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protoindoeuropean · 3 years ago

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Here’s a question you might have asked yourself before: what was the longest year in Earth’s history? First of all, you might wonder, is this a sensible question to ask yourself? — in short, it’s not. Still, if by any chance you’ve ever been on Wikipedia, you might have encountered three Wikipedia pages that make related claims that refer to this question:

/1972

Within the context of Coordinated Universal Time (UTC) it was the longest year ever, as two leap seconds were added during this 366-day year, an event which has not since been repeated. (If its start and end are defined using mean solar time [the legal time scale], its duration was 31622401.141 seconds of Terrestrial Time (or Ephemeris Time), which is slightly shorter than 1908).[1]

[1]=Stephenson, F. R.; Morrison, L. V. (1984). "Long-Term Changes in the Rotation of the Earth: 700 B. C. to A. D. 1980". Philosophical Transactions of the Royal Society A. Royal Society. 313 (1524): 47–70. Bibcode:1984RSPTA.313...47S. doi:10.1098/rsta.1984.0082. S2CID 120566848.

/1912_in_science

At the beginning of this year an extreme decadal variation in length of day produces mean solar days having a duration of 86400.00389 seconds of Terrestrial Time (or ephemeris time), the slowest rotation of Earth's crust ever to be recorded.[1]

[1]= same as above

/1908_in_science

If its start and end are defined using mean solar time then due to the extreme length of day variation this is the longest year of the Julian calendar or Gregorian calendar, having a duration of 31622401.38 seconds of Terrestrial Time (or ephemeris time).[1]

[1]= same as above

To explain what’s happening here — what all this talk of Coordinated Universal Time, mean solar time, Terrestrial Time, ephemeris time, length of day variation, leap seconds, even is — a somewhat Hugoesque detour is necessary.

Solar time: time based on the position of the Sun – it is synodic

A schematic demonstration of the difference between the sidereal rotational period that proceeds relative to the stars and the synodic period that follows the Earth’s orbit and accounts for the additional 4 minutes it takes for the Earth to face the Sun again

{https://rwoconne.github.io/rwoclass/astr1210/guide04.html}

it varies throughout the year because of the eccentricity of Earth's orbit (the orbit is silghtly elliptical and so the Earth doesn’t move along the path with a constant speed) and because of the the Earth’s axial tilt (if you project the Sun's yearly movement along the ecliptic onto the Earth's equator, it appears that the Sun apparently moves faster across the equinoxes (where the curve of the ecliptic passes the equator at the maximum angle) and moves slower across the solstices (where the curve evens out and turns around));

then there are also other effects like the variation in the axial tilt itself (which varies between 22° and 24.5° in a 41'040-year period), its precession (the tilt itself makes a circle around the imaginary center perpendicular to the solar plane; this takes about 25'770 years), nutation (the consequences of the gravitational effects of other bodies in the solar system, principally the Sun and the Moon — Earth tide) and polar motion (the effect of the complex systems on Earth itself, such as ocean currents, atmospheric systems, movement in the liquid outer core, post-glacial land rise etc.).

The effects of the two main factors on the yearly length of day variation are displayed on the graph below:

The sinusoid line with dashes and dots represents the effect of Earth's eccentricity — speeding up across the perihelion (around 3 January) and slowing down across the aphelion (around 3 July); the violet sinusoid line with dashes represents the effect of the Earth's axial tilt — speeding up across the equinoxes and slowing down across the solstices; the red line is the combined effect of the two, called "the equation of time"

Apparent solar day thus varies from about 20 s shorter to 30 s longer than the mean 24 hours and the cumulative effect of this is shown on the graph above (your clock is X minutes ahead when the line is below the mean and X minutes behind when it's above).

Mean solar day is represented by the horizontal line on the graph and is also the basis for mean solar time.

So this is then “(apparent) solar time” and “mean solar time” covered, as for the rest:

UT = Universal Time; mean solar time without taking into account the short-term changes in position of the Earth's rotational axis (that is, polar motion); measured by observations of the motion of stars and distant radio sources;

UT1 = Universal Time with corrections for polar motion;

UTC = Coordinated Universal Time; TAI with approximations to within 0.9 s of UT1, which has since 1972 been done by introducing leap seconds when necessary; currently (2021) TAI is exactly 37 s ahead of UTC;

TAI = International Atomic Time; measured by atomic clocks (mostly caesium – the SI second being defined as “equal to the time duration of 9′192′631′770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 atom”); makes no reference to the motion of the Earth or the Sun (that is the day or the year); it is therefore currently less than a minute (about 37 s) out of sync with Universal Time, but this difference will only increase in the future; atomic clocks initially did not correct for the different altitudes they resided on, so the value was simply an average of all the measurements;

TT = Terrestrial Time; atomic time with corrections to the surface of the earth's geoid (i. e. mean seal level); TT is exactly 32.184 s ahead of TAI in order to maintain continuity with ET;

ET = ephemeris time; older alternative uniform time (necessary once the irregular nature of mean solar time was discovered) defined as 1/31′556′925.9747 of the tropical year for 1900 January 0 at 12 hours, which is also the basis for choosing that particular number of periods of radiation of the caesium atom.

