SIMULATION OF DELTA-T
-------------------
jOHn Pazmino
NYSkies Astronomy Inc
nyskies@nyskies.org
www.nyskies.org
2017 January 2
Introduction
-----
The NYSkies Astronomy Seminar on 2016 October 7 discussed the
secular acceleration of the Moon, slowdown of Earth rotation, and
leapseconds. These subjects were suggested by the leapsecond insertion
on 2016 December 31 and the solar eclipse of 2017 August 21.
The interest in these subjects rises and falls according as
celestial events related to them are in the news. Th interest, for
instance, spiked for the sunset solar eclipse of October 2014 and the
sunrise one of November 2013. Both were observed, thru partly cloudy
sky, from new york City.
There are only a few celestial events useful for tracking the
Earth's rotation. They first of all must be determinate events,
calculated thru proper astronomy theory. Aurorae, most comets, solar
halos, meteorite falls are no good because they can not be retrodicted
to the date of the observation.
Solar and lunar eclipses and lunar occultations are the best
events. They can be computed for the observer's date and location,
then compared to what he actually saw. For brewity I work here only
with solar eclipses.
Horizontal eclipses
-----------------
In ancient times eclipses were carefully documented and recorded.
Those in high sky often missed the hour of occurrence, or stated it in
loose terms. That's because ancient timekeeping was crude, with times
commonly cited only to the whole hour. To monitor Earth rotation we
need timing to the minute.
We need an eclipse whose time is known
separately from the observer's recording of it. An eclipse
occurring at sunrise/sunset is a favored event because the local solar
time of the eclipse is that of the sunrise/sunset. That moment is
computed from the latitude and date of the eclipse and is
independent of the Earth slowdown and the observer's care to state
THE HOUR..
Further resolution of time is taken from the recorded aspect of the
eclipse as the Sun is rising or setting. It is usual to state the part
of the solar disc covered by the Moon in the observing record.
Commonly the altitude of the Sun is noted relative to the landscape
for certain phases of the eclipse. These reports can be compared to
the computed aspect of the eclipse.
In the 21st century, a large store of eclipse observations emerged
from the western Pacific Ocean, allowing in many cases a double-check
for horizontal eclipses. An eclipse could be seen at sunrise in Italy
and also at sunset in Japan.
Earth rotation
------------
One full turn of Earth was the mean solar day. This by long
tradition was divided into 86,400 mean solar seconds. These were
grouped into 24 hours, then 60 minutes, and then 60 seconds. Before
mechanical clocks in the Middle Ages, time was maintained by sundials.
They followed the Earth's rotation by the Sun's shadow. In ancient
towns there usually was a master sundial against which others were
calibrated as the standard of time.
In the early Middle Ages mechanical clocks were developed. They
replacing sundials as the master keeper of time with installations on
civic buildings and churches.
Mechanical clocks endured as timekeepers until the late 1940s.
Altho they were finely crafted and carefully tended, they did get out
of synch with the Earth from time to time. Any deviation of a clock
from mean solar time ws laid to clock malfunction. The clock was
adjusted to get back in step with mean solar time.
For almost the whole of human existence there was no separate
method of time independent from Earth's rotation. With nothing to
suggest otherwise, we felt assured that mean solar time was a
constant, uniform, immutable flow of time for all ages. By history
this standard of time was called Greenwich Mean Time or Universal
Time. Computed astronomy events were stated in GMT or UT.
GMT, UT, is the mean solar time maintained at the zero longitude.
Places at other longitudes are ganged to UT by the time equivalent of
their longitudes. New York City's Eastern Standard Time is UT minus
five hours. In daylight savings time it's UT minus four hours.
Observed vs calculated time
-------------------------
When we observe, record, document a celestial event we
instinctively use a clock ideally synchronized with GMT or UT. GMT/UT
is forced to coincide with a base position of the Sun, like a noon
meridian crossing.
When we compute a celestial event we use mathematical time with
numbers of absolutely the same 'size' or 'length' for all past and
future time. We assumed -- for absence of contrary clue -- that this
matched Earth rotation. Ephemerides and almanacs called the times
computed for celestial events 'GMT' or 'UT' in the belief that these
were exactly equal to the mathematical time in our computations.
