moira

Why Moira Does Not Compress DExx Files

Date: 2026-08-22 Status: Public technical note Context: wiki/01_doctrines/WHY_MOIRA_DOES_NOT_COMPRESS_DEXX.md

A JPL Development Ephemeris is already a compressed product. A .bsp is not the integrator’s state dump. It is Chebyshev segments over the integration, addressed by body and epoch. DE441 is large because its span is about thirty thousand years, not because the polynomials are wasteful. DE440 covers the modern range in about 114 MiB. That is the size reduction Moira already recommends for ordinary work.

Swiss Ephemeris .se1 is a second file: another Chebyshev series, fitted to a JPL kernel, packed into a private layout so the library can stay small and fast. It can be accurate. It is not the kernel.

This note is about how the two engines read. Moira evaluates the published SPK. Swiss evaluates the packed refit. Both interpolators are Chebyshev. They do not interpolate the same object.

It is not an attack on Swiss Ephemeris. The compressed files are a genuine engineering achievement. Official documentation states that they reproduce JPL data at about 0.001 arcseconds when the reduction matches. The issue is not that a second fit is impossible. The issue is what the fit replaces: a public kernel, a public format, and a named origin.

1. Two interpolators, two files

Planetary position at a moment is not a table lookup of every second. It is a polynomial on a time window. JPL already chose that representation. Swiss chose it again, with different windows, a different origin for the Moon, and integer packing.

  Moira Swiss Ephemeris
File JPL SPK / DAF (.bsp) private .se1
Whose series JPL’s published Type 2/3 a fit to a DExx kernel
Coefficients IEEE doubles variable-width packed integers
Address NAIF (center, target) pair body in semo / sepl / seas
After the read ICRF km, relative to that center equatorial J2000 3-vector, after rot_back
Reduction later, named, in planets.py later, in the same library (app_pos_etc_*)

Reduction — light-time, aberration, nutation, ecliptic of date — is a later layer in both engines. This paper stops at the file.

2. How Moira reads a DExx kernel

The runtime file is a JPL SPK. On the machine that produced the grid below, de441.bsp identifies itself from the DAF summary label as DE-0441LE-0441. That string is the kernel. Moira does not relabel it.

SpkReader is the only gateway. It opens the DAF catalog, groups segments by NAIF pair, and, for a requested (center, target, jd), selects the segment whose epoch range covers the date. DE441 splits each body across two long epochs at JD 2440432.5; the reader must take the covering segment, not the last one in the catalog.

Bodies are chains, not a planet table:

Product NAIF path
Mercury…Pluto, barycentric (0, body)
Sun, barycentric (0, 10)
Earth-Moon barycenter (0, 3)
Earth in EMB (3, 399)
Moon in EMB (3, 301)

Geocentric Moon is therefore two interpolations added: Moon relative to EMB, plus EMB relative to the solar-system barycenter, minus Earth in EMB. The kernel never stores a geocentric Moon.

Each Type 2 record is:

  1. INIT — start of the record, seconds from J2000 TDB
  2. INTLEN — length of the record, seconds
  3. three Chebyshev series (x, y, z) as IEEE doubles, kilometres, ICRF

Time inside the record is mapped to (s \in [-1, 1]):

[ s = 2 \cdot \frac{t - t_0}{\Delta t} - 1 ]

and evaluated with a Clenshaw recurrence. Velocity, when asked for, is the derivative of that same series, scaled by (2 / \Delta t). Type 3 records include velocity coefficients; Moira admits Type 2 and Type 3 and refuses anything else rather than falling back to a third-party reader.

The independent variable of an SPK is TDB. Moira’s planetary path converts civil time to TT before the reader; TDB−TT is milliseconds. The reader returns barycentric (or center-relative) rectangular km in ICRF. Ecliptic of date, apparent place, and topocentric parallax are not in the file.

