Universal Time, Atomic Time, and Terrestrial Time #

Civil clocks, the Earth’s rotation, and planetary orbits each run on a different drummer. Civil time (UTC) is a compromise between the uniform tick of atomic clocks and the irregular rotation of the Earth. Planetary ephemerides use a purely uniform time scale uncontaminated by Earth’s wobble. Chart calculation must navigate all of them. This article defines each time scale, explains why it exists, and traces the conversion pipeline from clock time to the time arguments that ephemerides and sidereal-time formulas actually need.

The Problem #

A single, universal “time” does not exist in practice because different physical processes demand different definitions:

Timekeeping requires uniformity: each second identical to the last. Atomic clocks provide this.
Earth orientation requires a time scale tied to the actual rotation of the Earth, warts and all. Sidereal time and the hour angle depend on this.
Orbital mechanics requires a time scale that is uniform and independent of the observer’s location in the gravitational field. Ephemeris calculations need this.
Civil life requires something close to both atomic uniformity and solar synchrony. UTC bridges these.

The result is a family of time scales, each optimal for one purpose.

Universal Time (UT) #

Universal Time is the family of time scales based on the Earth’s rotation.

UT0 #

UT0 is the raw universal time obtained from astronomical observations of the Earth’s rotation (historically, transit observations of stars). It is affected by the observer’s location because the Earth’s rotation axis wanders slightly with respect to the Earth’s crust (polar motion). Two observatories at different locations, measuring the Earth’s rotation simultaneously, obtain slightly different UT0 values. UT0 is never used directly in chart calculation.

UT1 #

UT1 is UT0 corrected for polar motion. It represents the mean solar time at the Greenwich meridian, as determined by the actual rotation of the Earth. UT1 is the fundamental observational time scale: it tells you where the Earth is in its rotation right now.

UT1 is irregular. The Earth’s rotation rate varies due to tidal friction (secular deceleration), angular momentum exchanges between the core and mantle, post-glacial rebound, and atmospheric/oceanic effects. Over the past century, the length of day has been increasing by about 2.3 milliseconds per century, but with significant irregular fluctuations superimposed.

UT1 is the time argument for sidereal time computation, as established in Sidereal Time.

UT1–UTC (DUT1) #

The difference between UT1 and UTC is called DUT1. It is broadcast in coded form in radio time signals and published by the IERS. By policy, $|\text{DUT1}| < 0.9$ seconds; when the difference approaches this limit, a leap second is inserted (or, in principle, deleted) in UTC.

As of 2024, typical DUT1 values are around $-0.05$ to $+0.3$ seconds. For chart calculation, a DUT1 error of 0.9 seconds shifts the Ascendant by at most about $0.004°$ — negligible. Many astrological programs ignore DUT1 entirely and treat UT1 = UTC. This is acceptable for all practical purposes.

Coordinated Universal Time (UTC) #

UTC is the civil time standard. It is the time on your clock, on your phone, on NTP servers, and in time-zone databases. UTC ticks at the same rate as TAI (atomic time) — each UTC second is an SI second — but UTC is periodically adjusted by inserting leap seconds to keep it within 0.9 seconds of UT1.

Leap seconds are inserted (as a 61st second: 23:59:60) at the end of June 30 or December 31. As of 2024, 37 leap seconds have been inserted since UTC’s inception in 1972. The accumulation is:

$$ \text{UTC} = \text{TAI} - \Delta\text{AT} $$

where $\Delta\text{AT}$ is the cumulative number of leap seconds. As of January 2017: $\Delta\text{AT} = 37$ seconds. Updated values are published by the IERS.

The future of leap seconds is uncertain. The ITU decided in 2022 to phase out leap seconds by 2035, allowing UTC to drift from UT1 by more than 0.9 seconds. For software that needs to handle dates after 2035, this means the UTC-UT1 relationship will change. For historical chart calculation, the existing leap second table is fixed and well-documented.

UTC and Discontinuities #

UTC has a fundamental problem: it is discontinuous at leap seconds. The sequence 23:59:59 → 23:59:60 → 00:00:00 introduces a 61-second minute. Software that assumes 60 seconds per minute, or that computes time differences by simple subtraction, will produce errors at these boundaries. For chart calculation, this is unlikely to matter (a 1-second error is negligible), but ephemeris libraries that compute precise intervals must use proper UTC handling or work in TAI/TT instead.

International Atomic Time (TAI) #

TAI (Temps Atomique International) is the fundamental uniform time scale, maintained by averaging hundreds of atomic clocks worldwide. Each TAI second is one SI second, defined as 9,192,631,770 periods of the cesium-133 hyperfine transition.

TAI is continuous (no leap seconds), uniform (no rotation-dependent irregularities), and independent of the observer’s location (to the extent that relativistic corrections are applied). It has been running continuously since 1958.

The relationship to UTC is:

$$ \text{TAI} = \text{UTC} + \Delta\text{AT} $$

where $\Delta\text{AT}$ is the cumulative leap seconds (37 as of 2024).

TAI is not used directly in chart calculation, but it underpins all the other uniform time scales.

GPS Time #

GPS time was set equal to UTC on January 6, 1980, and has not been adjusted for leap seconds since. It therefore drifts from UTC by the number of leap seconds inserted since 1980:

$$ \text{GPS} = \text{TAI} - 19 \text{ s} $$

$$ \text{GPS} = \text{UTC} + \Delta\text{AT} - 19 \text{ s} $$

As of 2024, GPS time is 18 seconds ahead of UTC. If a time source reports GPS time (some GPS receivers do), subtract the current leap-second offset to obtain UTC.

