By Duncan Steel 20/03/2019 6


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We are generally habituated to using the Greenwich meridian as the global standard for mapping and time-keeping, despite it being only 135 years since its adoption. As I show here, if the Catholic Church had adopted in 1582 a more-precise calendar in terms of year length then a natural prime meridian results, in a location that might appear surprising.

My apologies for posting a new blog so soon after the previous one, but there’s something I need to communicate today. One could say that time is of the essence. Just how true those five words are will soon, I hope, become apparent as you read this piece.

Why today? Well, today’s Google Doodle gives a clue: 

Google being a US-based company, you’ll notice that it says ‘Fall Equinox 2019’. They mean ‘Autumn’ of course, but at least there is a recognition that here in the southern hemisphere the seasons are reversed. To an astronomer, the equinox in March is called the Vernal Equinox, and it’s a pivotal juncture in the year. Indeed for centuries the traditional date of this equinox was the start of the New Year in various countries; matter of fact, this is still the case in various calendars, one of which I will discuss below.


What I am going to describe here is not original to me. The core facts were explained to me by a British mathematician named Simon Cassidy, who over recent decades has spent his summers mainly in Picton, though mostly he has lived in California for decades. Simon’s concept was related to me over a rather nice Indian curry at a restaurant in Berkeley in September 1998. The three graphs presented below I drew up soon after so as to convince myself that what he described was true, and so I have had those plots on file ever since. As you might expect, twenty-year-old plots were made using old technology, and so they do not look so flash, but what they contain might be really important.

The extent to which I can argue their significance here is limited, by time and space. I will give merely an outline of the start of a far bigger story. When I understood what Simon had told me, I was astonished. I still am; and I hope you will be too. Just bear with me, please.


I never know how to start this story. Perhaps this is the best I can do… Imagine that you are an alien from the planet TVC15 come to map Earth. Is there a natural way to do this? That is, independent of human history and so on, is there a natural grid that could be applied?

Obviously enough there is a natural way to set lines of latitude, based on the spin axis and therefore the equator. But what about longitude? We use the Greenwich meridian (the location of a certain telescope in the old Royal Greenwich Observatory in eastern London) by international agreement, but that is clearly a contingent choice based on human affairs. Is there a natural prime meridian?

The answer is yes. And funnily enough it passes through both the building that is the seat of government in a certain country, and also through the national astronomical observatory…


The vernal equinox this year occurs at 21:58 on March 20th, in Coordinated Universal Time (UTC). In New Zealand the equivalent is 10:58 on March 21st, because we are currently (on NZDT) 13 hours ahead of UTC. The preceding two sentences tell you why I need to publish this blog post today. It’s timely.

UTC can be thought of in various ways. I like to think of it as being a high-technology version of time based on atomic clocks rather than the rotation of the Earth. After the first electronic (quartz) clocks were developed close to a century ago, it was as if precise time-keeping was removed from the astronomical observatory and transplanted into the physics laboratory. To that extent it is peculiar that GMT (Greenwich Mean Time) is still widely regarded as being the standard. Really, it’s UTC.

The definition of the second is based on the spin rate of the Earth (that is, the day length) in the late nineteenth century, using precise determinations of when certain stars crossed the meridian. Quartz clocks and then ever more sophisticated electronic and atomic clocks use that consistent length of a second.

In the meantime, however, the Earth’s spin rate has slowed very slightly – the rate of deceleration is about 1.7 milliseconds per day per century – and as a result of that our planet’s rotation phase gradually gets out of step with those super-precise physics clocks. Essentially, what happens is that GMT wanders away from UTC.


In passing I note simply that the major cause for Earth’s rotation rate slowing is the drag force imposed by the tides moving across the oceans and running up against the continents. Those tides are raised largely by the Moon. Reducing the terrestrial spin rate means that our planet’s spin angular momentum is reducing. Thinking of the Earth-Moon pair as being an isolated system, the total angular momentum is conserved, and so the orbital angular momentum of the Moon must increase. And so it does. The Moon is drifting away from us by about 38 mm per year, as determined using laser ranging to retroreflectors left on the lunar surface in the Apollo programme.


The technological fix for the fact that our spin rate is slowing, resulting in a day no longer lasting for 86,400 seconds precisely, is to introduce leap-seconds every so often. (This has absolutely nothing to do with leap years.) A leap-second is inserted, effectively requiring us to make our everyday clocks stand still, so as to keep UTC within 0.9 seconds of GMT.

But what is GMT itself? GMT is the time on the Greenwich meridian according to a theoretical construct known as the mean sun (hence the M in GMT). The mean sun is the position that the real Sun would occupy if Earth’s orbit were precisely circular, and our spin axis were perpendicular to the plane of that orbit (the ecliptic). That mean sun can be up to eight solar diameters away from the real sun in the sky. If you look at a good sundial you will see moulded into the horizontal plate a graph indicating how to correct the apparent time from the gnomon’s shadow into mean solar time, that graph (formally termed the Equation of Time) indicating deviations of up to 16 minutes at different times of year.