When an event was observed to occur at a moment different from
predicted, we routinely searched for an external physical cause for
the discrepancy.
Earth spindown
------------
In the 1690s a suspicion grew up that there was something
peculiar with the Moon. When Halley compared observations of ancient
eclipses with his calculated aspect of these eclipse, it seemed that
the Moon was always running ahead of her proper position in her orbit.
At first this was supposed to be a weak understanding of the then-new
Newton gravity theory or loose timekeeping methods in early eras.
By the mid 1700s the effect was well confirmed, to be called
'secular acceleration of the Moon'. In the 1800s a similar speeding up
was found with Jupiter's moons. The effect was by far the greatest for
the Moon because she moved faster thru the stars than any other
permanent celestial object and had the longest span of detailed
observations..
In the mid 1800s we suspected, with new knowledge of fluid
mechanics and energy transfer, that the lunar acceleration could
possibly be really a deceleration, slowing, of the Earth's rotation.
There was no way to demonstrate this idea without an independent means
of time flow to lock the Earth's rotation.
The secular acceleration was described in two ways. One was the
angular advance of the Moon per century over the predicted position.
The other was the time advance per century of the Moon's arrival at a
predicted position.
For short time spans both quantities were small, sometimes
smothered in observational and mechanical clock errors. Over long
periods, millennia for ancient eclipses, the effect was gross, many
degrees or minutes of displacement. As yet coming into the 20th
century there was no plausible credible cause for the lunar
acceleration.
Atomic time
---------
In the 1930s atomic labs invented clocks governed by the
vibrations of atoms or molecules. these clocks were immune to the
ambient circumstances that affect mechanical clocks, like humidity,
tremors, wind, temperature. By the 1940s atomic clocks proved to be
far more uniform and constant than any mechanical clock could be. When
celestial events were checked with atomic time, the mystery of lunar
acceleration disappeared. The Moon sat at the very predicted position
and eclipses occurred 'on time'.
All deviation from computed motion and position was in fact caused
by a deceleration of diurnal rotation of Earth.
An other advantage of atomic clocks was their extreme time
resolution. Timings could be done to the nanosecond, not hundredth of
a second for the best mechanical clocks. The secular deceleration of
the Earth could be monitored over just a year or so.
After deep dialog among world time services, we in the mid 1950s
cut loose from 'mean solar time' and bolted onto the atomic clocks.
The atomic clock was synched to UT at a certain instant, then left to
run then after.
Our confidence that atomic time is a stable timekeeping source
derives from the way atomic clocks work. The beats of the clock are
generated by quantum physics. Quantum physics is also, from study of
radiation from cosmological look-back times, constant for the entire
life of our universe.
Atomic 'second'
-------------
In order that the atomic clock tick off seconds we had to redefine
the second as so many vibrations of the clock's atoms. We could not
use the current, 1950s, mean solar second because we didn't yet have
observations to compare it to atomic time.
By history the new second, the International System second, ended
up being what the actual mean solar second was in about the year 1820.
This second, banking off of a past, faster, spin of Earth, is a bit
SHORTER than the current mean solar second. This would kick us in the
pants by 1970.
By 1970 the too-short IS second caught up to us. When atomic Time
ticked off 365 atomic days, each with 86,400 atomic seconds, Earth
didn't complete its own 365 mean solar days. The annual shortfall is
some 300 milliseconds, one full second in three to four years.
To get the atomic time back in synch with Earth's mean solar time,
we insert a leapsecond.
Skipping the fascinating story of leapseconds as a distinct topic,
the atomic time is called International Atomic Time, TAI, that runs
continuously without adjustment against mean solar time. The time
signals generated by TAI, running at the same rate as TAI, is
Coordinated Universal Time, UTC. This is the primary time service
thruout the world.
The leaspsecond is inserted into UTC as the 61st second at the end
of march, June, September, or December, as needed to keep UTC in step
with mean solar time. The call for leapsecond is issued after dialog
among the world's time services. In many years it is skipped as not
needed and in most years only one insertion is done, usually in
December.
