Solar time versus TAI discrepancy

Believe it or not, this is a computing question! I am interested
in finding out whether there is a generally accepted formula for
converting TAI to solar time and, much more importantly, whether
there are generally accepted bounds for its uncertainty. I have
a suspicion that there isn't :-)


Regards,
Nick Maclaren.

In article ,
"David J Taylor" -this-bit writes:
| "Nick Maclaren" wrote in message
| ...
|
| Believe it or not, this is a computing question! I am interested
| in finding out whether there is a generally accepted formula for
| converting TAI to solar time and, much more importantly, whether
| there are generally accepted bounds for its uncertainty. I have
| a suspicion that there isn't :-)
|
| Nick, could you point to a reference as to _which_ solar time you mean?
| Do you mean the 20minute or so variation between (for example) local noon
| and highest solar elevation? The so called "Equation of the Sun", if I
| recall correctly?

Oops. Mea Culpa. I posted before doing enough research to check
that all of the terms I used were well-defined :-(

The problem is this:

I want to be able to convert TAI to UTC/GMT/civil time at Greenwich,
for every date from the origin to the heat death of the universe.
Now, obviously, doing so to the nearest second is a failing known
as Delusion of Accuracy, so I am not making that mistake. But,
equally, simple numerical accuracy is not enough, as a historical
record may well be a 'precise' time of day.

Now, the conversion between TAI and UTC (or, rather, the one that
computer people always refer to as UTC) is defined from its start
to the present. GMT is a bit messier, but not too bad. But I
should like to know error bounds for civil solar time before GMT
and into the future.

Note that, because of the way that I am thinking of doing this,
I don't need the ACTUAL correction - what I need to define my
interface is some approximate BOUNDS on the correction. This is
to know how many bits to allow for it rather than to specify a
value. And, yes, of course I am thinking of using a sort of
floating-point format for far-flung times :-)


Regards,
Nick Maclaren.

Nick Maclaren wrote:

In article ,
"David J Taylor" -this-bit writes:
| "Nick Maclaren" wrote in message
| ...
|
| Believe it or not, this is a computing question! I am interested
| in finding out whether there is a generally accepted formula for
| converting TAI to solar time and, much more importantly, whether
| there are generally accepted bounds for its uncertainty. I have
| a suspicion that there isn't :-)
|
| Nick, could you point to a reference as to _which_ solar time you mean?
| Do you mean the 20minute or so variation between (for example) local noon
| and highest solar elevation? The so called "Equation of the Sun", if I
| recall correctly?

Oops. Mea Culpa. I posted before doing enough research to check
that all of the terms I used were well-defined :-(

The problem is this:

I want to be able to convert TAI to UTC/GMT/civil time at Greenwich,
for every date from the origin to the heat death of the universe.
Now, obviously, doing so to the nearest second is a failing known
as Delusion of Accuracy, so I am not making that mistake. But,
equally, simple numerical accuracy is not enough, as a historical
record may well be a 'precise' time of day.

Now, the conversion between TAI and UTC (or, rather, the one that
computer people always refer to as UTC) is defined from its start
to the present. GMT is a bit messier, but not too bad. But I
should like to know error bounds for civil solar time before GMT
and into the future.

Note that, because of the way that I am thinking of doing this,
I don't need the ACTUAL correction - what I need to define my
interface is some approximate BOUNDS on the correction. This is
to know how many bits to allow for it rather than to specify a
value. And, yes, of course I am thinking of using a sort of
floating-point format for far-flung times :-)


Regards,
Nick Maclaren.


The short answer is, no one knows by how much the earth will spin up or spin
down in the future (long before the heat death of the Universe, the Sun
will become a red giant, which is expected to have an impact on the
length of
the day). For a much more comprehensive answer, dig deep into
http://hpiers.obspm.fr
especially at the leap seconds section.

Pete.

PS, GMT is historic.

In article ,
Peter Bunclark writes:
The short answer is, no one knows by how much the earth will spin up or spin
down in the future (long before the heat death of the Universe, the Sun
will become a red giant, which is expected to have an impact on the
length of
the day). For a much more comprehensive answer, dig deep into
http://hpiers.obspm.fr
especially at the leap seconds section.

Pete.

PS, GMT is historic.

Day length is already increasing due to the transfer of angular momentum
to the moon via tides, and there will be a smaller exchange with the sun.
In principle you should be able to model this, but there are also
changes to the earth's moment of inertia which affect angular velocity,
and these seem to be quite unpredictable - who would have thought
before the fact that we wouldn't need leap seconds for the past
5 years, given the previous insertion rate?

J


[s.a.r. mod. note -- quoted text trimmed -- mjh]

(John Sager) writes:

Day length is already increasing due to the transfer of angular momentum
to the moon via tides, and there will be a smaller exchange with the sun.
In principle you should be able to model this, but there are also changes
to the earth's moment of inertia which affect angular velocity, and these
seem to be quite unpredictable - who would have thought before the fact
that we wouldn't need leap seconds for the past 5 years, given the
previous insertion rate?

One of the major sources of this variability comes from long-term cycles
and trends in weather and climate. For example, during those phases of
the biennial and decennial atmospheric oscillations when the jet stream
is more vigorously active, it carries a higher angular momentum, and
therefore the rotation of the Earth must slow down a bit to conserve the
total angular momentum of the Earth-plus-atmosphere; the effect is small,
but the anticorrelation between jet-stream activity and the rotation rate
of the Earth is indeed measurable --- albeit not long-term predictable.
(It is quite likely that changes in circulating ocean currents may also
have a similar effect, albeit on a much longer timescale.)

