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Time Scales And Epoch Storage

DiffOrb uses Time for one physical instant. It uses State for one dynamical state at one epoch. The same instant can be viewed as Terrestrial Time (TT), International Atomic Time (TAI), Coordinated Universal Time (UTC), Universal Time 1 (UT1), mixed UT, or Barycentric Dynamical Time (TDB). Time stores the instant in TT. State uses the same instant in TDB.23

Core Contract

Time is the main epoch container in DiffOrb. One Time object can show several time-scale views without changing the instant it represents. State uses the same idea at the dynamical layer, but it keeps one canonical epoch form for propagation and reference-frame conversion.

DiffOrb uses different canonical scales in these two layers. TT is the canonical scale for Time. TDB is the canonical scale for State.2

Two-Part Julian Dates

DiffOrb stores epochs as split Julian dates: jd = jd1 + jd2.3 The large part stays in jd1. The small remainder stays in jd2. This reduces precision loss when a large Julian date is combined with a small offset or a time-scale correction.

DiffOrb keeps this split form through the whole conversion chain. If you exchange data with SOFA-style code, keep both parts. Do not collapse them into one floating-point Julian date.

Time Scales Used By DiffOrb

In the modern International Astronomical Union (IAU) framework, some time scales are uniform atomic or coordinate scales, and some follow the Earth's real rotation.12 DiffOrb follows that split. The current API exposes TAI, TT, UTC, UT1, mixed UT, and TDB. Geocentric Coordinate Time (TCG) and Barycentric Coordinate Time (TCB) matter in the formal background, but the current API does not expose them as standard Time views.

Terrestrial Time

TT is the canonical storage scale of Time. In practice, DiffOrb uses the standard relation TT = TAI + 32.184 s.3 Civil UTC connects to TT. Earth-rotation UT1 also connects to TT. TDB is derived from TT.

International Atomic Time

TAI is the continuous atomic scale behind TT. In DiffOrb it mainly acts as the stable intermediate between UTC and TT.

Coordinated Universal Time

UTC is the civil broadcast scale. DiffOrb defines it only for epochs on or after 1962-01-01. For earlier epochs, use UT1 instead.

UTC started to appear in 1961, but DiffOrb uses 1962-01-01 as the boundary because the high-precision Earth Orientation Parameter (EOP) data used for Earth-based timing starts there. This also matches the JPL Horizons convention. Horizons treats observer-table UT as UT1 before 1962-01-01 and as UTC on and after 1962-01-01.

Before 1972, UTC used linear rate adjustments instead of the modern leap-second system. DiffOrb keeps that historical distinction so converted observation times keep the right civil meaning.

Universal Time 1 And Mixed UT

UT1 is the Earth-rotation time scale. It follows the actual rotation angle of the Earth and is the UT scale used by Earth-rotation geometry.24

For modern dates, DiffOrb converts between TT and UT1 with EOP data. When the needed EOP span is not available, it falls back to the historical Delta T = TT - UT1 polynomial model summarized by Espenak and Meeus.5

DiffOrb also exposes a mixed UT view. This is a library convention, not an IAU standard time scale. It means UT1 before 1962-01-01 and UTC on and after 1962-01-01.

Barycentric Dynamical Time

TDB is the practical barycentric dynamical scale used for state epochs and ephemeris arguments. It is not the same as TCB. It is designed to stay close to TT in average rate.12

DiffOrb uses the same practical TT -> TDB model as SOFA iauDtdb.3 The inverse TDB -> TT path is built by fixed-point inversion of that same forward model.

In the topocentric form of the model, TDB can depend on observer position. For that reason, Time.tdb(...) accepts an ITRS location. If no location is supplied, DiffOrb uses the geocentric case.

Why Time Stores TT While State Uses TDB

These canonical choices serve different jobs. Time needs one uniform scale that can connect Earth-based inputs and outputs such as UTC, UT1, and EOP to barycentric dynamical work. TT is the bridge for that job. State is already a dynamical Cartesian object, so TDB is the more natural time scale for its epoch.

Connections To The Rest Of The Library

Earth Rotation And Terrestrial Geometry uses TT, UT1, and EOP together because the ITRS -> GCRS transformation depends on both the Earth's real spin and the precession-nutation and frame-bias model.

Frames And State Representation starts one layer later. When a Cartesian State is transformed between reference frames, its epoch is already handled as TDB.

Higher-level objects follow the same split. Ground rows in Site start with Earth-based time and Earth rotation. EphemerisBody, SmallBody, space rows in Site, and generic State transforms use TDB epochs.

References

  1. International Astronomical Union. Resolutions adopted at the XXIVth and XXVIth General Assemblies, especially the 1991 and 2000 resolutions on reference systems and time scales. https://www.iau.org/Iau/Iau/Publications/List-of-Resolutions.aspx ↩↩

  2. Kaplan, G. H. The IAU Resolutions on Astronomical Reference Systems, Time Scales, and Earth Rotation And Terrestrial Geometrys: Explanation and Implementation, especially the sections on TT, TDB, UTC, and UT1. ↩↩↩↩↩

  3. Standards of Fundamental Astronomy. SOFA Tools for Earth Attitude and SOFA Time Scale and Calendar Tools, including the two-part Julian date convention and the practical iauDtdb model. https://www.iausofa.org/ ↩↩↩↩

  4. International Earth Rotation and Reference Systems Service. IERS Conventions (2010), especially the sections on UT1, Earth rotation, and Earth orientation parameters. ↩

  5. Espenak, F., & Meeus, J. Polynomial Expressions for Delta T. NASA Eclipse Web Site. https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html ↩