In the previous plot it is evident that the form of Delta T has been
roughly parabolic. This is consistent with a
roughly linear
increase in length of day (LOD).
The next plot shows details of the vertex of the parabolic form.
On both plots I show the span of the observations which were used
to produce Simon Newcomb's
Tables of the Sun for the US Naval Observatory. Celestial
navigation was strategic, and Newcomb had the resources of the US
federal government behind his efforts to analyze observations of the
moon and planets. Newcomb and his team of computers reduced
more than 60000 observations, along with input from other observatories.
In 1896 the directors of the principal national ephemerides met
in Paris. They recognized that Newcomb's tables exceeded any
other effort, and they decided that all ephemerides would
begin to use Newcomb's expressions starting in 1901.
As a result of that decision Newcomb's tables produce the form of the
plots that we see here.
The choice of Newcomb's tables meant that the length of the
ephemeris day, and thus later the ephemeris second and the
SI second, was roughly equal to the mean length of day over
the span of observations used by Newcomb, or roughly 1820.
That guaranteed that whatever the functional form of Delta T
might be, it would have a slope of zero around 1820.
The choice of starting to use the tables in 1901 meant that
whatever the functional form of Delta T might be, it would have
a value of zero around 1901.
Most applications use TDB instead of TCB.
Note that TCB is in some sense the most uniform time scale on these
plots, for it is the rate of time measured by an observer moving with
the solar system but not affected by the relativistic effects of
orbital motion and gravitational fields. There are, however, no
clocks in a position to tick at the rate of TCB.
TDB runs at a rate defined to match the current rate of TT, and as
such it is suitable for calculating planetary ephemerides, but
the motion of the earth around and within the gravity well of the
sun leads to an annual variation with an amplitude of about
2 milliseconds.
Therefore these plots choose TT (effectively equivalent to ET which
was based on the non-relativistic tables of Newcomb) as the zero
point, for that it a uniform timescale that best correponds to
measurements made by the chronometers that humans have built and operated on
the surface of the earth.
Througout most of history, however, humans have used chronometers for the
purpose of matching the position of the sun in the sky. As such the
clocks used for civil purposes have always followed the roughly
parabolic form of UT -- the rotation of the earth. It has only been
since the 20th century that there has been any use of time scales
which are "more uniform" than the time of day indicated by the
rotation of the earth.
All of the straight and level time scales in these plots
were created and disseminated for the purposes of navigation.
Until now the broadcasts of time signals have recognized that
the needs of human navigators and the general public supersede
the needs of machines for predictably uniform time.
Recently we have seen civil authorities changing the civil time by
hours to support notions such as the 2000 Olympics in Australia, the
unproven saving of energy in the US, or the whims of Hugo Chavez in
Venezuela. This means that computers relying on broadcasts of UTC
must already have a scheme for finding the offset between UTC and
civil time. In most systems this is based on some version of the
zoneinfo database.
The zoneinfo database has typically been used to represent offsets of
integral or half hours between broadcast time and civil time.
It is capable, however, of representing offsets of seconds, and
the "right" forms of the zoneinfo files have represented
leap seconds.
The "right" zoneinfo files serve as an example of how UTC could
continue to have leap seconds even if broadcast time signals
abandoned them. This would allow everyone to have their cake
and eat it too -- but only if broadcasts adopt a different name
for the time scale that they are disseminating.
In 2003 the ITU-R subgroup investigating the future of UTC held
an
international colloquium in Torino Italy.
The
result of that colloquium recommended that a broadcast time scale
without leap seconds be given a new name.
(The
original website has been moved to
here,
and the
internet archive has the document, too.)
In the plots above and below it should be evident that if UTC
stops having leap seconds it will begin a serious departure
from what civil time has meant throughout human history.
The figure shows the differences between the different time-like
arguments and time scales between 1950 and 2020.
The periodic terms of TCB and TDB are magnified by 100 to make them
visible.
TAI us used as the reference, and ET, TDT, and TT are all taken
as (TAI + 32.184 s).
Wikipedia has details on the
Augustan realignment of the Julian calendar and the
cessation of the intercalary month in the Islamic calendar
Wikipedia has details on
February 30, and I hardly dare to mention
other
aspects of the switch from Julian to Gregorian calendars.
Relativistic variation of TCB and TDB exaggerated by factor of 1000.
Note distinction between astronomical time scales (nearer top)
which are based on physics of planetary motion
and time scales in practical use (nearer bottom)
which are based on earth-based measurements.
Most applications use TT (really TAI, but practically UTC) instead of TCG.
If, however, the broadcast (and internet) time scale is
re-named to TI (as suggested by the ITU-R colloquium in Torino)
then computers and other systems which desire a predictably
uniform time scale can be happy.
At the same time UTC can, as far as the machines are concerned,
effectively become a time zone with the offset between TI and UTC
being described by the zoneinfo files that already give the offset
between POSIX time_t and local civil time.
The inspiration for these plots comes from two astronomers
who have spent considerable time considering time.
In 1992
Seidelmann and Fukushima
published an explanation of why the IAU had introduced even more new
time scales in 1991 after they had already introduced new time scales
in 1976.
The following is Figure 1 from that paper.
Steve Allen <sla@ucolick.org>
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