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    Re: Navigation without Leap Seconds
    From: Richard B. Langley
    Date: 2008 Apr 19, 15:14 -0300

    A couple of relevant items:
    
    
    -- Richard Langley
    
    On Sat, 19 Apr 2008, George Huxtable wrote:
    
    >
    >
    >Geoffrey Kolbe has written-
    >
    >"Well, my Long Term Almanac is nominally good up to the year 2050 and will
    >actually work OK up until 2060. So this is a very real question for me. I am
    >assuming that if leap seconds are abolished, anyone using my tables - which
    >assume GMT, or UT1 as it is called these days - will know the difference
    >between broadcast time and GMT and use this as a correction to broadcast
    >time."
    >
    >And following a question from Lu Abel, elaborated-
    >
    >"Actually, the theory used to generate my tables includes an estimation for
    >delta T, the difference between ephemeris time and Universal Time. How delta
    >T will vary in the future is not that well understood, of course, which
    >means that by 2050 my tables will probably be out by a second or so. "
    >
    >=========================
    >
    >Response from George-
    >
    >I wonder how confident Geoffrey really is about that projection into the
    >future, to within a second "or so".
    >
    >Let me propose a simple test. If we take the date on which his tables were
    >based, and arrive at the number of years, to 2050, that the prediction of
    >delta-t was to be valid for (so, 42 years if the tables were issued in 2008,
    >for example). And then take whatever projection Geoffrey uses to predict
    >delta-T to 2050, and instead apply it backwards, for the corresponding
    >number of years, to "predict" changes in delta-T in the past. Then, even
    >though we are now enabled to use a certain amount of hindsight in making
    >that projection, I ask him what's the maximum difference, over those years,
    >between delta-t, "predicted" that way, and delta-t as it actually happened.
    >
    >It's an interesting question, what should be done in our measurement of
    >time, as the rotation of the Earth slows more and more into the distant
    >future. A second defined as a fraction of a day (which I will call an
    >Earth-second) will diverge more and more from the "scientific", constant,
    >second, to which physical laws conform. That is a fact of life, quite
    >inevitable, and we can do nothing about it except adapt to it as best we
    >can. To me, the answer isn't clear-cut.
    >
    >It's a problem that can only get worse, faster, and faster, into the future,
    >and we need to bequeath to posterity a system that is practical and
    >applicable into the far distance, not one that will call for some major
    >upheaval at some future date long after we're all dead and gone.
    >
    >The second was defined to correspond to the rotation of the Earth around
    >1900, and delta-t was set roughly to zero about then, and it's been growing
    >ever since, at a steadily increasing rate.
    >
    >There are two main causes at work here. One is rather well understood, now,
    >and can be readily predicted. It's due to slowing of the Earth's rotation,
    >due to the action of the tides, caused mainly by the gravity-gradient of the
    >Moon (and, to a much lesser extent, the Sun). This component can be
    >measured, rather well, because the same forces have a corresponding effect
    >on the Moon, driving it out to a larger radius from Earth, which can be
    >measured by radar ranging. Over the long term, that is the major effect,
    >that will cause delta-t to grow from its present 38 seconds or so to about
    >an hour, in a thousand years time. By then, leap seconds would have to be
    >inserted, not at intervals of a couple of years as at present, but every
    >couple of months. Another thousand years, and it will have reached four
    >hours, because it changes according to a square law. 5,000 years from now,
    >the times will have diverged to put the two dates one whole day different,
    >and by then there will be a leap second needed at fortnightly intervals! So,
    >in the far future, will leap-seconds be a viable proposition? I only ask.
    >
    >The other main cause of the variation in the Earth's rotation is due to
    >fluctuating motion in the fluid core. This is combined with smaller faster
    >changes that result from winds and ocean currents, and much slower changes
    >due to continental drift, which we can ignore for now. But its those effects
    >of the fluid motion that are unpredictable, and mask, to a large extent, the
    >predictable changes in rotation rate over time-scales of decades at a time.