Length of day
-----------
With the spindown of Earth thoroly confirmed we need a way to
specify it. One way is to cite the length of the mean solar day as
compared with today's atomic day length. Atomic days have 86,400
atomic seconds. These are disposed into hours and minutes, continuing
the historical practice. Because in past time the Earth span faster,
the time to complete a turn, say noon to noon, was shorter than now.
The day had fewer than 86,400 atomic seconds, but still contained
86,400 of its own mean solar seconds.
The qualitative diagram below shows the steady increase in day
length due to Earth's spindown. It sketches out that, yes, the day is
getting longer over time.
The day length at point '0' is a crossover from a too-short day
to a too-long day, as banked off of time maintained by the atomic
standard. This occurred in about 1820.
----------------------------------
| atomic day length / |
d | 86,400 atomic seconds / |
a +--------------------------------------0-----+
y | / |
| / |
l | / |
e | / |
n | / |
g | /Earth day length |
t | /steady increase over time|
h | / |
| |
| / |
| / |
| / |
| |
+-------------------------------------------+
date, typicly centuries
-------------------------
1820 was when the Earth day equals the atomic day. This was an
arbitrated date from a study done in the 1950s of lunar motions over
the period 1750-1900. During this span the Earth continued the
spindown and some weighted smooth average day length was worked out.
This happened to be what it really was in 1820, near the midpoint of
the interval.
Delta-T
-----
Comparing the hour of the computed and observed ancient eclipse we
find that the observed hour is earlier than the computed one. This
offset increases with deeper look-back times into the past. This
offset, the accumulated slippage of Earth rotation against the uniform
rate of atomic, or maths, time is 'delta-T'. Its value depends on both
the spindown rate of Earth and the year we zeroed the two times.
The name comes from the maths 'delta' for 'difference'. In typeset
work the capital Greek 'delta' is commonly printed. The '-' is a
hyphen, not a minus or subtract symbol.
Delta-T is
(delta-T) = (atomic clock hour) - (Earth clock hour)
this is a positive number for past eras because the Earth has been
decelerating for at least several millions of years.ú
delta-T must be zeroed at some epoch, a year when the atomic and
Earth clocks coincide. The epoch is the year 1820 from the atomic
second definition. This varies a couple years among authors, a shift
of little effect on events many hundreds to thousands of years ago.
Stricta mente the 1820 is when the length of the day was the same
for both clocks, not necessarily when the actual reading coincided.
Since atomic tome didn't kick in until the 1950s, the zeroing was done
around then. As noted above, for longterm astronomy work in millennia
past, the brief 200-year shift has little effect. Most formulae for
delta-T stay with 1820 as the epoch.
The value of delta-T is the accumulated divergence of the two
clocks during the interval from the look-back year to today..
Because the rate of Earth spindown may be irregular, according as
the delicacy of an author's study of it, but for this piece I take it
as a constant for all past time.
Assessing delta-T
---------------
delta-T is not a determinate value for a given year, like the
Sun's ecliptic longitude or Julian Day Number. We have too weak a
model for the long-term spindown of Earth to generate definite
ephemerides of delta-T.
Authors obtain delta-T by selecting ancient astronomy events,
mostly eclipses, to learn when in local time they took place. They
compute the eclipse in atomic/maths time. They see what the disparity
is in the two times. A table or graph of these experimental values is
good only for the peculiar set of events studied by the author and his
interpretation of them.
The interpretation is hardly simple or easy. apart from
deciphering the texts there is a skill in ekking out useful details
from allegorical or fantastical descriptions of the eclipse.
With such a table or graph some astronomers fit a maths curve to
the data points and then use the curve's equation to yield delta-T for
any year in the table's range.. The usual best fit curve is a
parabola, quadratic, zeroed on the epoch year.
There is, due to event selection, interpretation, equation of the
curves, a spread of delta-T values among astronomers. The dispersion
is greater in the farther remote past, sometimes a couple hours. You
may employ any of the delta-T value you please, being mindful to state
clearly which it is. Just saying 'delta-T for this event is 2h 32m' is
incomplete. Your study of the event can not correlate properly with
work by other astronomers.
