Re: What to do if International Time hits the International Date Line?
On Tue 2003-07-01T21:51:09 +0100, Markus Kuhn hath writ: > Is the Simon et al. formula considered good enough to predict the mean > longitude of the sun within half a day for the next few tenthousand > years? The authors make only a statement on the quality of ephimerides > derived for the years 1000-3000. Simon et al. write that they have attempted to make the expressions valid, in the sense of the mean, from 4000 BC to 8000 AD. The best other reference I know is Laskar in Astron. Astrophys. 157, 59-70 (1986) where the mean elements of the planets were studied over 1 years. The mean longitude of the inner planets are given as 10th order polynomials. I believe that in this paper the elements are more mean of a mean than in Simon, by which I mean that the cyclical variations of relatively short term are not present. (Apologies for that last sentence :-) Nevertheless, half a day is half a degree, and all these expressions are probably that good over those time spans. It is very hard to be more sure than that. The only valid checks that reach 4000 years before present are a few records of solar eclipses and the alignment of megalithic structures. These checks are not much better than half a degree. Extrapolating as far into the future is just as dangerous; it is really better to wait and see. Getting more directly back to the purposes of leap seconds... The current scheme of UTC with leap seconds should work for well over 1000 years. Around 1700 years from now it would become necessary to have a leap second at least once a month, and then the current scheme requires modification. In the absence of leap seconds, an atomic timescale will have deviated from UT by an hour in 1000 years. As Markus pointed out, the situation gets worse quadratically. Night becomes day between 3000 and 4000 years from now, and in around 5000 years today is tomorrow. For the purposes of broadcast time signals, it should be sufficient that any change which may be adopted will last for 1000 years without forcing posterity to implement a large discontinuity. As for 1 years -- there can be point in laying down specifications for activities to be carried out over 300 generations from now. IMHO, even planning for 500 years is hubris, but knowingly creating a problem which must be solved by somebody else in 500 years is criminal. -- Steve Allen UCO/Lick Observatory Santa Cruz, CA 95064 [EMAIL PROTECTED] Voice: +1 831 459 3046 http://www.ucolick.org/~sla PGP: 1024/E46978C5 F6 78 D1 10 62 94 8F 2E49 89 0E FE 26 B4 14 93
Re: What to do if International Time hits the International Date Line?
On Tue 2003-07-01T21:51:09 +0100, Markus Kuhn hath writ: > http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1994A%26A...282..663S&db_key=AST Caution. It is extremely important to note which reference frame is being used. > Thanks. If I understood it correctly, section 5.8.3 gives me with > > L = 100°.46645683 + 1295977422".83429*t - 2".04411*t^2 + 0".00523*t^3 All of the expressions 5.8 are with respect to the mean dynamical ecliptic and equinox J2000. That is a reference frame which is very nearly, but not quite, inertial. As such it does not give the longitude of the sun with respect to the seasons that the Gregorian calendar attempts to mark. The expressions 5.9 are referred to the mean dynamical ecliptic and equinox of date. Those relate more closely to the calendar, and as such they are a much better match to Newcomb's values. > The large number of decimal digits provided for the Newcomb formula in > the Metrologia leapsecond paper had suggested to me that all this is > rather exact science and that these digit are actually significant ... :-( precision vs. accuracy. The precision is necessary in the sense that UT1 is still determined in a fashion which refers to the fictitious mean sun of Newcomb's tables, such as they were. Whenever a new and better model is applied, the boundary conditions are set such that there is no measurable discontinuity in UT1 during the changeover. This practice has been followed for the past century, and was an issue of concern just this last year when the new IAU system (which abolished the ecliptic and equinox) was instituted on Jan 1. This means that whatever errors are present in the previous set of expressions are carried into the initial conditions of the new expressions. As such, the longitude the fictitious mean sun accumulates small errors based on the current amount of imprecision, and the mean time at which the sun actually crosses the Greenwich meridian does slightly deviate from 12:00 UT. This small drift is part of the motivation being used by the leap second haters to justify completely disconnecting civil time from the sun. But it should be pointed out that the calculation of TAI suffers from an analogous drift. The rules for calculating TAI have changed several times, which means that a best extrapolation of a completely uniform timescale back through the history of atomic time would deviate from the published values of TAI. > Is the Simon et al. formula considered good enough to predict the mean > longitude of the sun within half a day for the next few tenthousand > years? The authors make only a statement on the quality of ephimerides > derived for the years 1000-3000. The accuracies are given in table 7 as 6 arcsec for the earth/moon. For ranges outside the years 1000-3000 it would be better to see the referenced works of Bretagnon and Laskar. -- Steve Allen UCO/Lick Observatory Santa Cruz, CA 95064 [EMAIL PROTECTED] Voice: +1 831 459 3046 http://www.ucolick.org/~sla PGP: 1024/E46978C5 F6 78 D1 10 62 94 8F 2E49 89 0E FE 26 B4 14 93
Re: What to do if International Time hits the International Date Line?
