Let's drive the discussion forward into a region that we haven't touched here before:

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What happens with a leap-second and leap-hour free time scale (as the TI proposed at Torino) in the long run (>> 1 kiloyear into the future) and what interactions with the length of the year emerge there? Let's say, we get used to the idea of dropping all leap seconds from UTC from today and we rename the resulting new uniform atomic time scale into International Time (TI). This would put the point (or meridian) on Earth where International Time coincides with local time (currently for UTC this point wanders around somewhere near the Greenwich meridian) onto a slowly accelerating course eastwards, detaching International Time from London and making it truely international. Fine so far (apart from short-term concerns with legacy software over the next 10-20 years). How will local times have to be adjusted? Stephenson and Morrison give delta_T(T) = TAI - UT1 = (31 s/hy^2) T^2 - 52 s where T = (t - 1820-01-01T00:00) / (100 * 365.25 days) is the number of centuries (hectoyears, hy) since 1820. For Temps International TI = TAI - 32 s (if introduced today), we get equivalently delta_T(T) = TI - UT1 = (31 s/hy^2) T^2 - 84 s The offset between local civilian times would have to be adjusted by one hour when delta_T(T) = 0.5 h, 1.5 h, 2.5 h, ..., i.e. at about the years sqrt((1 * 1800 s + 84 s) / (31 s/hy^2)) * 100 + 2000 = 2780 sqrt((3 * 1800 s + 84 s) / (31 s/hy^2)) * 100 + 2000 = 3330 sqrt((5 * 1800 s + 84 s) / (31 s/hy^2)) * 100 + 2000 = 3712 ... 2780, 3330, 3712, 4023, 4292, 4533, 4752, 4956, 5146, 5326, 5496, 5658, 5814, 5963, 6107, 6246, 6380, 6511, 6638, 6762, 6882, 6999, 7114, 7227, 7337, 7444, 7550, 7654, 7755, 7855, 7954, 8050, 8146, 8239, 8332, 8423, 8513, 8601, 8689, 8775, 8860, 8944, 9027, 9109, 9191, 9271, 9350, 9429, 9507, 9584, 9660, 9735, 9810, 9884, 9957, 10030, 10102, 10173 The adjustment of a civilian time by one hour can easily be accomplished without particular disruption as part of the summer time arrangements (assuming that this 1% electricity saving measureis still of concern in the far future). This would have to be done for the first time near the year 2780, and then every few hundred years, and from the year 7700 on even several times per century. What I am still struggling with is the long-term perspective. At present, the maximum difference between any civilian local time and the international reference time (currently: UTC) is limited to +/- 13 h. That limit would be dropped if we replaced UTC with TI, and at about the year sqrt((12 h + 84 s) / (31 s/hy^2)) * 100 + 2000 = 5736 the point where International Time corresponds to local time will cross the International Date Line. What do we do then? Having International Time and local civilian time several days apart sounds rather unpractical for doing mental arithmetic and could lead to confusion far more severe than anything leap seconds might ever cause. I had briefly hoped that we can play around with 29 February and remove from the civilian time zones a 29 February (compared to what pope Gregory dictates) near the year 5700, in order to keep the maximum offset between any civilian time zone and International time at least limited to +/- 25 hours. International Time would continue to strictly follow the Gregorian rules, as it must be uniform and long-term predictable. A Gregorian "leap year" in TI that is ignored in local civilian times would bring civilian times back into sync with TI without much disruption. This would at first glance of course mess up the date of the spring equinox (the reason for the Gregorian calendar reform), and who knows whether people still worry about when Easter Sunday is by then. We need leap years, in order to compensate for the fact that the rotational frequency of the earth around the sun and around its own polar axis have a non-integer relationship. However, if the length of the tropical year were highly constant, the need to keep local civilian times and TI from diverging by more than a day and the need to keep the spring equinox on the same date every year would lead to compatible requirements for scheduling leap years in civilian time zones beyond the period when the Gregorian rule works. Unfortunately, the rotation of the Earth around the Sun accellerates far too fast for this idea to work: Newcomb's formula for the geometric mean longitude of the Sun is L = 279° 41' 48".04 + 129602768".13 C + 1".089 C^2 where C = (t - 1900-01-01T12:00Z) / (100 * 365.25 days) is the number of (Julian) centuries since 1900. Newcomb's third term represents the acceleration of the Earth's mean angular velocity around the sun. This term will grow to 0.5 days or equivalently a mean-sun longitude offset of 360°/(2 * 365.25) at C = sqrt(360/(2 * 365.25) * 60*60" / 1".089) = 40.36 centuries = 4036 years In other words, the longterm frequency stability of the annual oscillation of the earth is not significantly better than that of the daily oscillation (even worse: one speeds up and one slows down), therefore leap-days (29 February) cannot solve both problems at the same time. What else can we do? Shall we give up the long-term stability of the date of the spring equinox? Shall we hand over the authority of deciding, whether a year that is a multiple of 400 shall be a leap year in civilian time zones to someone like the IERS, while the insertation of leap days into TI will strictly follow the Gregorian rule in the interest of long-term uniformity? In other words, can we live with the spring equinox (and therfore religious dates) moving over the next few thousand years? Is the date of the spring equinox more important to people than having an upper limit for the offset between a uniform atomic International Time and local civilian time? (Perhaps it is time to get the theologians back into this discussion after so many centuries ... ;-) Reference: - Nelson, McCarthy, et al.: The leap second: its history and possible future. Metrologia, Vol. 38, pp. 509-529, 2001. http://www.cl.cam.ac.uk/~mgk25/time/c/metrologia-leapsecond.pdf -- Markus Kuhn, Computer Lab, Univ of Cambridge, GB http://www.cl.cam.ac.uk/~mgk25/ | __oo_O..O_oo__