LibEphemeris – Scientific Precision #

LibEphemeris is built on modern IAU standards and NASA JPL ephemerides. Every component – from nutation to planet center corrections – uses the most accurate models available in the astronomical literature. This document describes the scientific foundations, the specific models chosen, and measured precision for every calculation.

Table of Contents #

• 1. Ephemeris Foundation
• 2. Nutation Model
• 3. Precession Model
• 4. Aberration and Light Deflection
• 5. Planet Center Corrections
• 6. Velocity Computation
• 7. True Ecliptic Coordinates
• 8. House Calculations
• 9. Lunar Points
• 10. Delta T (TT − UT1)
• 11. Fixed Stars
• 12. Ayanamsha (Sidereal Modes)
• 13. Eclipses and Occultations
• 14. Rise, Set, and Transit
• 15. Heliacal Events
• 16. Planetary Positions – Measured Precision
• 17. Photometric Models (Phenomena)
• 18. Minor Bodies
• 19. Thread-safe Context API
• 20. Comprehensive Precision Audit
• References

---

1. Ephemeris Foundation #

NASA JPL Development Ephemeris #

LibEphemeris uses NASA JPL DE440 and DE441, the most recent planetary ephemerides produced by the Jet Propulsion Laboratory (Park et al. 2021). These are the same ephemerides used for Mars rover navigation and the James Webb Space Telescope.

DE440 and DE441 have identical precision – DE441 is simply the extended-range version. DE440s is a reduced-size subset of DE440 with no loss of precision within its range.

Precision tiers #

LibEphemeris organizes these files into three precision tiers:

Select by tier or by file directly:

import libephemeris as eph

# By tier
eph.set_precision_tier("extended")   # uses de441.bsp

# Or by file
eph.set_ephemeris_file("de441.bsp")

Environment variables: LIBEPHEMERIS_PRECISION=extended or LIBEPHEMERIS_EPHEMERIS=de441.bsp.

Resolution priority (highest to lowest):

1. LIBEPHEMERIS_EPHEMERIS environment variable
2. set_ephemeris_file() / set_jpl_file() programmatic call
3. Precision tier (LIBEPHEMERIS_PRECISION env var or set_precision_tier())
4. Default: de440.bsp (medium tier)

Swiss Ephemeris comparison #

Swiss Ephemeris uses JPL DE431 (older generation, 2013) repackaged into its own binary format. DE440/DE441 (2021) incorporate 8 additional years of observational data, including improved Juno-era Jupiter observations and MESSENGER-era Mercury data, and use the updated ICRF 3.0 reference frame.

When SEFLG_MOSEPH is passed, Swiss Ephemeris falls back to the Moshier semi-analytical ephemeris (VSOP87 for planets, ELP2000-82B for Moon), which has errors of ~1 arcsecond for inner planets and ~10+ arcseconds for outer planets at historical dates. LibEphemeris accepts SEFLG_MOSEPH for API compatibility but silently ignores it – all calculations always use the full JPL numerical integration.

---

2. Nutation Model #

IAU 2006/2000A (1365 terms) #

LibEphemeris uses the IAU 2006/2000A nutation model via the IAU ERFA library (erfa.nut06a()). This is the highest-precision nutation model currently adopted by the International Astronomical Union.

The model computes nutation in longitude (Δψ) and nutation in obliquity (Δε) from the five Delaunay fundamental arguments plus nine planetary fundamental arguments, with corrections from the IAU 2006 precession-rate adjustments (Capitaine et al. 2005).

Swiss Ephemeris comparison #

Swiss Ephemeris uses the same IAU 2006/2000A model. Both implementations achieve sub-milliarcsecond nutation. The difference between the two is negligible (<0.01 mas).

However, Skyfield’s internal nutation (used before pyerfa integration) defaults to IAU 2000B, a truncated model with only 77 terms and ~1 milliarcsecond precision. LibEphemeris overrides this with the full 1365-term model via pyerfa for all planet and house calculations.

