of the "winter" ratio, and producing a different non-inverse the following year. (I'm oversimplifying a bit, since the elliptic orbit produces a repeatable asymmetry in the Sun's zenith pattern).

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  • $\begingroup$ I am trying to understand your last point in light of my historical subquestion. Do you mean that, with an incomplete sample that averages out winter and summer rather than the whole year, one might have the impression of a change in the ratio of day to night? In other words, the ratio of day to night per month changes in that sometimes the extremes flatten out and the mid-seasons pick up the difference, and in this case, comparing only the month of January over several years might lead to the inference that there is trend in the ratio? $\endgroup$ – Modal Dec 2 '16 at 14:06
  • $\begingroup$ @Modal I think you could say that -- suppose there's some polar axis wobble. Then Januarys might get darker, but Julys would get lighter. $\endgroup$ – Carl Witthoft Dec 2 '16 at 14:13
  • $\begingroup$ If change the axis of rotation, you change the latitude of every point on earth. That'll effect day/night ratio over the course of a year. Such changes happen, but are quite small: Japan Quake May Have Shortened Earth Days, Moved Axis: nasa.gov/topics/earth/features/japanquake/earth20110314.html "The position of Earth's figure axis also changes all the time, by about 1 meter (3.3 feet) over the course of a year, or about six times more than the change that should have been caused by the Japan quake." You might get a few microseconds excess day or night in a given year in Montreal. $\endgroup$ – Wayfaring Stranger Dec 3 '16 at 14:50

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