What a sundial shows directly is local solar time; that is, the time at your longitude according to the Sun in the sky. For most of history that is what was used to keep time. It was not until the development of the telegraph that it was possible to transmit time signals over large distances, enabling mechanical (and later electric) clocks to be coordinated.

For example, the Lyttelton time ball that was wrecked in the Christchurch earthquakes earlier this decade was built in order to provide a time reference to ships in the harbour (and others), the ball being dropped at 1pm daily on the basis of astronomical observations. Pulling a longer bow from Christchurch, at the Oxford college from which that NZ city derives its name there is a clock on a building known as Tom Tower. That clock for many years had two minute hands: one showed Oxford time (which is five minutes behind Greenwich because Oxford is about 1.25 degrees west of the old Greenwich Observatory), while the other showed London/Greenwich time, that being the time which the railways used. If you didn’t want to miss your train, you had to follow the later of the two times indicated and quickly make your way to the nearby railway station.


The intent of my preceding text is to show that if you stepped back a few centuries, the time used was local solar time, and that depended on your longitude. So, let us step back to when the Roman Catholic Church introduced the Gregorian calendar (named for Pope Gregory XIII) in 1582.

Before going further, let me write that I have no religious beliefs myself. All I am relating here is a story based on the astronomy and history as I understand it. If I get anything wrong – and please do check on me – then it is an honest mistake rather than a deliberate deception. All the results I present below can easily be verified (or falsified).

Okay, so what I did was I wrote some software code to determine the time of the vernal equinox in years past (and some into the future). Why the vernal equinox? Because it’s what the date of Easter is predicated on (along with other things), and therefore a pivotal matter for the design of the Gregorian calendar. That calendar was not introduced to ‘put the seasons in step’, as many imagine; it was set up to regularise the date of Easter.

So, I calculated the instants of the vernal equinox as defined by when the Sun crosses the celestial equator so as to mark the beginning of northern Spring. In doing so I needed to take into account how Earth’s spin has slowed over the past four-plus centuries, but we know that through various means (such as records of past total solar eclipses). Here is a graph of those equinox times, in local solar time on the Greenwich meridian and following the Gregorian dating system. (In passing I note that the Greenwich meridian was adopted as the international standard prime meridian by many nations at a conference held in Washington DC in 1884; as you will see later, that is quite remarkable, in terms of where the meeting was held.)


This plot begins in 1582, with leap years every fourth year causing the time to jump back earlier by almost 24 hours in a quadrennial cycle until 1700 comes along, when there was no backwards jump. The reason for this is that on the Gregorian calendar every fourth year is leap unless it is a century year (like 1700, 1800, 1900) which is not divisible by 400 (as in 2000, and again in 2400). Thus bridging 1700, 1800, 1900 and 2100 there are eight-year sequences in which the equinox time gets later and later in the year, because there was/will be no leap-year correction in the middle.

The outcome of all this is that in a 400-year cycle there are 97 leap-years, making an average year duration of 365 days plus a fraction 97/400 = 0.2425. That seems to be a pretty good approximation to the current (last millennium, this millennium) value of the year as defined specifically by the interval between vernal equinoxes, this being about 365.242374 days.

Just to return momentarily to the Gregorian calendar: in the Easter computus the equinox (the ecclesiastical equinox) is defined to be the whole of March 21st, regardless of where the Sun is in the sky. Looking at the plot above you might note that the astronomically-defined equinox will not occur again on March 21st (for the Greenwich prime meridian) until the year 2102.


Could one do better in terms of the accuracy of the average year length? That is, could one design a calendar with a year length closer to the target 365.242374 days than the Gregorian’s 365.2425 days?

In some parts of the world (notably Iran and Afghanistan) the Jalali calendar is used. This is termed a rules-based calendar: a new year (Nowruz) occurs on the day (midnight to midnight at Tehran’s longitude) that contains the vernal equinox. Apparently this calendar was at least in part the work of Omar Khayyam in the 11th century.

Whilst deviations into single 29-year or 37-year cycles are feasible due to various astronomical vagaries, the Jalali calendar performs rather consistently with 33-year cycles containing eight leap-years. That is, there are seven quadrennial cycles followed by one quinquennial sequence.

Divide 8 by 33 and you get 0.242424,,, recurring. This is indeed rather closer to the target of 0.242374 days than the Gregorian 97/400 = 0.2425.