Home astronomers are routinely astounded at the huge delta-T in
moderately past eras, like the Nile and Euphrates cultures. delta-T
can be several hours! At first it's hard to see how this can happen
since the Earth spindown is milliseconds per year. Over a few thousand
years delta-T should be only a few seconds, hardly enough to distort
the reports of celestial events.
The deceleration of Earth, like that of a vehicle under braking,
is a square function of time as in, from mechanics, d = d0 + (v0*t) +
(a*t^2)/2. In fact, most formulae put out for delta-T are of this
form. d for large t does race away to huge values.
An other way to see the cause is thru bank interest. In simple
interest the money grows at the same amount each year, regardless of
the amount already built up. In compound interest the money increases
by the same percent or fraction, building on the accumulated amount
from prior years. The growth of money under compound interest runs
away from simple interest
An other specification
--------------------
Some authors state the actual rate of slowdown, the 'compound
interest' and not the 'built up amount of money'. While the value of
spindown aries among authors, it clusters in the mi d20s of seconds
per square century. Here I use 25 sec/cy2.
Can this tiny deceleration generate the accumulated delta-T we
find from studying early eclipses?
It can and does.
The Earth slows down, loses angular momentum, from the braking
action of ocean tides. These are caused by differential gravity pull
on Earth by the Moon. Considered as a unit, the angular momentum of
the Earth and Moon remains constant. The Moon]s angular momentum
increases to cancel the Earth's loss of momentum.
The Moon gains momentum by sliding away from Earth. This recession
is directly measured by laser pinging off of the mirrors placed on the
Moon during the lunar visits of the 1960s and 1970s. The Moon slides
away at 37mm/yr. This small amount is utterly undetectable by ordinary
astrometric methods, fooling us to believe the Moon's distance from
Earth was truly constant.
The 37mm/ur adds to the length of the Moon's mean distance from
Earth, the lever arm of her angular momentum. This increase in lunar
angular momentum should equal the decrease of Earth's angular momentum
as f the lengthening of the day.
We have
(inc Moon AM) = (lever arm increase) / lever arm)
= (37e-3 m/yr) /(384e6 m)
= 936354e-11 /yr
Over a century this is 100 times more, or
(inc Moon AM) = (9.6354e-11 /yr) * (100 yr/cy)
= 9.6354e-9 /cy
The equals the decrease in Earth angular momentum, in terms of the
length of a century
(dec Earth AM) = (inc Moon AM) * (Earth century length)
= (9.6354e-9 /cy) * (31.56e6 sec/cy)
= 30.4034 sec/cy2
which is consistent with the values published by far more refined
assessment of Earth deceleration.
The table here gives the delta-T as it builds up in past
centuries, with 1800 nearly enough the epoch for zero delta-T . I use
a more reasonable deceleration of 25 dec/cy2.
----------------------------------------------
delta-T in past enturies based on 25 sec/cy2
----------------------------------------------
year | delta-T || year | delta-T || year | delta-T
- ---+---------++------+---------++------+--------
2000 |-0h01m40s|| 1000 | 0h26m40s|| 0 | 2h16m40s
1900 |-0 00 25 || 900 | 0 33 45 || -100 | 2 30 25
1 800 | 0 00 00 || 800 | 0 41 40 || -200 | 2 46 40
1700 | 0 00 25 || 700 | 0 50 25 || -300 | 3 03 45
1600 | 0 01 40 || 600 | 1 00 00 || -400 | 3 21 40+
1500 | 0 03 45 || 500 | 1 10 25 || -500 | 3 41 25
1400 | 0 06 40| | 400 | 1 21 40 || -600 | 4 00 00
1300 | 0 10 25 || 300 | 1 33 45 || -700 | 4 20 25
1200 | 0 15 00 || 200 1 | 46 40 || -8900 |4 41 40
1100 | 0 20 25 || 100 | 2 00 25 || -900 | 5 03 45
--------------------------------------
See how the accumulated delta-T swells in remote past years, to
many HOURS. An eclipse predicted for a given location could well have
been missed because the Sun already set or didn't yet rise. It was
this feature of Earth's spindown, unknown before atomic time, that
fooled us to treat many early eclipses as made-up events to beef up
local history.