Impact on ecliptic longitude #

Nutation in longitude (Δψ) directly shifts ecliptic longitudes. The maximum amplitude of Δψ is ~17.2 arcseconds (the 18.6-year lunar nodal cycle). Using a 77-term model vs. a 1365-term model introduces up to ~1 mas error in this correction, which over decades accumulates to measurable differences in planetary longitudes.

---

3. Precession Model #

IAU 2006 (Capitaine et al. 2003) #

LibEphemeris uses the IAU 2006 precession model via erfa.pmat06(), implementing the Fukushima-Williams four-angle formulation with polynomial terms up to T^5.

Swiss Ephemeris comparison #

Swiss Ephemeris also uses IAU 2006 precession. Both implementations are equivalent for this component.

Frame bias (ICRS to J2000) #

The rotation from the International Celestial Reference System (ICRS) to the mean equator and equinox of J2000.0 is applied via the combined bias-precession-nutation matrix from erfa.pnm06a(). This matrix incorporates the frame bias angles (dα₀ = −14.6 mas, ξ₀ = −16.617 mas, η₀ = −6.819 mas) defined in the IERS Conventions.

---

4. Aberration and Light Deflection #

Annual aberration #

For planet calculations, LibEphemeris uses Skyfield’s full relativistic treatment via the .apparent() method, which implements IERS 2003 conventions for annual aberration (Bradley formula + relativistic corrections to order v²/c²).

The maximum annual aberration is ~20.5 arcseconds. Relativistic corrections to the classical Bradley formula amount to ~0.003 arcseconds.

Gravitational light deflection #

Skyfield’s .apparent() method also applies gravitational light deflection by the Sun (maximum ~1.75 arcseconds at the solar limb, falling as 1/sin(θ)). This correction is significant for planets near solar conjunction.

Swiss Ephemeris comparison #

Swiss Ephemeris implements the same corrections (annual aberration + solar gravitational deflection). Both libraries omit diurnal aberration (~0.3 arcseconds maximum), which is below the threshold of astrological significance.

---

5. Planet Center Corrections #

The barycenter problem #

JPL DE440/DE441 provide positions for outer planets as system barycenters – the center of mass of the planet plus all its moons – not the planet body center. The maximum angular offset between barycenter and body center:

For inner planets (Mercury, Venus, Earth, Mars), the barycenter effectively equals the body center because their moons (if any) have negligible mass relative to the planet.

Three-tier correction strategy #

LibEphemeris corrects barycenters to body centers automatically using a three-tier fallback:

Tier 1: SPK-based planet centers (<0.001 arcsec) #

A bundled planet_centers.bsp file (~25 MB) contains precise center-of-body segments for NAIF IDs 599 (Jupiter), 699 (Saturn), 799 (Uranus), 899 (Neptune), and 999 (Pluto). These segments are extracted from JPL satellite ephemerides:

The _SpkCenterTarget class in planets.py adds the SPK offset to the DE440 barycenter position at the retarded time (when light left the planet), ensuring the correction is applied correctly for light-time-corrected observations.

If the date falls outside the SPK coverage, Tier 1 silently falls back to Tier 2.

Tier 2: Analytical satellite theories (sub-arcsecond) #

The _CobCorrectedTarget class computes the barycenter-to-center offset using analytical theories for major satellites. The correction formula:

offset = -Σ(m_i × r_i) / M_total

where m_i is the satellite mass and r_i is the satellite position relative to the planet center.

Jupiter – Lieske E5 theory (Meeus implementation)

Theory for Io, Europa, Ganymede, and Callisto based on Lieske (1998), as presented in Meeus “Astronomical Algorithms” ch. 44.

GM values from JUP365:

Jupiter GM = 126,686,531.9 km³/s² (JUP365).