Steve Allen wrote on 2003-07-01 19:52 UTC: > On Tue 2003-07-01T20:34:58 +0100, Markus Kuhn hath writ: > > Newcomb's formula for the geometric mean longitude of the Sun is > > > > L = 279° 41' 48".04 + 129602768".13 C + 1".089 C^2 > > not really valid more than 200 years into the future. > Please don't use Newcomb for that. > > You want to use something intended to match integrations that have > moved much farther into the future. > > For a start, see Simon et al., Astron. Astrophys 282, 663-683 (1994) http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1994A%26A...282..663S&db_key=AST Thanks. If I understood it correctly, section 5.8.3 gives me with L = 100°.46645683 + 1295977422".83429*t - 2".04411*t^2 + 0".00523*t^3 the mean longitude of the sun, where t is kiloyears from the year 2000. Oops, I am mildly shocked to see that the sign of the t^2 term has changed its sign compared to how Newcomb's formula is printed on page 4(512) of http://www.cl.cam.ac.uk/~mgk25/time/c/metrologia-leapsecond.pdf while the magnitude changed by a factor of 2 whereas the scale of t has changed by a factor of 0.1. The large number of decimal digits provided for the Newcomb formula in the Metrologia leapsecond paper had suggested to me that all this is rather exact science and that these digit are actually significant ... :-( Given the new formula, unless I made a silly mistake with my pocket calculator, the second term in the mean longitude of the sun will have grown to 0.5 days by (360/(2 * 365.25) * 60*60" / 2".044)^1/2 = 29 kiloyears from now whereas the third term will have accomplished the same (with opposite sign) by (360/(2 * 365.25) * 60*60" / 0".00523)^1/3 = 70 kiloyears from now Sounds much better! If the annual oscillation of the earth does really not diverge from atomic time by more than one day for the next 30 kiloyears, then adjusting the leap year rules for civilian time zones might really help to keep the a) civilian time zones b) international (atomic) time c) the date of the spring equinox synchronized more or less for the next few ten thousand years. So there might be hope not to mess up everything completely by dropping leap seconds. Perhaps this idea is not that crazy after all and deserves being scrutinized by professional astronomers. Comments welcome. Is the Simon et al. formula considered good enough to predict the mean longitude of the sun within half a day for the next few tenthousand years? The authors make only a statement on the quality of ephimerides derived for the years 1000-3000. Markus -- Markus Kuhn, Computer Lab, Univ of Cambridge, GB http://www.cl.cam.ac.uk/~mgk25/ | __oo_O..O_oo__
Re: What to do if International Time hits the International Date Line?
On Tue 2003-07-01T20:34:58 +0100, Markus Kuhn hath writ: > Newcomb's formula for the geometric mean longitude of the Sun is not really valid more than 200 years into the future. Please don't use Newcomb for that. You want to use something intended to match integrations that have moved much farther into the future. For a start, see Simon et al., Astron. Astrophys 282, 663-683 (1994). -- Steve Allen UCO/Lick Observatory Santa Cruz, CA 95064 [EMAIL PROTECTED] Voice: +1 831 459 3046 http://www.ucolick.org/~sla PGP: 1024/E46978C5 F6 78 D1 10 62 94 8F 2E49 89 0E FE 26 B4 14 93
What to do if International Time hits the International Date Line?
Let's drive the discussion forward into a region that we haven't touched here before: 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