As for the time variations in the Earth's moment of inertia, one
contributing factor is thought to be changes in the amount of water
locked up as ice in the polar caps versus in liquid form in the ocean's
equatorial bulge; another is wind-driven variations in sea-surface height;
yet a third is changes in the density distribution of the ocean due to
variations in salinity and temperature. Again, all these effects are small,
and measurable, but not predictable over the long term.


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'

In article ,
John Sager wrote:

Day length is already increasing due to the transfer of angular momentum
to the moon via tides, and there will be a smaller exchange with the sun.
In principle you should be able to model this, but there are also
changes to the earth's moment of inertia which affect angular velocity,
and these seem to be quite unpredictable - who would have thought
before the fact that we wouldn't need leap seconds for the past
5 years, given the previous insertion rate?

Quite.

What I was (and am) looking for is some bounds, not necessarily
down to the last second. I have received some very useful pointers,
and will be studying them - which will continue my education, if
nothing else :-)

To put this in perspective, the accuracy of times is very roughly
proportional to the distance from the present. Beyond about a few
hundred years, measuring to seconds is meaningless. By the stage
we get back to the Carboniferous, exact year counts are amusing
but not science ....


Regards,
Nick Maclaren.

Peter Bunclark wrote in message ...
Nick Maclaren wrote:

In article ,
"David J Taylor" -this-bit writes:
| "Nick Maclaren" wrote in message
| ...
|
| Believe it or not, this is a computing question! I am interested
| in finding out whether there is a generally accepted formula for
| converting TAI to solar time and, much more importantly, whether
| there are generally accepted bounds for its uncertainty. I have
| a suspicion that there isn't :-)
|
| Nick, could you point to a reference as to _which_ solar time you mean?
| Do you mean the 20minute or so variation between (for example) local noon
| and highest solar elevation? The so called "Equation of the Sun", if I
| recall correctly?

Oops. Mea Culpa. I posted before doing enough research to check
that all of the terms I used were well-defined :-(

The problem is this:

I want to be able to convert TAI to UTC/GMT/civil time at Greenwich,
for every date from the origin to the heat death of the universe.
Now, obviously, doing so to the nearest second is a failing known
as Delusion of Accuracy, so I am not making that mistake. But,
equally, simple numerical accuracy is not enough, as a historical
record may well be a 'precise' time of day.

Now, the conversion between TAI and UTC (or, rather, the one that
computer people always refer to as UTC) is defined from its start
to the present. GMT is a bit messier, but not too bad. But I
should like to know error bounds for civil solar time before GMT
and into the future.

Note that, because of the way that I am thinking of doing this,
I don't need the ACTUAL correction - what I need to define my
interface is some approximate BOUNDS on the correction. This is
to know how many bits to allow for it rather than to specify a
value. And, yes, of course I am thinking of using a sort of
floating-point format for far-flung times :-)


Regards,
Nick Maclaren.


The short answer is, no one knows by how much the earth will spin up or spin
down in the future (long before the heat death of the Universe, the Sun
will become a red giant, which is expected to have an impact on the
length of
the day). For a much more comprehensive answer, dig deep into
http://hpiers.obspm.fr
especially at the leap seconds section.

Pete.

PS, GMT is historic.

The term 'leap' day or second denotes the less geometrical calendar
system based on the equable 24 hour day.To determine the annual
cyclical motion of the Earth as 365 days 5 hours 49 minutes,the
equable 24 hour day must of neccesity be defined and determined first.

Originally,the Equation of Time adjustment was employed by astronomers
and later by navigators to reduce the natural unequal day to the
equable 24 hour day to facilitate the seamless transition from one 24
hour day to the next 24 hour day.With this method there is no need to
take into account fraction of days as with the calendar system for it
is based on the rotation of the Earth wrt the Sun,the addition and
subtraction of minutes and seconds which is the mathematical bridge
between the observed natural unequal day and equable 24 hour clock day
equalises the variation in orbital motion (Kepler's second law) to
facilitate the isolation of axial rotation to the 24 hour/360 degree
equivalency.The following graphic should be adequate for presenting
where equable variable orbital motion is equalised by the Equation of
Time by addition and subtraction of minutes and seconds even though
there is a natural variation causing the asymmetry between one noon
and the next.

http://ircamera.as.arizona.edu/NatSc...res/kepler.htm

The following Equation of Time tables in conjunction with the above
graphic express the annual cyclical loop system which precedes the
calendar system and Flamsteeds isochronos sidereal method,again,there
are no 'leap' factor involved.

http://www.burnley.gov.uk/towneley/tryall/eot3.htm

Perhaps priority in dealing with this matter and the unwarranted
assertion that GMT or the 24 hour/360 degree equivalency for the axial
rotation of the Earth is merely historical exists in noting that to
derive the sidereal value based on the annual orbital cycle as 365
days 5 hours 49 min approx,the equable 24 hour days must of necessity
be determined first.

Apply the sidereal value to heliocentric modelling of the Earth and it
generates circular orbits and constant axial rotation wrt to the
Sun,this is something that does not occur and is in direct conflict
with Kepler's second law and subsequently Newton's gravitation laws.

http://www.absolutebeginnersastronomy.com/sidereal.gif

http://ircamera.as.arizona.edu/NatSc...res/kepler.htm