The table can be extended further back but by around year -800 the
dispersion of delta-T among authors gets too large for reliable use.
By around -1000 the error is about one full hour, rendering any
discussion of ancient events too loose.
Do se that in shallow past, back to the Middle Ages, delta-T is
only a few minutes, up to a quarter hour. Before we appreciated the
Earth slowing, we assumed any discrepancy between predicted and
observed events was the rough statement of the observed times. While
there were mechanical clocks, there was no sure way to keep them in
synch with each other.
Effect on eclipses
----------------
delta-T affects all celestial observations but most sensitively on
eclipses. Because eclipses were such major events, typicly occurring
without warning and being easily witnessed, they were carefully
chronicled. If an eclipse is predicted without mind or mood for delta-
T the eclipse path is always WEST of the observed path. In severe
cases the eclipse took place after local sunset even tho credible
records show it was seen during the local daytime.
Conversely an observed path is always EAST of the no-delta-T path,
with instances of an event seen in early day when it was supposed to
occur later in the day.
With the loose or vague or missing specification of hour for an
eclipse in high sky, use of horizontal eclipses is all the more
crucial. They occur at the known moment of local sunrise/sunset.
The path displacement on the ground is the longitude equivalent
of the instant delta-T, at 1 degree per 4 minutes or 15 degree per
hour. A computed path with delta-T of 1h40m is shifted 50 degrees west
of its observed alignment, or the observed path is 50 degrees east of
its predicted alignment.
The diagram here illustrates the effect. It shows a region of the
Earth with two places A and B marked.
+-----------------------------------------------------------+
^ | |
| | / / / |
| | path without--/ / |
L | delta-T / B---place |
a | A---place path with / observing |
t | / misses delta-T---/ eclipse |
i | / eclipse / |
t | | | |
u | |----longitude offset----->| |
d | equivalent of delta-T |
e +-----------------------------------------------------------+
longitude (east from Greenwich) ---> ---->
We calculated that the eclipse should be seen at place A. We have
no reports of this eclipse from A. We also find no other place along
our predicted path saw this eclipse!
In the stead we find reports of an eclipse from place B, for which
we have no predicted path. We also turn up eclipse sightings from
other places along this observed path.
In the days before we appreciated Earth spindown we assumed that
observers at B made up an eclipse to jazz up some local civic event,
like the seating of a new king. Or perhaps they knew from travellers
of the eclipse at A (where there really was no eclipse) and shifted
the location to B in assimilation. In fact, 'assimilation' is an
archaeological term meaning that a society moved the occurrence of a
remote major event to its own place to enhance irs history.
In this diagram the paths do not overlap. No place has a chance to
to observe the eclipse on both paths. An eclipse path can be aligned
east-west. Both can cross the one place. In this case the observed
eclipse differs from the prediction not only in time but also aspect.
The observer is at a farther west point on the actual path compared to
the predicted one. The calculated scene of the eclipse is NOT merely
slided to a more eastern longitude. The eastern observer sees the
eclipse according as the path crossing over him, NOT as it 'should'
occur on the predicted path farther to the west.
At the time of the predicted eclipse, in atomic time, the mean
solar time at the observer is LATER by the time delta-T span of time.
Because the real path passes over the observer, he sees the eclipse at
his own mean solar time EARLIER than the predicted atomic time.
Eclipse of 2013 November 3
------------------------
NYSkies had two recent horizontal solar eclipses, perfect for
demonstrating the effect of delta-T. The were on 2013 November 3 at
sunrise and 2014 October 23 at sunset. Because ignoring delta-T throws
the predicted path west from the actually observed path, the sunset
eclipse is not a good example. The predicted eclipse occurs after
sunset with nothing seen from New York.
The 2013 November 3 eclipse is a a partial one from the City,
there being no totality phase. With no delta-T the predicted path is
shifted westward to put the City away from the sunrise zone. The
eclipse occurs in early morning.
In the stead it takes place during sunrise.
