Wikipedia:Reference desk/Archives/Science/2018 April 11

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April 11

Day length in AD 2,500 & 5,000

Due to measurements performed half a century ago, the length of a second was determined to be about 9192631770 ± 20 Caesium-133 ground state hyperfine transition periods. Since day length is constantly increasing due to the effects of tidal acceleration on the Earth's rotation period, I wonder how this value would have looked like, if the experiments in question would have been performed in the year 2525 or 5,000, instead of the late 1960s. (One of the linked articles mentions the value of 30 ms/century², but I am not sure how accurate it is, or how to apply it). — 79.113.201.154 (talk) 06:15, 11 April 2018 (UTC)

That's the delta-T, not the day lengthening. What you're looking for is the non-cumulative version of that which for the years you're interested in should be somewhere around 1.7 milliseconds per century, starting not from the 1960s but in about 1820. 1820 cause that's about the weighted average year of Sun position measurements between the deadline and "enough precision-to-newness ratio to be used (1750 AD) to tweak the God equations of Earth's orbit" in Newcomb's Tables of the Sun, copyright 1895. Which were so good they were state of the art till about atomic clocks and weren't replaced in the official almanac of astronomy till 1983. They were state of the art when it was realized that seconds aren't actually identical so the Tables of the Sun second became the second that will never change. When the second was defined by the most accurate clock known to man a number of atom vibrations was chosen to fit the ephemeris second to within it's accuracy (hence no need for the number to have more than 9 non-zero digits even if the atomic clock counts every last cycle (1890s calculations were much slower than even very slow electronic computers so maybe it took half a decade just to calculate the thing)Sagittarian Milky Way (talk) 12:28, 11 April 2018 (UTC)

It's not steady because the exact shape of the Earth changes the rotation speed like a spinning figure skater: frozen water accumulating and melting, continents rising, tectonic plates getting stuck and moving again, sea levels changing.. If it was steady it'd look like a vertical parabola that barely touches 0 at 1820 (which would look like a straight rising line if it was 24 hours and x milliseconds at the top and 23 hours 59 minutes 59 seconds 1000 minus x milliseconds at the bottom instead of 70 and minus 10 seconds of delta-T) Sagittarian Milky Way (talk) 18:58, 11 April 2018 (UTC)

Parabola. Sagittarian Milky Way (talk) 18:58, 11 April 2018 (UTC)

Thank you for your intervention ! Are you saying that the day in the year 2,100 will be 1.7 ms longer than it was in the year 2,000 ? Also, how am I to interpret the expression 31 × ( Year - 1820 ) ² × 10^-4 from the article on ΔT ? What does it refer to, exactly ? (It yields the value 600 for the year 2260, but I have no idea what it means). — 79.113.201.154 (talk) 13:20, 11 April 2018 (UTC)

Not exactly. Your calculation is assuming the length of the day is varying in a direct, simple, linear relationship, and that's not true. The speed of the earth's rotation seems to vary about 1.7 milliseconds per century slower based on calculated tidal effects, but that assumes some huge "spherical cow"-type approximations. See the graph he posted with his post (on the right). The actual speed of the Earth's rotation varies in a highly non-linear (and non-functional!) way over time, such that in some years it speeds up, some years it slows down, and some years it remains rather constant. It's very messy, and it is the sort of thing that is corrected for on the fly based on direct observations, rather than by predictive calculation. This is covered at the article titled Leap second, which notes "Leap seconds are irregularly spaced because the Earth's rotation speed changes irregularly. Indeed, the Earth's rotation is quite unpredictable in the long term, which explains why leap seconds are announced only six months in advance." --Jayron32 13:43, 11 April 2018 (UTC)

What if we were to define, for instance, a slightly longer time unit of 9192631770 + 50 = 9192631820 Caesium-133 ground state hyperfine transition periods ? How would such a unit fare with regards to reducing the number of future leap seconds, when compared to our current second ? — 79.113.201.154 (talk) 14:46, 11 April 2018 (UTC)

We could play what if all day long; but that's not how things are done. The second is standardized to a universal, constant time, and we just adjust the length of earth-based times instead using leap seconds. If you have a unit that varies in size, it's not a standard unit. --Jayron32 15:11, 11 April 2018 (UTC)

It is constant, and it does not vary. (I was just curious to see, by way of a concrete example, how adding about five parts per billion would fare, when compared to the length of the current second, over the next three millennia, in eliminating the need for leap seconds during that particular time frame). — 79.113.201.154 (talk) 15:35, 11 April 2018 (UTC)

Besides unnecessarily throwing off all time-based measurements made before your correction, it would have no meaningful effect since, as noted, we can't predict the need for a leap second more in advance than about six months. Knowing how many we would have in 3 millennia is completely unknowable. --Jayron32 16:53, 11 April 2018 (UTC)

Knowing is not unknowable! We know with high confidence that we don't know. —Tamfang (talk) 10:05, 12 April 2018 (UTC)

That depends on whether it is a Known unknown or an unknown unknown. --Jayron32 12:18, 12 April 2018 (UTC)

