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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Brad Morris
Date: 2013 Jun 11, 17:22 -0400
Hi Geoffrey
Your chronometer, be it electronic or mechanical, counts increments of time. A well regulated chronometer has uniform increments.
Why do you expect such an instrument to magically match a discontinuity injected at random intervals? By this I mean that the chronometer is "know" when the discontinuity is to occur and to inject its own leap second. It cannot and will not. Unless you believe that a chronometer has powers other than counting increments.
If your purpose, as you state, is to match UT1 which is subject to this arbitrary discontinuity, then by all means, add that constant offset to your chronometers face value after adjustment for rate. That is
myTime = myChrono*rate+leapSeconds
Note that this assumes that myChrono starts with the same value as UT1's value. If that delta exists (as is most likely), it should also be added.
If your purpose is to determine the rate, then the discontinuity should be subtracted from the UT1 value and then the division done.
myRate =(myChrono-(UT1Chrono-leapSeconds)/period
If you include the discontinuity in the rate, INDEPENDENT of the length of the rating period, then you will have an error in the rate and no manner of further manipulation will correct it.
6 days, 200 days, 3650 day periods merely affect the magnitude of that error. At 2 seconds (my period) the rate error is huge if you include the discontinuity. The error becomes smaller as the period becomes longer; but the rate error is never zero.
I note that you have carefully posed the question but never answered it yourself. Are you arguing that the discontinuity be included in the rating (yielding a 0.5 second per second rate in my period)? For your ten year period thats 1 second/3650 days or an error in your rate of 274 microseconds per day. Are you arguing that we should subtract it out, as Bill and I apparently state? Please don't sit on the fence anymore ... choose!
Brad
Brad Morris wrote:
Would anyone think that the rate of their chronometer is 0.5 seconds per second? Now why in the world would the LENGTH of the rating period adjust your thinking?Â
Well Brad, I have attempted to explain the problem twice now. At the risk of inducing jaw breaking boredom I will have a third stab, then I am done.
Gary was comparing his clocks against WWV, which is UTC or "broadcast time". But UTC is itself being constantly compared to UT1 and periodically a second of time is inserted (or taken away) from UTC so that UTC continues to agree with UT1 to within +/- 0.9 seconds. So, what Gary is actually comparing his clocks against is UT1, not UTC. This is actually what Gary wants as the almanac for the position of the Sun, Moon, planets and stars is calculated for UT1 time and so he wants a clock that will give him UT1 time.
Since UTC maintains its rate against UT1 by the addition (or subtraction) of a quantum of time (the second) in a discontinuous way, this needs to be accounted for when rating a UT1 clock against UTC. Clearly, if you have been rating a clock for six days against WWV and you find that it has gained six seconds in that time, the clock is gaining a second a day. But suppose that at midnight on the sixth day the powers-that-be insert a leap-second into UTC and you see that on the seventh day that your clock is now 8 seconds fast. It would appear to have gained two seconds over the previous day instead of the expect one second. There is no argument that for the purposes of continuing to rate your clock against UTC, the discontinuity of the inserted leap second should be accounted for here by subtracting one second from your clock's given time.
Now, suppose that instead of rating a clock for a period of one week, you observe the drift of a clock against WWV for a period of ten years. Suppose the clock had been 'dead beat' with WWV at the start, but after ten years, the clock was now 45 seconds fast against WWV. We could surmise that this clock is gaining 4.5 seconds a year. But supposing that during the ten year period there had been six leap-second additions of time. How should we account for those six leap seconds? Should we remove 6 seconds from the clock's observed time and say that it is really only 39 seconds fast against WWV and so it is actually running 3.9 seconds a year fast? (Remember, UTC is being forced to agree with UT1 in the long term by the intercalation of leap-seconds. And here, ten years is definitely 'long term'.)
Next, suppose you set your clock to be 'dead beat' with WWV at the start of a rating period, and 200 days later you observe that your clock is running 5.2 seconds fast against WWV. From this, you calculate that your clock is gaining 0.026 seconds a day. Suppose that the powers-that-be decide to insert a leap-second at midnight on the 200th night and so the next day you see that your clock is running 6.2 seconds fast against WWV. Should you now say that your clock is actually gaining 0.0308 seconds a day (6.2/201)? Or should you remove the leap second and revert to a rate of +0.026 seconds a day? Or should you decide that neither is the correct rate for your clock against UT1 time?
Geoffrey Kolbe
