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