Perhaps of more significance is this. Looking at the plot shown earlier, the instants of the vernal equinox on the Gregorian calendar vary over a range of 53 hours. Currently we are close to the mid-point in such a range, because the year 2000 was leap: the latest time of the equinox in that graph was in 1903, whilst the earliest will be in 2096. This large range is due to the long cycle time (400 years in toto, though the 193 between 1903 and 2096 comprise the significant period here). If one used the 33-year Jalali cycle, then the total spread is far less; in fact less than 24 hours. (Think about it: on the middle year in the 5-year long interval in amongst the 33 years, the equinox two years before was earlier by two times a bit less than 0.25 days, and the equinox two years after is also a bit below two times 0.25 days later, and so overall across that quinquennial sequence the total range of the equinox time is below one day, or less than 24 hours.)

So, to illustrate the point I take precisely the same set of data (equinox times) as in the first graph, and instead now plot them in 33-year cycles containing seven 4-year leap sequences followed by one five-year sequence, starting in 1582 and all for the Greenwich prime meridian.


Now, I don’t think you need to be super-smart to take a look at that plot and realise that you could shift the whole lot sideways, and then the equinox would always occur on the same calendar date. That is, you choose (instead of Greenwich) a different prime meridian, its location not being determined by human history, politics and the like, but rather a definition based solely on scientific matters*. (*In a later post I will discuss how all this can lead to a better, more-accurate Easter computus, but at the same time we will see that it is not quite true that the choice is based solely on scientific matters.)

So, here we go: the same data yet again, but now plotted using longitude 77 degrees west as the prime meridian. One can choose any date for the equinox by altering the number of days you knock out of the year when you revise the calendar, just as the Catholic Church dropped ten days from 1582, and Britain dropped eleven when it came in line with the Gregorian system in 1752, the extra one being due to 1700 having been a leap year on the Julian calendar but not the Gregorian.


So, where is longitude 77 degrees west? I’ll give you a visual clue. Here is a satellite photograph showing a building that happens to be on that meridian; in fact 77 degrees west goes precisely through the centre of that cupola, because it was deliberately placed there:

 

 

If case you haven’t got it yet, let me pan out a little:

 

 

Still struggling? Let’s pan out again. Now you can see the whole length of the National Mall, the Washington Monument, and the Lincoln Memorial. That red place marker is largely obscuring the White House:

 

 


So here below is where the world’s natural prime meridian lies, slap bang along the longitudinal axis of Washington DC. On that meridian lies not only the Capitol, but also (a small distance to the north) the U.S. Naval Observatory, effectively the national observatory… and the place where the master clock (and others) is operated, disseminating time signals to much of the world.

 

Obviously this is simply a fluke… Personally I mostly veer away from conspiracy theories and towards cock-up explanations. There is more to be said, however, in a later blog post.

 


6 Responses to “Does Earth have a natural prime meridian?”

  • It is difficult to grasp that someone who studies time systems and calendars can fall into the trap like so many people to suggest that leap seconds are applied to correct for the slowing of Earth’s rotation. As the author says above, this slowing amounts to 1.8 milliseconds per century (he says 1.9 but lets not argue about that). How could a whole second that is applied every so many years be related to that? This is 5 orders of magnitude different! This misunderstanding is not directly related to the issue raised in this otherwise interesting article, so it fortunately doesn’t really destroy its conclusions, but it is really sad that this serious misconception is repeated here. In 1971 atomic clocks (TAI) replaced the rotation of the earth (UT1) as the basis of world time. Earlier in 1967 the new standard time (the SI second) had been precisely defined (together with fixing the value of the speed of light). Since 1971 the (atomic) day is precisely 86,400 TAI seconds. Sadly (in hindsight) this definition of the standard second has been made a little too short and therefore TAI is running slowly away from the earth’s rotation (UT1). THIS is the reason that the IERS (https://www.iers.org/IERS/EN/DataProducts/EarthOrientationData/eop.html) has to apply leap seconds to keep civil time to within 0.9 seconds of Solar time. This is what has become UTC: it is TAI corrected with whole seconds to keep following the average motion of the sun. In average the difference TAI – UT1 is about one second in every 1.25 years, but it fluctuates because earth rotation fluctuates. The latest leap second was applied at the end of 2016.

    I do applaud the author for noticing that erroneously the term GMT is still used when UTC is meant. This is another widespread cause of confusion. GMT is Solar time and thus by definition different from UTC which is an atomic time.

  • Unfortunately Mr Vermaat is incorrect in his criticisms because he has mistaken a deceleration for a velocity.