Terrestrial Time (TT) #

Terrestrial Time is the uniform time scale used as the time argument for geocentric ephemerides and for the equations of motion of Solar System bodies. It is the modern replacement for Ephemeris Time (ET) and Terrestrial Dynamical Time (TDT).

TT ticks at the same rate as TAI but with a fixed offset:

$$ \text{TT} = \text{TAI} + 32.184 \text{ s} $$

The offset $32.184$ seconds is a historical artifact that ensures continuity with Ephemeris Time at the moment of the transition (1977). It has no physical significance; it is a constant that will never change.

Combining with the UTC relationship:

$$ \text{TT} = \text{UTC} + \Delta\text{AT} + 32.184 \text{ s} $$

As of 2024: $\text{TT} = \text{UTC} + 37 + 32.184 = \text{UTC} + 69.184$ seconds.

TT is the time argument for:

Planetary ephemeris evaluation (computing where planets are)
Precession and nutation computations
Most dynamical quantities in the Explanatory Supplement

TT is not the time argument for sidereal time (which uses UT1). This distinction is subtle but important: planetary positions depend on where the planets are in their orbits (a dynamical question, using TT), while the orientation of the sky as seen from the ground depends on where the Earth is in its rotation (a rotational question, using UT1).

Barycentric Dynamical Time (TDB) and Barycentric Coordinate Time (TCB) #

TDB is the time scale used for barycentric ephemerides (referenced to the Solar System barycenter rather than to the Earth). It differs from TT by periodic terms arising from the Earth’s motion in the Sun’s gravitational field (a relativistic effect). The largest term has an amplitude of about 1.7 milliseconds with a period of one year.

For chart calculation, the difference between TT and TDB is negligible (< 2 ms). Most ephemeris engines accept either TT or TDB and handle the conversion internally. In practice, use TT as the ephemeris time argument and let the engine manage the TT→TDB conversion if it needs to.

TCB (Temps Coordonné Barycentrique) is the coordinate time in the barycentric reference frame according to General Relativity. It ticks faster than TT by about 49 seconds per century due to the Earth’s position in the Sun’s gravitational well. TCB is used in fundamental astronomy but never in chart calculation.

The Conversion Pipeline #

The practical conversion from civil clock time to the time arguments needed for chart calculation:

Civil time (with time zone)
    ↓  subtract UTC offset (from timezone database)
UTC
    ↓  DUT1 correction (add DUT1, typically ignored)
UT1 → used for sidereal time (GMST, GAST, LAST)
    
UTC
    ↓  add ΔAT + 32.184s
TT → used for ephemeris evaluation, precession, nutation

Both UT1 and TT are needed for a chart:

UT1 determines the sidereal time and therefore the chart angles.
TT determines the planetary positions (via the ephemeris) and the precession/nutation corrections.

For a modern chart (after 1972), the conversion is straightforward: look up $\Delta\text{AT}$ from a table, add $32.184$ seconds for TT. For historical charts, the relationship between clock time and UT1 is more complex; Delta T and Time Zones treat these issues.

Historical Time Scales #

Before 1972 (the start of the UTC/leap-second system), the relationship between civil time and UT1 was different in each era:

Before ~1884: local mean time (LMT), based on the observer’s geographic longitude. No time zones.
~1884–1972: standard time zones existed, but the broadcast time signals were directly tied to UT (first UT0, then UT2 = UT1 corrected for seasonal variations). Civil clocks were effectively on UT, with time-zone offsets. No leap seconds; no TAI.
1972–present: UTC with leap seconds.

For charts before 1972, the most practical approach is: determine the civil time as recorded, convert to UT using the applicable time zone (or LMT correction), and then use the UT directly as UT1 (the distinction between UT1 and earlier forms of UT is at the sub-second level). TT is then obtained as UT1 + $\Delta T$, where $\Delta T$ is the historical value from Delta T.

Implementation Notes #

For modern charts (after 1972), the computation is: UTC → UT1 (add DUT1, usually ignored) → GMST/GAST/LAST for chart angles; UTC → TT (add $\Delta\text{AT} + 32.184$) for ephemeris queries. The leap second count $\Delta\text{AT}$ must be looked up from a table; it is not computable from a formula.
For historical charts, the dominant uncertainty is $\Delta T$ (the difference between TT and UT1). See Delta T. The time-zone and DST reconstruction is also non-trivial; see Time Zones.
Leap second tables are available from the IERS and are embedded in most operating systems’ timezone data (the leap-seconds.list file). They must be updated when new leap seconds are announced — though since the last leap second was in December 2016, and the ITU plans to phase them out, this may become a historical concern.
Avoid mixing time scales. A common bug is to use UTC where UT1 is needed, or UT1 where TT is needed. For modern charts, the errors are small but real. For historical charts (centuries ago, where $\Delta T$ exceeds minutes), the errors can be large enough to change the Ascendant’s sign.
Julian Date: all time-scale formulas ultimately work with Julian Dates (JD). The Julian Date can be expressed in any time scale: JD(UT1), JD(TT), JD(UTC). The numerical value differs depending on the time scale. Be explicit about which time scale a JD refers to. See Julian Date.

References #

McCarthy, D. D., & Seidelmann, P. K. (2009). TIME — From Earth Rotation to Atomic Physics. Wiley.
Explanatory Supplement to the Astronomical Almanac, 3rd ed. (2013). University Science Books. Chapter 2.
IERS Conventions (2010). IERS Technical Note 36. Chapters 1, 5.
Meeus, J. (1998). Astronomical Algorithms, 2nd ed. Willmann-Bell. Chapter 10.
Nelson, R. A. et al. (2001). “The leap second: its history and possible future.” Metrologia, 38, 509–529.