However, as mentioned in the Wikipedia articles above, mean solar time itself is “irregular” — what does that mean? It means that, mainly due to tidal damping (the “Earth tide” that has been mentioned before does not mean the tides of the seas and oceans, but the daily bulging of the Earth’s geoid itself, which amounts to as much as 55 cm at the equator) the Earth’s rotation around its axis is gradually slowing down, meaning that days are slowly getting longer. Even though the days are getting longer at a rate of about +1.7 ms per century (based on the relatively short period of Earth’s history for which observational data is available), because of all the previously mentioned effects, this is not a straightforward linear progression. In fact, during most of the 20th century, days have been slightly longer than they currently are.

A graph of the change in the length of day (“lod”) from –2000 to +2500; the data from about –700 onwards (telescopic since about +1600; measured up to +2019) indicates that the progression is steady (average: +1.72 ms/cy), but with periods of faster change as well as plateaus during which the length of day does not change significantly, each of these lasting multiple centuries

{taken from the website http://astro.ukho.gov.uk/nao/lvm/ that hosts the data for Stephenson, F. R.; Morrison, L. V.; Hohenkerk, C.Y. (2016). "Measurement of the Earth's rotation: 720 BC to AD 2015". Philosophical Transactions of the Royal Society A. Royal Society. 472: 20160404. https://doi.org/10.1098/rspa.2016.0404 and Stephenson, F. R.; Morrison, L. V.; Hohenkerk, C.Y.; M. Zawilski, M. (2021). "Addendum 2020 to ‘Measurement of the Earth's rotation: 720 BC to AD 2015′". Philosophical Transactions of the Royal Society A. Royal Society. 477: 20200776. https://doi.org/10.1098/rspa.2020.0776 which are themselves updates to the 1984 article that the Wikipedia articles reference}

For the moment, then, the longest mean solar day (a yearly mean, to be sure) in Earth’s history does lie in the past. So then, was it in 1972? Or perhaps 1912? Or 1908? The answer is none of those, in fact — the highest tick on the graph above is the year 1903 with the length of day variation of +4.0 (±0.1) ms.

A closer look at the length of day variation during the last 300 years with the peak in 1903, showing also the historical reasons for the 32.184 s difference between TT (as continuation of ET) and TAI as well as the 37 s difference between TAI and UTC

{https://www.ucolick.org/~sla/leapsecs/dutc.html, a website I recommend for more info about leap seconds and the different time scales}

So where do the claims from the Wikipedia articles come from then?

The 1912 claim (“At the beginning of this year an extreme decadal variation in length of day produces mean solar days having a duration of 86400.00389 seconds of Terrestrial Time (or ephemeris time), the slowest rotation of Earth's crust ever to be recorded.“) is the most accurate, since it does not actually talk about the length of the year — only about the length of the mean solar day. It is actually correct with regards to the source it references as well, because the 1984 article does in fact give the largest value of length of day variation for 1912: +3.89 ms (while 1903: 3.69 ms). The claim should then only be updated given the more recent data.

The 1972 claim about it being the longest year in the context of UTC is of course also correct — this is the only calendrical year within an international standard valid for the entire Earth that lasted 366 days and 2 seconds (being both a leap year and having two leap seconds; put in seconds only, this is 31′622′402 s, cf. the values discussed below).

The other part of the claim refers to it being shorter than the year 1908 if mean solar time is taken into account. The first problem is of course that solar time does not have leap years – a solar or tropical year is always around 365.242189 days (i. e. 365 days 5 h 48 min 45 s) long, with variations of up to 30 mins — the longest tropical year since 1900 was between the spring equinoxes of 1997 and 1998: 365 days 5 h 59 min 59 s (taken from https://www.timeanddate.com/astronomy/tropicalyearlength.html); this is also why the initial question, “what was the longest year in Earth’s history?” is not actually sensible — there probably was or will be at some point an actual longest year in Earth’s history (the maximum variation from the mean value), but given the limitations on our data, this is — and will very likely remain — unanswerable. The second problem is that the value provided for the length of the year 1908 in mean solar days does not follow from the source. The value for 1908 given in the 1984 article is +3.61 ms, which — even if multiplied by 366 and not the standard astronomical year (365.25) that the calculations in the article used — does not yield 31′622′401.38 s; that’s the number it would yield if the length of day variation for that year were +3.77 ms, which, as you’ll note is still less than the +3.89 ms for 1912 in that same article, and also less than the maximum value of +4.0 (± 0.1) ms for 1903 in the updated articles.

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