Having followed some of the arguments in this thread:
For the very long time as the length of the day increases, leap
seconds are imperative as they will become progressively more
common and archaelogists may curse those that don't use them. There
might be a case for temporarily discontinuing them until computer
systems become sufficiently advanced to handle all the changes
automatically in perhaps another 50 years.
In a similar vein, leap days will become progressively less
frequent as the length of the day shortens,
There was never an AD 0 in either the Julian or Gregorian
calendars, the concept of using zero in counting scales was
developed in Asia and adopted by the West many centuries later.
(I hope the formatting comes across OK - if not don't bother to
read further - Robert)
I have developed a formula to determine the effect of combined
increase in day length and decrease in year length. It calculates
tropical year lengths measured in units of the mean solar day of
the date under investigation. (I hope the formatting comes across
OK - if not don't bother to read further - Robert)
0.0000061 days per century decrease in year length. This is mean
solar days of 86,400 SI seconds per Julian year. For these
purposes, the Julian year and tropical year can be assumed to be
the same, because the current discrepancy is about one part in a
million, so the effect on the factor 0.0000061 is well below the
level of accuracy in its specification. The effect of the
difference between the current mean solar day and 86,400 seconds is
also well below the level of accuracy of the factor. These
assumptions are true provided that the equation is used to work out
projections from dates close to the present, otherwise the factor
must be adjusted appropriately.
units are tropical years, mean solar days and SI second
a = no. of years ahead (positive) or past (negative)
b = current no. of days per year (365.242193)
c = decrease in year length per 100 years (0.0000061 days)
d = current day length in seconds (86,400.003 seconds in 1984)
e = increase in day length per 1000 years (0.020 seconds) - this
varies according to various factors such as core/mantle changs, ice
ages and tectonic plate rearrangemens, plus major meteor impacts
days/year = (b - (c/100 * a)) * (d /(d + e/1000 * a))
days/year = (b - (c * a/100)) * (d /(d + e * a/1000))
(The second form suits my spreadsheet better, as it reduces the
roundings problem with the divisions.)
A more comprehensive formula from the more mathematically capable
would contain factors for changes in the rates of change if any,
and would also accommodate factors for the Milankovitch and other
possible cycles. Incorporating these cycles would require a
reference to a specific base date for their synchronisation.
A list of date related future events follows:
(I have left a few dates of past events in the list for interest
and to illustrate the types of problem that can arise or need
consideration.)
A.D. 1999 August - first GPS rollover, repeated nearly every
nineteen years, the next will be in A.D. 2019, I don't know whether
GLONASS has similar peculiarities.
A.D. 1999 - various dates that may cause problems with nines in
date fields
A.D. 2000 1st January, etc - main Y2K rollover problem
A.D. 2000 28th February, etc - first leap year of new millennium
A.D. 2000 31st December, etc - first year end of new millennium,
some may argue that it should be 2001
A.D. 2001 28th February, etc - first non-leap year of new millennium
A.D. 2004 28th February, etc - second leap year of new millennium
A.D. 2019 6th April - next GPS rollover, they occur every 1024
weeks, as GPS is a "true" timescale it does not have leap seconds,
so there is a slight drift from UTC. (Probably fixed by now)
A.D. 2038 - older UNIX systems may have a roll over problem, while
current redevelopments are in progress to prevent this occurring,
there may still be residual problems
A.D. 2100 - about two leap seconds per year
A.D. 2100 - second century of new millennium (not a leap year)
A.D. 2132 - count of Modified Julian Days exceeds 99,999.
A.D. 3268 - first Julian period of 7980 years ends
A.D. 4000 - at current rates of change this should not be a leap year
A.D. 4595 - count of Modified Julian Days exceeds 999,999.
A.D. 10000 - probable rollover problem similar to Y2K, if the
expected automated computer systems don't resolve it in good time
A.D. 10000 - about sixty leap seconds per year, by now it would
probably be inadvisable for non-scientific applications to pretend
they don't exist.
A.D. 22,378 - Julian days exceed 9,999,999.
A.D. 50,000 - about one leap second per day
A.D. 1,900,000 - 365 days per year
A.D. 7,800,000 - 364.25 days per year
A.D. 70,000,000 - sixty one seconds per minute
A.D. 1,000,000,000 - seventy five seconds per minute
A.D. 1,000,000,000 - 250 days per year
A.D. 1 billion to 6 billion - Sun may be a red giant, rendering
Earth uninhabitable, sources vary as to when this may occur, but
agree that it will.
************************************************************************************************
Robert
On 09/01/2017 12:41, Preben Nørager wrote:
On Tue Jan 3 14:18:52 EST 2017, John Sauter wrote:
"I regard leap seconds as a reasonable compromise between the
needs of civil time and of science. Civil time needs a clock that
tracks the days and the seasons. Science requires a clock that
measures time in precise intervals. UTC provides both, using leap
seconds to keep atomic time synchronized with the rotation of the
Earth."
I think there is something wrong with that argument. Civil
timekeeping holds both a clock, and a calendar. The calendar track
the seasons, while the clock track the time. If it is to be said,
that the clock track the days, it is important to notice the
difference between apparent time, and mean time. The clock track
either the sun (apparent time), or the seconds (mean time).
When the Nautical Almanac in 1833 substituted mean for apparent
solar time, an important step was taken. From now on chronometry
was to rely on mechanical clocks, and with the invention of atomic
clocks, the tracking of the 24-hour day (86400 international
seconds) can now happen without any daily tracking of the sun.
The question really is whether the calendar needs the daily
tracking of the sun or not. And the answer to that question
obviously depend upon which calendar we want!
I think the disagreement about leap seconds, really is a
disagreement about which calendar to use for civil timekeeping. If
we agree to use the proleptic gregorian calendar (ISO 8601) there
is really no need for leap seconds. That calendar track the
seasons well, and with the slight modification, to add the
additional rule that years evenly divisible by 4000 are not leap
years, it would track them even better.
Leap seconds are really only a need for those who do not want to
see the proleptic gregorian calendar become universal. For
instance for those who want to use the julian period, as the basis
for one calendar or another, because they must somehow rely on
apparent time, and not mean time, because the julian period count
apparent solar days.
Let us use ISO 8601, and abolish leap seconds all together.
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