Precise date and time handling in Rust built on top of lossless fractions (with 128 bits on the numerator and 16 bits on the denominator). The Epoch used is TAI Epoch of 01 Jan 1900 at midnight, but that should not matter in day-to-day use of this library.
simulation feature)TimeUnit::Hour * 2 + TimeUnit::Second * 3)Epochs and Durations)Almost all examples are validated with external references, as detailed on a test-by-test basis.
Validation is done using NASA's SPICE toolkit, and specifically the spiceypy Python wrapper.
The most challenging validation is the definition of Ephemeris Time, which is very nearly the same as the Dynamic Barycentric Time (TDB). These calculations in hifitime are from ESA's Navipedia.
Hifitime uses a fixed offset for the computation of Ephemeris Time, as is recommended in Navipedia. For TDB however, the offset is based on the centuries since J2000 TT and therefore time varying. I believe that SPICE uses TDB for all dates after J2000 TT. Hence, in the following validation, we will be comparing the SPICE ET with the Hifitime TDB.
The following examples are executed as part of the standard test suite (cf. the function called spice_et_tdb).
In SPICE, we chose to convert the UTC date 2012-02-07 11:22:33 UTC into Ephemeris Time. SPICE responds with 381885819.18493587.
Initializing the same UTC date in hifitime and requesting the TDB leads to 381885819.18493646, which is an error of 596.05 nanoseconds.
In SPICE, we chose to convert the UTC date 2002-02-07 00:00:00.000 UTC into Ephemeris Time. SPICE responds with 66312064.18493876.
Initializing the same UTC date in hifitime and requesting the TDB leads to a difference 618.39 nanoseconds.
This tests that we can correctly compute TDB time which will have a negative number of days because the UTC input is prior to J2000 TT.
In SPICE, we chose to convert the UTC date 1996-02-07 11:22:33 UTC into Ephemeris Time. SPICE responds with -123035784.81506048.
Initializing the same UTC date in hifitime and requesting the TDB leads to a difference 610.94 nanoseconds.
In SPICE, we chose to convert the UTC date 2015-02-07 00:00:00.000 UTC into Ephemeris Time. SPICE responds with 476580220.1849411.
Initializing the same UTC date in hifitime and requesting the TDB leads to a difference 596.05 nanoseconds.
In SPICE, we chose to convert the TDB Julian Date in days 2452312.500372511 into Ephemeris Time, and initialize a Hifitime Epoch with that result (66312032.18493909).
We then convert that epoch back into days of Julian Date TDB and Julian Date ET, both of which lead a difference below machine precision on a f64 (the equivalent of a double in C/C++).
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Each time computing library may decide when the extra leap second exists as explained
in the IETF leap second reference.
To ease computation, hifitime decides that second is the 60th of a UTC date, if such exists.
Note that this second exists at a different time than defined on NASA HEASARC. That tool is
used for validation of Julian dates. As an example of how this is handled, check the Julian
day computations for 2015-06-30 23:59:59,
2015-06-30 23:59:60 and 2015-07-01 00:00:00.
ET and TDB should now be identical. However, hifitime uses the European Space Agency's definition of TDB, detailed here. It seems that SPICE uses the older definition which has a fixed offset from TDT of 0.000935 seconds. This difference is more prominent around the TDB epoch of 01 January 2000.
as_jde_tdb_days() in Epoch. In version 2.2.1, the ephemeris time and TDB days were identical down to machine precision. After a number of validation cases in the rotation equations of the IAU Earth to Earth Mean Equator J2000 frame, the new formulation was shown to lead to less rounding errors when requesting the days. These rounding errors prevented otherwise trivial test cases. However, it adds an error of 40.2 nanoseconds when initializing an Epoch with the days in ET and requesting the TDB days.