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    Re: Navigation without Leap Seconds
    From: George Huxtable
    Date: 2008 Apr 22, 20:19 +0100

    Geoffrey Kolbe wrote-
    |
    | As I understand it, the formula adopted by the International Astronomic
    | Union in 1952 and used till around 1985 was:
    |
    | Delta T = 24.349 + 72.318*t + 29.950*t^2
    |
    | where t = centuries since 1900.0
    |
    | However, you are correct that the observed Delta T seems to have been
    about
    | - 2.7 seconds in 1900. All of which goes to show that time can be a very
    | confusing subject.
    
    =================
    
    Indeed it does. There's no such simple formula that can match the
    complexities of the way in which delta-t has fluctuated in the past, and
    will continue to do so in the future. Some attempts have been made to make a
    best-fit over restricted periods, but if a long-term fit is attempted it
    will show large short-term errors, such as the prediction, from the equation
    above, as +24.349 sec in 1900, when it was really -2.7 sec
    
    =================
    
    Actually, the approximation quoted in part by Geoffrey seems to be a bit
    more complicated than he made out, according to my 1974 Explanatory
    Supplement, which states on page 87-
    
    "... In term's of the departure of the Moon from Brown's tables, the
    relation of ephemeris time to universal time, found from discussions of
    observations of the Sun, Moon, and planets extending back to ancient times,
    is represented by :
    delta-t = +24s.349 +72s.318 T +29s.950 Tsquared + 1.82144 B,
    where T is reckoned in Julian centuries from 1900 January 0 Greenwich mean
    noon, and where
    B = (Lo - Lc) +10".71 sin (140 .0 deg *T  +240.7 deg) - 4".65 - 12".96 T -
    5".22 Tsquared,
    in which Lc is the tabular mean longitude of the Moon and Lo is the observed
    mean longitude, referred to Newcomb's equinox, at the observed universal
    time."
    
    However, I don't pretend to understand the meaning of those terms that
    Geoffrey missed out, nor even what units they are in, arc or time.
    
    ==================
    
    There's a useful section in Meeus, Astronomical Algorithms ; Chapter 10,
    Dynamical Time and Universal Time. He quote values of delta-t right up to
    publication date, which was 1998 (then = +63.0).
    And he even makes a shot at predicting future values, as best he can,
    saying-
    "For instance, we can use the provisional values-
    +65 seconds in 2000
    +69 seconds in 2005
    +80 seconds in 2015
    
    Interpolating between those numbers, we would arrive at a figure of 72
    seconds for 2008, and as we have seen, that's a far cry indeed from the
    current delta-t of +65.
    
    So how could Meeus' predictions be so spectacurly wrong, with an error of 7
    seconds after only 10 years? It was quite unexpected, that leap-seconds
    would be called for so rarely, over recent years, because the slowing of the
    Earth's rotation suddenly became so much less. It's a problem for
    geophysicists to solve, not for astro-mathematicians. Indeed, Geoffrey Kolbe
    tells us that their art is advancing, and their ability to predict the
    "weather" of the currents in the Earth's core. But there's a long way to go
    before they are able to predict Earth rotation 50 years ahead, as Geoffrey
    now acknowledges.
    
    ================
    
    What if a rather bigger hiccup were to occur, and if, for a time, the
    Earth's crust rotation were to actually speed-up rather than slow down? In
    principle, it could happen, and I can envisage the occasional negative
    leap-second being called for. I wonder how well the computer amd hardware
    systems that deal with these matters could cope. Has there ever been a
    negative leap-second, since their introduction, I wonder?
    
    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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