3. How Swiss reads .se1

A Swiss ephemeris file begins with three ASCII lines: a version stamp SWISSEPH, the file name, and a copyright line that names the parent JPL kernel. The 1800–2400 files used for the grid below still say DE431 on that line (2014 for semo_18 / sepl_18; 2023 for seas_18). Then binary:

Three files do the work of one SPK:

A read at time tjd (Swiss ET/TT) computes the segment index (tjd - tfstart) / dseg, seeks a 3-byte file pointer, and unpacks coefficients. Packing is the actual size trick. Each coordinate’s series is split into size groups (four or six). Coefficients then arrive as 4-byte, 3-byte, 2-byte, or 1-byte integers, then nibbles, then two-bit fields, reconstituted as

[ c = \pm \frac{\mathrm{int}/2}{10^9} \cdot \frac{r_{\max}}{2} ]

Some bodies set SEI_FLG_ELLIPSE: the stored series is a residual from a reference orbit, which is added back before use. Some set SEI_FLG_ROTATE: the series lives in the orbital plane and rot_back() rotates it to equatorial J2000 with the stored equinoctial elements. Only then does swi_echeb evaluate the same shape of Chebyshev polynomial Moira evaluates on the SPK, with

[ t = 2 \cdot \frac{tjd - t_{\mathrm{seg}0}}{dseg} - 1 ]

The vector that comes out is Swiss’s ephemeris state, equatorial J2000, already in the origin that file chose (geocentric Moon, barycentric or heliocentric planets). Apparent place is a later function in the same C library, behind swe_calc.

4. The two grids

JPL chose short windows and modest degree. Swiss chose windows on the order of the orbit and high degree, then packed the extra coefficients. Numbers below are from one DE441 SPK (DE-0441LE-0441) and the matching 18xx .se1 headers, read on 2026-08-22. Swiss order is ncoe − 1. JPL ncoe is the coefficient count in the Type 2 record.

Body JPL window JPL ncoe Swiss window Swiss order
Moon 4 d (EMB-relative) 13 27.55 d (geocentric) 28
Mercury 8 d 14 87.97 d 38
Venus 16 d 10 224.70 d 20
Earth / EMB / Sun 16 d EMB, 4 d Earth-in-EMB, 16 d Sun 13 / 13 / 11 365.26 d 25
Mars 32 d 11 687 d 25
Jupiter 32 d 8 4000 d 25
Saturn 32 d 7 4000 d 25
Uranus 32 d 6 4000 d 15
Neptune 32 d 6 4000 d 15
Pluto 32 d 6 4000 d 15

The Swiss intervals are not a secret law of nature. They are dseg in the .se1 header. Fast bodies still need more coefficients; Swiss pays with degree instead of with shorter records. JPL pays with more records of smaller degree, stored as doubles.

5. Why the Swiss file is tiny

The 18xx pack on disk (semo_18 + sepl_18 + seas_18) is 2.01 MiB and covers roughly 1800–2400. The DE441 kernel next to it is 3154.6 MiB and covers 13201 BCE–17191 CE. Those two numbers are not a verdict on polynomial waste.

Three decisions make .se1 small:

  1. Span. Six centuries, not thirty millennia.
  2. Long windows. One lunar month of order-28 Chebyshev instead of a 4-day order-12 record, repeated.
  3. Integer packing. High-order coefficients are almost zero; they collapse into nibbles. A DAF record does not do that. It stores the double JPL wrote.

DE440 already offers the first decision in public form: the modern range, same Type 2 series, about 114 MiB. That is an install tier, not a new astronomy. Whole-file zstd of a .bsp would shrink a download and destroy random access, which both readers need.

6. What a second file does not carry

A competent refit at the Swiss grid can stay at milliarcseconds against its parent kernel when both sides interpolate the same instant, in the same frame, from the same origin. Accuracy is a max-norm check per segment.

What the second file does not buy you, unless you publish it:

Without that ledger, a disagreement between Swiss and JPL cannot be assigned. It might be the Chebyshev residual. It might be DE431 versus DE441. It might be geocentric versus barycentric. It might be a reduction flag. The public SPK does not have that ambiguity: the file is the series.