    >It's these fluctuations that I predict will cause Geoffrey Kolbe a bit of
    >grief.
    >
    >So what would be the practical effect of arresting  change in delta-t,
    >presumanly at its current value, so that Earth-time is forced to follow the
    >constant seconds that scientists use? For navigators, not a lot, I predict.
    >Almanac-makers, including Geoffrey Kolbe, would be able to produce their
    >wares for dates far into the future, instead of them having to anticipate
    >changes in the value of delta-t, for a few years ahead. Instead of using a
    >special time-scale (ephemeris time, now called terrestrial dynamical time)
    >to compute their dynamics, differing unpredictably from the UT (same as GMT)
    >that ordinary mortals use, then everyone would be forced to use the same
    >rational time as astronomers do.
    >
    >The snag comes when converting sky-positions to a geographical position with
    >respect to the Earth's surface, in calculating Greenwich Hour Angles (GHA).
    >In doing that, the increasing  and unpredictable discrepancy corresponding
    >to delta-t will have to be allowed for. If the almanac is to remain valid
    >for many years ahead, that can't be done within its pages, but only by the
    >navigator, knowing what the correction happens to be at his current date.
    >
    >Any difficulties resulting from such a change, in freezing leap-seconds,
    >would be felt by the ordinary person in real-life, way into the far future,
    >who would become aware that the time given by his clock on the wall no
    >longer corresponded with his time-by-the-Sun. Would that matter? We already
    >have got so used to tinkering with our clocks these days, first with mean
    >time, then with daylight saving and time-zones, that it's no longer sacred
    >any more for the Sun to be overhead at noon.
    >Perhaps an all-change in the time zones by an hour, a millenium or so from
    >now, would be called for. From then on, the interval between such changes
    >would get less and less.
    >
    >Should such things matter? We should ponder hard about the consequences of
    >our actions before making changes. What's a few thousand years in the future
    >when we consider how long civilisation has been going? How far ahead was
    >Julius Caesar thinking, when he reformed the calendar? And then, Pope
    >Gregory?
    >
    >Freezing leap-seconds at some date would create a bit of a mess, anyway. We
    >would end up with three different "scientific" time-scales, running in
    >parallel, with constant differences between them. First, there's Ephemeris
    >Time, (or TDT), a constant measure of time frozen from Greenwich Time as it
    >was in 1900, . Then there's GPS time, which was effectively Greenwich Time
    >but frozen at some date around 1980. And then we would have a new measure of
    >time, frozen from Greenwich time at some date a few years from now. There
    >would be a range of several tens of seconds spanning these three
    >time-scales. What chaos!
    >
    >I have tried to offer a balanced view of this matter, being somewhat
    >undecided about it myself. I would resist any hurry to change.
    >
    >A curious fact has struck me, in thinking about all this. Nobody seems to
    >have coined a word for delta-T, except "delta-T", sometimes expressed as a
    >Greek symbol. Isn't that a bit of a surprise? It doesn't really describe
    >well what it represents, and it certainly gives no clue as to which
    >time-scale is lagging on which. Delta-T , as defined, is normally positive,
    >but can be negative, as it was for a few years near 1900. Is there another
    >word for this difference, used in any other language? In many ways, it's
    >similar to the confusion that surrounds another time-difference, that
    >between mean and apparent time, which is so confusingly expressed by the
    >words "equation of time".
    >
    >George.
    >
    >contact George Huxtable at george@huxtable.u-net.com
    >or at +44 1865 820222 (from UK, 01865 820222)
    >or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    >
    >
    >
    >
    >
    >>
    >
    
    
    ===============================================================================
     Richard B. Langley                            E-mail: lang@unb.ca
     Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/
     Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506 453-5142
     University of New Brunswick                   Fax:      +1 506 453-4943
     Fredericton, N.B., Canada  E3B 5A3
         Fredericton?  Where's that?  See: http://www.city.fredericton.nb.ca/
    ===============================================================================
    
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