Get the difference between TAI and UT1 times at the beginning of January 1, 2000:

This number of leap seconds had been inserted by then to approximate that result:

Find the observed duration of July 19, 2020:

The excess over 86400 seconds is negative, so this day was shorter than the standard civil day:

Report the result with its uncertainty:

Find the geodetic location of the instantaneous rotational axis of the Earth for a given date:

It was more than 30 feet away from the geodetic North Pole:

Specify dates as DateObject expressions:

Get property values for a list of dates:

Get a time series of property values for a DateInterval input:

Obtain the list of 27 leap seconds introduced since 1972:

There were no leap seconds added in the year 2020:

Mean obliquity angle between the mean equatorial and the ecliptic planes:

Display the evolution of the mean obliquity angle for Julian years to :

Compute the difference in right ascension between the mean and true equinoxes:

It can also be computed with AstroPosition:

Plot the evolution of the nutation angles over a period of 18 years, almost a complete 18.6-year cycle:

Find the excess in day durations for all days since January 1, 1962:

It has changed a few milliseconds in the last few decades:

Recently, the day has been getting shorter:

Show the behavior in the last few years:

Show the behavior in the last few months:

Find the difference between TAI and UT1 for the first day of each month since 1960:

Also get the difference between TAI and UTC, which was piecewise linear from 1960 to 1973 and is now piecewise constant:

UTC follows UT1 in such a way that their difference is never larger than 0.9 seconds:

Locate the instantaneous rotation axis with respect to the geodetic North Pole between 2010 and 2015:

The result is given as a list of pairs of the and components of the rotation axis, usually given as small angles with respect to the North Pole:

The standard convention makes the axis point toward Greenwich on the left and the axis toward 90 degrees west on the top:

Convert to a representation in meters:

Average the polar motion of the instantaneous rotation axis around the geodetic North Pole:

Convert to a representation in meters:

Represent the evolution in time:

Plot the jumps of the 27 leap seconds introduced since 1972:

Each jump corresponds to a second:

The long-term behavior of TT-UT1 is parabolic:

Atomic time TAI was synchronized with UT1 at the beginning of 1958:

Compute the mean sidereal time at zero longitude on a given date:

This can also be computed with SiderealTime at any location with zero longitude:

Compute the apparent sidereal time at zero longitude on a given date:

This can also be computed with SiderealTime at any location with zero longitude:

Compute the angle between the North Celestial Pole and the North Ecliptic Pole:

It can also be computed with AstroAngularSeparation:

Or with AstroPosition, using the true ecliptic frame:

Or with AstroPosition, using the true equatorial, true equinox (TETE) frame:

Compute the difference in right ascension between the mean and true equinoxes:

It can also be computed with AstroPosition:

Find the right ascension difference between the true equinox and the celestial intermediate origin (CIO):

It can be computed with AstroAngularSeparation:

Or with AstroPosition, using the true equatorial, true equinox (TETE) frame:

Or with AstroPosition, using the celestial intermediate reference system (CIRS) frame:

International Atomic Time TAI time did not exist before 1956:

Coordinated Universal Time UTC did not exist before 1960: