# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---