Time Standards in Modern Ephemerides: UT1, TT, TAI, and the Leap Second

Astronomy has more clocks than it has planets. The reason is that no single time scale serves every purpose. The Earth's rotation is irregular and slowing; atomic clocks tick uniformly but are tied to the SI second on Earth's geoid; the equations of motion that propagate planets through the solar system require yet another scale that does not see the Earth's rotation at all.

This note documents which time scales we use, why, and where the choice matters. Anyone replicating LokLab calculations to arcsecond precision needs to know this material; anyone working only to degree precision mostly does not.

The four time scales we use

Scale	Symbol	Definition	Realized by
Universal Time 1	UT1	Mean solar time at the Greenwich meridian	Astronomical observation, Earth-rotation measurement
International Atomic Time	TAI	SI seconds since 1958-01-01	Ensemble of ~450 atomic clocks worldwide
Coordinated Universal Time	UTC	TAI offset by an integer number of leap seconds, kept within 0.9 s of UT1	Defined by IERS
Terrestrial Time	TT	Dynamical time on Earth's geoid; TT = TAI + 32.184 s (exact)	Theoretical; realized through TAI

The ephemerides we use (JPL DE441 and Swiss Ephemeris) are computed and indexed in TT. Observations made on Earth, and all wall-clock measurements, are in UTC or UT1. The conversion between them is essential and non-trivial.

Why ΔT matters

The Earth's rotation is irregular at the level of milliseconds per day, and is slowing on geological time scales. The accumulated difference between a uniform time scale (TT) and a rotation-based time scale (UT1) is called ΔT:

$\Delta T = TT - UT1$

ΔT cannot be predicted from first principles. It must be measured. Historical ΔT has been reconstructed from records of eclipses and occultations going back to ancient observations. The IERS publishes ΔT historically and prospectively (extrapolated 1–2 years into the future).

For 2026.0, ΔT ≈ 71.4 seconds. For 1919.0 (the year of the Eddington eclipse), ΔT was approximately 24.0 seconds. For 1610.0 (when Galileo observed Jupiter's moons), ΔT was approximately 92 seconds. For 100 CE, ΔT was approximately 9000 seconds, or two and a half hours.

This matters because if you specify a historical observation in UT1 ("Galileo observed at 22:00 local apparent time on January 7, 1610") and then look up planetary positions in an ephemeris indexed in TT, you have to apply ΔT first. Skipping the conversion would shift Jupiter by approximately 12 arcseconds in 1610: small, but more than enough to misalign moon positions.

Leap seconds and the UTC-UT1 dance

Since 1972, UTC has been kept within 0.9 seconds of UT1 by inserting an integer-second offset whenever the deviation grows too large. These insertions are leap seconds. There have been 27 leap seconds added between 1972 and the most recent insertion. The IERS announces leap seconds approximately six months in advance.

The leap-second system is scheduled to end in or around 2035, after which UTC and TAI will simply differ by a constant. The IERS will allow UT1−UTC to drift, and astronomical observations requiring tight UT1 alignment will need to apply a published correction.

For LokLab's calculations:

1. Historical observations (pre-1972): UT1 is used; ΔT historical tables apply.
2. Recent observations (1972 onward): UTC is recorded; UTC → UT1 correction (DUT1, published by IERS) is applied; ΔT is then trivial.
3. Ephemeris lookup: All calls to Swiss Ephemeris pass TT, computed as UT1 + ΔT.

What this looks like in code

Each historical reconstruction includes a header section with the time scale conversions explicitly:

Observation: Galileo, Padua, January 7, 1610 22:00 local apparent time
Local apparent time → UT1:   22:00 LAT → 21:13 UT1  (longitude correction -47 m)
UT1 → TT:                    21:13 UT1 + 0:01:32 ΔT(1610) = 21:14:32 TT
Ephemeris call:              swe_calc(jd_tt = 2308857.385, ipl = SE_JUPITER, ...)

The 92-second ΔT correction for 1610 produces a Jupiter longitude shift of approximately 12 arcseconds. This is small in absolute terms but represents 0.7% of the Galilean moons' orbital separation at the date of observation. It matters.

The Galileo Julian-Gregorian wrinkle

Galileo's own journal entries use the Julian calendar (10-day offset from Gregorian in 1610). Our published reconstructions convert to Gregorian first, then compute the time scale conversions described above. The Julian conversion is the largest single source of historical-record confusion, far larger than ΔT.

A standard rule of thumb: if a European observation between 1582 and 1752 is given in a primary source without specifying the calendar, suspect Julian. If the date includes "OS" or "NS" annotations, take them at face value. If neither applies, cross-check against a second source.

Precision floor

The LokLab pipeline operates with a numerical floor of one arcsecond. For positions involving the Moon or close planetary conjunctions, we report to 0.1 arcseconds where the ephemeris supports it. Errors in time scale conversion of more than ~0.5 seconds will exceed our reported precision; this is the limit of what ΔT historical tables guarantee for dates within the last few centuries. For deep antiquity reconstructions (BCE), the ΔT uncertainty dominates everything else and we report wider confidence intervals accordingly.

What's next

A companion methodology note on coordinate systems (equatorial vs. ecliptic, ICRF vs. FK5, topocentric vs. geocentric corrections) will follow as the next item in the methodology series. After that, a note on the JPL DE441 ephemeris configuration we use, including local cache decisions and the small differences between DE441 and DE440 that show up at the milliarcsecond level.

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Methodology notes are updated as our practice evolves. Corrections welcome at contact@loklab.org.