Saturn – TASS 1.7 theory (Vienne & Duriez 1995)

Full analytical theory for 8 Saturnian satellites, ported from the Stellarium implementation (Johannes Gajdosik, MIT license).

Titan dominates the correction (GM = 8978.137 km³/s², 96% of total Saturnian moon mass). Saturn GM = 37,931,206.23 km³/s² (SAT441).

Neptune – Triton Keplerian model

Simple Keplerian orbit with secular J2 nodal precession, based on NEP097 elements (Jacobson 2009).

Triton GM = 1428.495 km³/s², Neptune GM = 6,835,099.97 km³/s² (NEP097). Mass ratio = 2.09 × 10⁻⁴.

Pluto – Charon two-body Keplerian

Two-body Keplerian solution from PLU060 (Brozovic & Jacobson 2024).

Pluto-Charon is a binary system: the barycenter lies ~2130 km outside Pluto’s center. Charon GM = 106.1 km³/s², Pluto GM = 869.3 km³/s² (PLU060). Mass ratio Charon/(Pluto+Charon) = 0.109.

Uranus: Currently returns zero offset. The total mass ratio of Uranian moons to Uranus is ~1.0 × 10⁻⁴, corresponding to a maximum geocentric offset of ~0.01 arcsec. This is below the precision of most astrological applications.

Tier 3: Raw barycenters (last resort) #

If both SPK and analytical methods fail, the raw barycenter position from DE440/DE441 is used. This path is not reached under normal operation.

Velocity correction #

The velocity component of the COB offset is computed via central difference numerical differentiation with a 1-second step:

v_offset = [offset(t + 0.5s) - offset(t - 0.5s)] / 1s

Swiss Ephemeris comparison #

Standard Swiss Ephemeris returns system barycenters for outer planets. The SEFLG_CENTER_BODY flag (a newer, less commonly used feature) enables planet center positions, but requires additional satellite ephemeris files. LibEphemeris applies the correction transparently to all calculations, achieving better default precision for Jupiter, Saturn, Neptune, and Pluto without requiring any user configuration.

---

6. Velocity Computation #

Central difference method #

LibEphemeris computes all velocities via numerical differentiation using the central difference formula:

dp/dt = [p(t + dt) - p(t - dt)] / (2 · dt)

The central difference method is O(h²) accurate, meaning halving the step size reduces the error by a factor of 4.

Swiss Ephemeris comparison #

Swiss Ephemeris computes velocities analytically by differentiating the Chebyshev polynomial representation of the JPL ephemeris. This avoids the O(h²) truncation error of numerical differentiation but requires maintaining separate derivative code.

The practical difference is <0.001°/day for all planets. For the Moon, speed differences of up to ~0.01°/day have been measured, primarily because the numerical method samples the position function at different points than the analytical derivative.

---

7. True Ecliptic Coordinates #

From ICRS to ecliptic of date #

The full pipeline from JPL ephemeris to ecliptic longitude:

1. JPL state vector (ICRS Cartesian, barycentric or geocentric)
2. Light-time correction (iterative, typically 3 Newton iterations)
3. COB correction (barycenter → planet center, Tier 1/2/3)
4. Apparent position via Skyfield: annual aberration + gravitational deflection
5. Ecliptic of date via frame_latlon(ecliptic_frame): applies combined IAU 2006 precession + IAU 2006/2000A nutation matrix (erfa.pnm06a()) to rotate from ICRS to true ecliptic of date

For J2000 ecliptic (SEFLG_J2000), step 5 uses a fixed rotation by the J2000 obliquity (23°26’21.406") without precession or nutation.

Mean obliquity of the ecliptic #

IAU 2006 polynomial (Capitaine et al. 2003):

ε₀ = 84381.406" − 46.836769"·T − 0.0001831"·T² + 0.00200340"·T³
     − 0.000000576"·T⁴ − 0.0000000434"·T⁵

where T is Julian centuries from J2000.0.