On the contrary, you seem to be relying on the possibility that it's an unknown known. —Tamfang (talk) 07:32, 14 April 2018 (UTC)

(edit conflict) We just don't know because the rotational speed of the earth varies in an unpredictable way. Melting of ice shelves, or a caldera eruption might suddenly make a big difference in the need for leap seconds. During the six years from 1999 to 2004 there was no leap second correction necessary, so your proposal would have caused extra problems during those years. Dbfirs 15:16, 11 April 2018 (UTC)

What if we were to restrict the question to the next three millennia, specifically ? Would that help ? Or is it really that unpredictable ? — 79.113.201.154 (talk) 15:35, 11 April 2018 (UTC)

It is unpredictable to the point that when the rotation increases or decreases, scientists go back and look for a reason. They don't see an event and calculate the change it will cause before it happens. It is like the stock market. When a big change happens, everyone looks for the cause. However, given an identical cause, they cannot predict how the market will change with any accuracy. 209.149.113.5 (talk) 16:05, 11 April 2018 (UTC)

As noted in the article titled Leap seconds, already cited, it is so unpredictable, the addition of leap seconds can only be reliably done six months in advance. We can't predict the need for leap seconds to anything longer than that time frame; if we can't predict even 1 year out, three millenia would be beyond silly. --Jayron32 16:09, 11 April 2018 (UTC)

This is the actual graph. Jiggly. Sagittarian Milky Way (talk) 18:28, 11 April 2018 (UTC)

First, I would like to sincerely thank you guys for your continuous patience. Secondly, I really have to make this point clear: I was under the impression that the passage in question referred to the unpredictability of its `exact` occurrence, which is not quite the same as the inability to estimate an average. Are you saying that the quoted paragraph is to be understood as having this latter, stronger meaning ? (To make a parallel to the stock market example: one may not be able to exactly predict the value of a rolling dice, but one may safely expect that, given an unbiased dice, out of 600 dice-rolls, roughly 100 will correspond to each of its six possible outcomes). — 79.113.201.154 (talk) 09:26, 12 April 2018 (UTC)

Yes, I see why we seemed to be talking at cross-purposes. As I understand the situation, there is an expectation the the rate of rotation will slow over many centuries, but random variations are at least as significant over a decade, and it is possible that we might need to omit a second (a negative leap second) in the near future if some geological event increases the rotation rate. It hasn't happened yet, but it might. No-one knows. Dbfirs 10:55, 12 April 2018 (UTC)

There's a good explanation at [1]. Looking at the graph, roughly 1,000 leap seconds will be needed by AD 2400. Using the formula 31(Y-1820/100)² gives a requirement of 1042.84. The OP suggests increasing the length of the second by five parts in a thousand million and asks what effect that will have on the incidence of leap seconds. The effect is the same as adding a leap second every 200,000,000 seconds, or roughly one every 6 1/2 years. In 400 years that's about 60 leap seconds compared to the 1,000-odd needed. So the answer is "not very much". 92.19.172.40 (talk) 13:38, 12 April 2018 (UTC)

Things like Earth's rotation are chaotic; small changes to the inputs to the system have unpredictable effects. Add to that the fact that many of these inputs, like plate tectonics, are themselves chaotic, and you might see why we can't predict Earth's rate of rotation with any fine-grained accuracy. We can make a broad estimate as to what it will be over a long period—centuries or longer—because that's just simple Newtonian mechanics: calculate the tidal force applied to Earth by the Moon. Another good example of a chaotic system is weather. We can't predict what the weather will be in a location on this day three months from now, because there's so much going on in the system. But of course, we can say on average it will be warmer in the Northern Hemisphere and colder in the Southern, because again, that's just simple physics: the Earth's tilt and orbit mean the insolation of the hemispheres cycles each year. Similarly, we can predict climate, as opposed to weather, over longer periods, because the chaotic short-term effects tend to cancel out over time, while long-term trends like the effect of rising carbon dioxide levels don't. --47.146.63.87 (talk) 07:05, 13 April 2018 (UTC)

Has anyone calculated what's a likely time frame for a butterfly wing flap to become part of the weighted random number generator that chooses the weather? Can a Norwegian butterfly "cause" a Southern Hemisphere hurricane in say 2 years or is it only bigger air movements at such short notice (like a jetliner crash or Shohei Ohtani pitch?) Sagittarian Milky Way (talk) 08:40, 13 April 2018 (UTC)

Biology

What is the role of the liver in digestion ? — Preceding unsigned comment added by 197.212.89.145 (talk) 09:55, 11 April 2018 (UTC)

See Enterohepatic circulation amongst other things - the liver has many functions. Mikenorton (talk) 10:04, 11 April 2018 (UTC)

The secretion of bile is a particularly "digestive" function, while the circulation is arguably more, well, circulatory in nature, though the liver does get first pass at intestinal nutrients and toxins through the portal system. Wnt (talk) 14:33, 11 April 2018 (UTC)

Link: hepatic portal system. --47.146.63.87 (talk) 07:08, 12 April 2018 (UTC)