I pretend we are in some far future year when the delta-T for the
2010s is 3600 seconds, one full hour.We run an eclipse software with
and without this delta-T. The results are in the table below. Each
main column has three parameters: the hour of the eclipse event, the
altitude of the Sun at that hour, and the position angle of the event
on the Sun's disc. This last is measured counterclockwise around the
solar limb from celestial north. this eclipse is a partial one,
I also note local sunrise, the eclipse magnitude, ratio of
Moon/Sun angular diameter.
-----------------------------------------------
PREDICTED AND OBSERVED ECLIPSE, 2013 NOVEMBER 3
-----------------------------------------------
eclipse | pred New York | obsd New York | pred Chicago
event | no d-T | with d-T | no d-T
------------+--------------+----------------+
1st contact | ----- --- --- | 05:16 -14 271 | ----- --- ---
1st contact | ----- --- --- | ----- --- --- | 05:19 -13 269
1st contact | 06:18 -03 265 | ----- --- --- | ----- --- ---
max eclipse | ----- --- --- | 06:11 -04 198 | ----- --- ---
max eclipse | ----- --- --- | ----- --- --- | 06:13 -03 198
SUNRISE Ch | ----- --- --- | ----- --- --- | 06:25 +00 ---
SUNRISE NY | 06:29 +00 --- | 06:29 +00 --- | ----- --- ---
4th contact | ----- --- --- | 07:11 +06 125 | ----- --- ---
max eclipse | 07:16 +07 199 | ----- --- --- | ----- --- ---
4th contact | ----- --- --- | ----- --- --- | 07:16 +07 122
4th contact | 08:19 +17 139 | ----- --- --- | ----- --- ---
------------+---------------+---------------+--------------
magnitude | 0.602 | 0.723 | 0.689
Moon/Sun | 1.001 | 0.997 | 0.998
-----------------------------------------------------------
Nota magis bene the link between predicted and observed eclipse given
by the time of sunrise. This is why we strive to find horizontal
eclipses .. We need a base moment in each to bring out the shift of
path caused by accumulated deceleration of the Earth.
In the first column the eclipse is calculated to begin 06:18 in
new York, only ten minutes before sunrise. Observers there should see
most o the eclipse, losing only a small part around 1st contact..
Maximum phase is a comfortable 3/4 hour after sunrise and 4th contact
close to 2 hours after sunrise.
The second column shows what is actually observed. 1st contact and
maximum eclipse take place before sunrise. Most of the eclipse is
lost. 4th contact is only 45 minutes after sunrise.
A fair question is: where is this eclipse predicted to occur at
local sunrise? or, the same thing, where is the sunrise zone of the
predicted path? From a plot of the path i find that Chicago, a town
about 1100 kilometers west of the City, at the bottom of lake
michigan, is in the sunrise zone.
The third column give Chiago's predicted view. 1st contact is
about an hour before, and maximum is about 10 minutes before, sunrise.
4th contact follows about 40 minutes later.. In fact Chicago sees
nothing of this eclipse. It's all over about 15 minutes before
sunrise.
An other delta-T!
---------- ----
Nota magis bene that the delta-T we played with so far relates
atomic time with Earth rotation as Universal Time or Greenwich Mean
Time. When we cut in the atomic time service in the 1960s and then
patched in the leapsecond adjustment, a NEW delta-T -- with the same
name -- was defined. It is trotted out when a leapsecond is coming,
like in December 2016. The leapsecond announcement also states that
'delta-T will be minus so-many seconds'.
This new delta-T keeps track of the number of leapseconds , netted
positive against negative, inserted since the leapsecond scheme began.
It is an integer that notches up, or down, irregularly as leapseconds
are inserted.
So far all leapseconds were positiver, added, making the new
delta-T coniunually grow. If negative leapseconds are calld in or the
Earth suffers a momentary spinyp, delta-T could decrease.
It is crucial to understand that leapseconds are needed to
compensate for the too-short IS second. If the Earth rotation were to
stabilize today, no longer slowing down, positive leapseconds would
still be inserted every couple years. The common belief, even among
experienced astronomers, that the leapseconds compensate for Earth
spindown, is simply erroneous. IA person claiming the slowdown of
Earth since 1970 built up to some 40 seconds truly has much too much
idle time on his hands.