    Vermaat wrote: “…this slowing amounts to 1.8 milliseconds per century (he says 1.9 but lets [sic] not argue about that).” Two points, the first trivial:

    (1) As a matter of fact I wrote “the rate of deceleration is about 1.7 milliseconds per day per century.” That figure (1.7) is the generally accepted one, based on the analysis of Stephenson and Morrison (Phil. Trans. Roy. Soc. A, 351, 1995), who wrote: “Using the change in the length of the mean solar day (l.o.d.) in units of milliseconds per century (ms cy-1 ) as the measure of acceleration in the rate of rotation, it is found that the l.o.d. has increased by (+1.70 ± 0.05) ms cy-1 … on average over the past 2700 years.”

    (2) As I indicated in point (1) and in my original text this is a deceleration (a negative acceleration), whereas Vermaat imagines it to be a velocity. Thus, for example, if one looks at Figure 2 in Stephenson and Morrison’s paper one will see that the accumulated delta-T (the difference between the actual rotational phase and the phase that would have existed were the terrestrial spin rate not decelerating) going backwards in time is a curve rather than a straight line, and amounts to about 20,000 seconds by around 700 BCE.

    That the slow-down of Earth’s spin under tidal drag is a deceleration rather than a constant rate as Vermaat apparently thinks (“this slowing amounts to 1.8 milliseconds per century”) should be obvious to most readers familiar with Newton’s Second Law of Motion (F=ma) and its expression for rotational motion (T=Iα where T is the torque imposed, I is the moment of inertia, and α is the angular acceleration).

    Turning now to the frequency with which leap-seconds are inserted, as I wrote in the blog post in question “The definition of the second is based on the spin rate of the Earth (that is, the day length) in the late nineteenth century…” There are easily-accessible sources that cover this (e.g. Wikipedia on the ‘Second’), showing how Newcomb’s Tables of the Sun (1895) provided the basis for the much-later definition of what might be termed the ‘atomic second’ in terms of the number of seconds in a (mean) tropical year as at the start of the year 1900. I will take that year to be precisely 1.2 centuries ago, for simplicity.

    One of the familiar equations for uniformly accelerated motion (although I note that Earth’s spin rate is not uniformly decelerated, instead showing seasonal and multi-year trends as depicted in the second graph in the Wikipedia page for ‘Leap second’) is: v = u + at. Using 1900 as the radix, u = 0 and so v = at = (1.7 msec/day/century) × (1.2 centuries) = 2.04 msec/day in the current epoch (i.e. 2019).

    Thus the time taken for a full ‘discrepancy’ of one second to accumulate is (1 / 0.00204) = 490 days. That is why leap-seconds have been inserted erratically, but typically with 18-month spacings (given that they are introduced at the end of either June 30th or December 31st). Note that this is the interval over which a second accumulates at present; in 120 years from now the time for such a slippage to accumulate will be (one would anticipate) half as long (i.e. about 245 days).

    Vermaat asked: “How could a whole second that is applied every so many years be related to that? This is 5 orders of magnitude different!” I trust that my discussion above has answered his question.

    If anyone is interested in reading more (at a popular level, as opposed to technical tomes) then there are several excellent books out there, including two of my own: Marking Time (Wiley, New York, 2000), and Eclipse (National Academies Press, Washington DC, 2001).

    Finally I need to express the view that in discussions on scientific matters ad hominem attacks and personal comments are inappropriate and actually hinder progress and understanding. This is especially the case when one’s own ideas are poorly-based, because one can end up looking very foolish.

  • > The technological fix for the fact that our spin rate is slowing…

    is to use rockets or mirrors to speed it back up again! Leap-second just make life hard for us poor programmers.

    • Dear Moz Guy,

      Thanks for the comment, appreciated!

      However, I am not sure whether your suggestion of rockets and mirrors would be viable. Actually, what I just wrote is untrue; it’s not viable.

      What you highlight is a real problem, though, and it’s one that has been argued about for some years. The last time I read anything serious about this was seven or eight years ago, and by dragging out an old external drive I found two papers/reports that might be of interest, from 2010 and 2011. These I have made available here and here.

      In the meantime the matter has been debated by relevant international bodies, and a decision repeatedly deferred.

      Of course, you could always opt out (of leap seconds). In essence, this is the case for the GPS time system, which has not inserted leap seconds since it ‘began’ in 1980 such that it now differs from UTC by 18 seconds. To see comparative values of UTC, GPS time, Loran-C time, and TAI, see here.

  • Yes, sadly I am far more involved in dealing with leap seconds than is really compatible with sanity. As with so much timekeeping software, the major problems come from bridging between different standards and implementations. Fortunately the systems I work on can simply allow a few minutes of “settling time” as the systems I talk to work through the process of implementing a leap second. Then minutes-to-hours later, the leap second is manually applied on some of the systems that rejected it. Meanwhile users complain if our local time service was unavailable at any time or gave different answers from whatever other reference they were using (and others complain that their system was unable to cope with second 61 of 60…).

  • Thanks for the papers. I deal with the various time standards and implementations more than I’d like to (does anyone *like* dealing with them?)