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    Re: Navigation without Leap Seconds
    From: George Huxtable
    Date: 2008 Apr 19, 18:10 +0100

    
    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.
    
    
    
    
    
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