jOHn Pazmino
 NYSkies Astronomy Inc
 2017 January 2

   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 
        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 
    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 

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 

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. 
    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. 
    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. 

 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 

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 
    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 
    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. 
    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