Astronomy & Celestial Mechanics
the sky, computed
Concept

Terrestrial time — where it appears

The time scale an ideal clock on the rotating Earth's geoid would keep, realised from atomic clocks and used for ephemerides seen from Earth. It is defined by its rate against the SI second and is offset from International Atomic Time by exactly 32.184 seconds.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

TCB has gained 23.5 seconds on TT since 1977. How far four of the solar system's time scales have drifted apart, against years since they were set equal. TT is the time a clock on the Earth's geoid keeps, and it is flat here by definition. TCG is the time a clock at rest just outside the Earth's gravitational well would keep, and it runs faster by seven parts in ten thousand million — 0.0220 seconds a year. TCB is the time a clock at rest outside the Sun's well would keep, and it runs faster by fifteen parts in a thousand million, or 0.4893 seconds a year. TDB is TCB with that rate divided out so that it stays within milliseconds of TT, which is what makes it usable as an ephemeris argument and what makes it a coordinate rather than a proper time. The differences are constants and they are not corrections: an ephemeris tabulated against one of these and evaluated against another is wrong by the whole of this plot.

A second that depends on where the clock is

A clock in orbit runs fast, a clock at the bottom of a gravity well runs slow, and a clock at rest far from the Sun runs faster than anything on Earth by fifteen parts in a thousand million. Astronomy therefore has four different seconds, two of them longer than the others, and an ephemeris has to declare which one it is tabulated against.

sky · Timescales How steady each kind of clock is, by how long it is averaged. The Allan deviation — the typical fractional difference in frequency between successive averages of length τ — against τ, for representative noise models of caesium beam, hydrogen maser, caesium fountain, optical lattice clock. Each falls as τ^−½ while random frequency noise dominates, then levels off at a floor set by slower, correlated noise, and a clock with a systematic drift eventually rises again. A caesium beam is still improving at the longest averaging drawn, reaching 10⁻¹⁴; a hydrogen maser reaches its best, 7.3·10⁻¹⁶, after about 27 hours; a caesium fountain is still improving at the longest averaging drawn, reaching 1.2·10⁻¹⁶; an optical lattice clock is still improving at the longest averaging drawn, reaching 10⁻¹⁸. No clock is best at every averaging time — the maser is steadiest over hours and wanders over weeks, the fountain is noisier over minutes and more accurate over months — and a time scale is built by using each where it is best. The curves are typical shapes, not the specification of any particular instrument.

A time scale that is finished after it is used

The world's reference time is not kept by any clock. It is an average of about four hundred and fifty, weighted by how steady each has been, published a month late, and then recomputed a year later against the handful of clocks that define the second — so the best available time for any moment is known only long after the moment has passed. The best clocks are now so good that averaging them requires knowing each one's height to a centimetre.

sky · Timescales The stability of a pulsar clock against atomic clocks, over averaging times from a day to thirty years. Fractional frequency instability, on a logarithmic axis, against averaging time from a day to thirty years. A single millisecond pulsar timed to 300 nanoseconds every 14 days improves as τ^(−3/2) while its white timing noise averages down, and flattens where its slow spin noise, drawn at 10⁻¹⁵ at ten years, takes over. An ensemble of 20 such pulsars is 4.5 times better if their noises are independent. The atomic curves are representative: a hydrogen maser, excellent at hours and drifting at years, and a steered atomic time scale limited near 3·10⁻¹⁶ at long times. In this representative comparison the pulsar ensemble becomes the steadier of the two beyond about 3 years of averaging. At a day a pulsar is a billion times worse than an atomic clock; over decades it is competitive, because nothing inside a neutron star changes on the timescales on which laboratory clocks are rebuilt.

A clock made of neutron stars

The best atomic clocks are rebuilt every decade and averaged every month. A millisecond pulsar has kept its own time for a billion years. Averaged over years, an ensemble of pulsars is as steady as the world's atomic time scale — steady enough to find its errors — but it can never say how fast that time scale runs.

sky · Timescales

Named alongside it

The objects these essays reach for when they reach for this one.

Allan deviationClock ensembleGeoidGravitational redshiftInternational Atomic TimeAtomic clockBarycentric coordinate timeClock rateCoordinate timeEphemeris timeGravitational-wave backgroundMillisecond pulsar

All concepts