---

8. House Calculations #

Sidereal time #

Houses require Greenwich Apparent Sidereal Time (GAST). LibEphemeris uses Skyfield’s t.gast, which implements the IAU SOFA algorithm:

1. Earth Rotation Angle (ERA) from UT1 (IERS 2003 conventions)
2. Greenwich Mean Sidereal Time (GMST) via ERA + equation of origins
3. Equation of equinoxes: Δψ · cos(ε) (nutation in RA from IAU 2006/2000A)
4. GAST = GMST + equation of equinoxes

Precision: ~0.001 seconds of time (~0.015 arcseconds in hour angle).

True obliquity #

Houses use the true obliquity (mean obliquity + nutation in obliquity) from erfa.obl06() + erfa.nut06a(). This is the same IAU 2006/2000A model used for planet calculations.

ARMC #

ARMC = (GAST × 15°/h + geographic_longitude) mod 360°

Supported systems (24) #

All major house systems are implemented with the same spherical trigonometry as Swiss Ephemeris:

P Placidus, K Koch, O Porphyry, R Regiomontanus, C Campanus, E Equal (Asc), A/D Equal (MC), W Whole Sign, M Morinus, B Alcabitius, T Polich-Page/Topocentric, U Krusinski, G Gauquelin (36-sector), V Vehlow, X Meridian, H Horizontal, F Carter, S Sripati, L Pullen SD, Q Pullen SR, N Natural Gradient, Y APC, I/i Sunshine.

Convergence tolerance #

Iterative systems (Placidus, Koch) use a convergence threshold of 10⁻⁷ degrees (~0.00036 arcseconds).

Polar latitude behavior #

Above the polar circle (~66.56° = 90° − obliquity), Placidus and Koch are geometrically undefined because some ecliptic points never rise or set. LibEphemeris raises PolarCircleError with the option to fall back to Porphyry via swe_houses_with_fallback().

Measured precision vs Swiss Ephemeris #

---

9. Lunar Points #

True Node (osculating lunar node) #

The True Node is where the Moon’s instantaneous orbital plane intersects the ecliptic. LibEphemeris uses a two-stage approach.

Stage 1: Geometric osculating node from JPL DE440

1. Get Moon’s geocentric position r and velocity v from JPL DE440 (~1 milliarcsecond source precision)
2. Compute angular momentum vector: h = r × v
3. This vector is perpendicular to the instantaneous orbital plane
4. Find intersection with the ecliptic: Ω = atan2(h_x, −h_y)
5. Apply IAU 2006 precession (J2000 → date)
6. Apply IAU 2006/2000A nutation (1365 terms)

This computes exactly what the True Node is by definition: the intersection of the orbital plane with the ecliptic. Deriving the node directly from the state vectors avoids the approximation errors inherent in analytical series — the geometric construction is exact by definition.

ELP2000-82B perturbation series (available but not applied)

The codebase contains a comprehensive ELP2000-82B perturbation series (~170 terms, ~900 lines) organized into the following categories:

The Earth eccentricity factor E = 1.0 − 0.002516·T − 0.0000074·T² is applied to Sun-dependent terms per Meeus convention.

Note: These perturbation corrections are not currently applied to the True Node calculation. Investigation revealed that the ELP2000-82B series was designed for the mean lunar node, not the geometric node derived from state vectors via h = r × v. Applying the series to the geometric node produced errors of tens of degrees, confirming the two approaches are incompatible. The geometric method from Stage 1 is used alone. The residual vs Swiss Ephemeris (~8.9 arcsec mean, ~0.14° max) reflects the fundamental methodological difference. See Precision History for the full investigation record.

Mean Node #

Meeus polynomial for the mean ascending node longitude, extended with T⁴ and T⁵ corrections from Chapront et al. (2002) and Simon et al. (1994).

