- Contemporary messages sorted: [ by date ] [ by thread ] [ by subject ] [ by author ] [ by messages with attachments ]

From: Markus Kuhn <Markus.Kuhn_at_cl.cam.ac.uk>

Date: Tue, 01 Jul 2003 20:34:58 +0100

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 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

Date: Tue, 01 Jul 2003 20:34:58 +0100

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 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__Received on Tue Jul 01 2003 - 12:35:46 PDT

*
This archive was generated by hypermail 2.3.0
: Sat Sep 04 2010 - 09:44:54 PDT
*