Astronomy software
----------------
Many astronomy softwares incorporate the historical delta-T for
simulating events in the past. All such software can only be
approximate because delta-T is not an analytic function that is
computed by a physical theory. The software author selects one of the
several schemes of delta-T in circulation. The program reference
manual may discuss its regime of delta-T to assess the validity of the
simulations.
Please be aware that delta-T can not be reliably forecast for
future events. The software may simply trend the recent history of
past delta-T. This situation makes ALL astronomy software less and
less secure in their simulations ever farther into the future. It is
possible, but not usual, for the author in his web to offer an updated
delta-T file every so often.
Some softwares allow an input value of delta-T, replacing the
built-in value. You may choose from the several schemes by look-up
table or fitted maths equation.
A common practice is to manually set delta-T to zero for future
events because values can not de confidently projected or trended into
the future.
Be careful with older astronomy software written prior to the
diffusion of atomic time into the world. It may lack any provision for
delta-T. It may cite its predictions in 'UT' or 'GMT', being that
these were the standard of time in astronomy prior to atomic time. The
software really uses maths time, which you may treat as a time flow
with zero delta-T. Simulations of events far in the past will be off
by an amount roughly that of historical delta-T.
Old vs new calculations
---------------------
It is tempting to see if delta-T shows up in calculations of
eclipses in decades before atomic time and in those after then, An
eclipse path of an ancient eclipse in a book from, say, the 1940s
should be shifted west of the same eclipse path from a 1980s book, no?
The older work presumed that maths time and Earth rotation time were
the same.
In the late 19th century Oppolzer computed eclipses of the Sun
and Moon. His book 'Canon of eclipses' summarized his work with plots
of eclipse paths.
The paths were approximate, plotted on equidistant polar world
maps. he actually computed, probably to save some effort?, only the
sunrise, noon, and sunset points of each path. On the maps he drew a
geometric circular arc thru the three points.
In the 1970s Dover Publications reprinted the book, with English
translation. Home astronomers following eclipses bought a copy.
In the 1980s Meeus issued his own canon worked up with modern
computing and map-making devices. He, like Oppolzer, plotted eclipse
paths on worked maps. The maps were more detailed than Oppolzer's,
with paths more faithfully delineated. . Most eclipse chasers got a
copy.
Meeus's book incorporated delta-T. Oppolzer's did not because the
concept didn't exist. Could we demonstrate delta-T by comparing a
Meeus map with an Oppolzer map for the same ancient eclipse?
If the two authors used the exact same formulae, equations,
algorithms and the same parameters and constants, we could give it a
try. We could compare only the end and middle points of each eclipse
path, being that Oppolzer marked only these.
The attempts have mixed results. In the hundred years from
Oppolzer to Meeus the lunar theory and computational skills improved.
The methods of Oppolzer and Meeus are distinct enough to thwart direct
eyeball comparing of the same eclipse in the two books.
if you want to try for yourself, both sets of maps are in the
Internet for download and printing.
A more extensive eclipse canon was built by Espenak and
offered via the NASA web. In addition to deep lists, tables, maps, the
web has elaborate explanation of eclipse theory, including delta-T.
Almost all of this material is for use in computer applications like
spreadsheets, word processors, and image editors.
Conclusion
--------
Understanding how time is maintained by astronomy never was easy.
I myself used the short textbook 'Tome retimed and why it came out the
same' by Rizzp and it took many rounds of discussion with my mentors
and elders to get things right way round in my mind. The booklet,
predating atomic time, explained the classical time standard based on
the rotation of Earth.
Since World War II we obtained precise time via shortwave radio
from WWV or CHU broadcasts. Most young astronomers were handy with
electronics to build or choose such a radio. The time was either
Eastern Standard Time or UT..
By the late 20th century home astronomers took time from dial-up
computer services, like USNO, without worrying much about what the
received time was. It was usually called UT or GMT anyway.
It wasn't until the turn of the millennium, when we endured a
dozen leapseconds and had personal GPS receivers, that home
astronomers were forced to pay closer attention of modern timekeeping.
That's when they ran into the wall of haphazard or simplistic
explanations, often plain wrong.
The discussion here, tedious in places, offers a clear
description, with a real example, of atomic time, Earth deceleration,
and delta-T