7. When both interpolators are asked the same question

On 2026-08-22 the two readers were given the same TT and the same geometric-of-date reduction (no light-time, no aberration, no nutation; ecliptic of date). Swiss 2.10.03 read the DE431 .se1 pack. Moira read de441.bsp.

Instant Moon Sun Mercury Mars Jupiter
1900-01-01 0.000″ 0.000″ 0.000″ −0.006″ −0.009″
2000-01-01 0.001″ 0.000″ 0.000″ 0.000″ 0.002″
2026-08-18 −0.004″ 0.000″ 0.000″ 0.000″ 0.003″
2050-09-01 −0.005″ 0.000″ −0.001″ −0.005″ 0.006″

That is DE431-pack versus DE441-kernel, plus the second fit. It is not a different astronomy. Apparent of date on the same instants stays in the same milliarcsecond band (largest residual in that pass: Mars in 1900 at 0.065″). Swiss’s 0.001″ claim against a matching reduction and a matching parent kernel is compatible with this. The files still disagree about what the bytes are.

8. Two products people confuse

A smaller archive is a distribution problem. You may ship DE440 for 1550–2650, leave DE441 as the long kernel, or someday publish a second Chebyshev pack with a residual budget. The caller’s API can stay whatever it was. The file is still an ephemeris.

A drop-in Swiss replacement is a surface problem. It owes calc_ut, the flag bits, house letters, and body IDs. The packed file then exists so that call stays fast without opening a multi-gigabyte BSP. Libraries that take this path are keeping an old door. They are not making a new astronomy.

Moira is an alternative, not a replacement. It does not implement swe_calc_ut. Positions take a timezone-aware datetime or an explicit Julian day. Time conversion is named before the reader opens. A compressed DExx would only make sense here as an install tier. The moment it has to answer Swiss flags, the file has been sold with the door.

9. Why Moira leaves DExx as published

The kernel is the evidence. Moira’s planetary path is JPL DE430, DE440, or DE441, read by a sovereign SPK/DAF reader. Type-2/3 Chebyshev evaluation is the interpolation JPL already published. There is no Moira-owned .se1.

The interpolation is inspectable. Segment selection, Clenshaw evaluation, and NAIF chaining live in SpkReader and planets.py. The native path is a faster evaluation of the same Type 2 record, not a different series.

Validation needs a public original. Horizons, ERFA, and kernel-to-kernel checks are only honest if the runtime file is the one those oracles speak. A private second fit can be validated — but then it is the product, and it needs its own residual ledger. Moira would rather spend that work on the reduction it already names.

The small modern kernel already exists. DE440 is the recommended file for most users. DE441 is the long kernel. Compressing DE441 to avoid a download is a different offer from hiding DE441 inside a Swiss personality.

An alternative should not owe the replacement surface. Houses, nodes, Lilith, and ΔT in Moira are admitted identities, not SE_* aliases. See Migrating from Swiss Ephemeris and Beyond Swiss Ephemeris. A packed kernel that existed only to keep FLG_TRUEPOS cheap would pull the engine back onto that surface.

10. What a second pack would have to be, if it ever existed

This is not a promise to ship one. It is the bar that made us keep the kernel.

  1. Fit geometric barycentric ICRF (or another stated SPK product), not apparent longitude. Reduce after interpolation.
  2. Per-segment max residual against the parent DExx, same time scale, same origin, published with the archive.
  3. Segment index that preserves random access. Whole-file zstd shrinks a download and kills seeks.
  4. No Swiss flag personality. A Moira pack would be an install tier, addressed like a kernel, not like swe_calc_ut.

Until that bar is worth the file, Moira reads DExx as JPL published it. DE440 when the century is enough. DE441 when the span is the point. The interpolation is already in the kernel.

SPK format: NAIF SPK required reading (Type 2 Chebyshev). Kernel identity: JPL DE440/DE441 technical comments. Swiss file layout and swi_echeb: Swiss Ephemeris Programmer’s Manual and the distributed sweph.c (read_const, get_new_segment, rot_back). Official Swiss compression claim: Swiss Ephemeris overview.

This site is open source. Improve this page.