Mean Lilith (Black Moon) #

Mean longitude of the lunar apogee, computed from Meeus polynomials (ch. 50). Includes latitude computation. Velocity via central difference with 0.5-day step.

True Lilith (osculating apogee) #

Computed from JPL DE440 Moon state vectors via orbital mechanics: the eccentricity vector e is derived from position and velocity, and the apogee direction points from the focus along e.

Interpolated Apogee and Perigee #

Uses the Moshier analytical method: ELP2000-82B perturbation series (~50 harmonic terms) fitted to DE404 over a 7000-year span (Moshier 1992). Removes the spurious ~30° oscillations present in the osculating apsides.

Meeus polynomial validity ranges #

| Range | |T| (centuries) | Accuracy | |-------|---------------|----------| | Optimal | <2 (~±200 years) | <0.001° | | Valid | <10 (~±1000 years) | <0.01° | | Maximum | <20 (~±2000 years) | Significant degradation |

Fundamental arguments include T⁵ corrections from Chapront et al. (2002).

Measured precision vs Swiss Ephemeris #

J2000 frame (SEFLG_J2000) for lunar bodies: LibEphemeris is more accurate than Swiss Ephemeris for J2000 frame transformations of analytically-computed bodies. At J2000.0 epoch, tropical and J2000 ecliptic coordinates are identical by definition (zero precession). LibEphemeris correctly returns zero shift; Swiss Ephemeris applies a spurious ~14" offset. Verified independently against astropy/ERFA.

---

10. Delta T (TT − UT1) #

Model #

LibEphemeris uses the Stephenson, Morrison & Hohenkerk (2016) Delta T model via Skyfield:

IERS observed Delta T #

When enabled, LibEphemeris uses observed ΔT values from the International Earth Rotation and Reference Systems Service for recent dates (1973–present), achieving ~0.1 second precision.

from libephemeris import set_iers_delta_t_enabled, download_delta_t_data
download_delta_t_data()
set_iers_delta_t_enabled(True)

Swiss Ephemeris comparison #

Swiss Ephemeris uses Espenak & Meeus (2006) polynomials for historical Delta T. The Stephenson et al. (2016) model used by LibEphemeris is more recent and generally considered more accurate for dates before 1600 CE, where direct observations are sparse.

For modern dates (1900–2100), both implementations agree to within ~1 second.

Typical Delta T values #

---

11. Fixed Stars #

Star catalog #

116 stars from the Hipparcos catalog (ESA 1997), with proper motions updated to the van Leeuwen 2007 new Hipparcos reduction (A&A 474, 653-664). The catalog covers all bright and astrologically significant stars: the 4 Royal Stars, Behenian stars, Pleiades cluster, Hyades, and full zodiacal constellation coverage.

Independent verification: All stars cross-checked against SIMBAD J2000 positions. Principal stars verified to < 0.02" against SIMBAD. Two catalog bugs found and fixed during audit (Algedi wrong component, Asellus Borealis wrong HIP number). See swisseph-comparison.md §6.6 for full details.

Proper motion #

Rigorous space motion propagation from Hipparcos Vol. 1, Section 1.5.5, with second-order Taylor term for celestial sphere curvature:

correction = −0.5 · |V|² · P · t²

Precision: <0.01 arcsec over ±100 years; <1 arcsec over ±500 years.

Position pipeline #

1. Proper motion propagation (J2000 → date)
2. Create Skyfield Star object with propagated RA/Dec
3. Apparent position via observer.at(t).observe(star).apparent() (aberration + gravitational deflection)
4. Ecliptic coordinates via frame_latlon(ecliptic_frame) (IAU 2006 precession + IAU 2006/2000A nutation)

Swiss Ephemeris comparison #

Swiss Ephemeris uses a larger catalog (~1000+ stars from its own bundled star catalog). Both use Hipparcos data; LibEphemeris uses the updated van Leeuwen 2007 proper motions while Swiss Ephemeris uses original 1997 values. Star positions agree to < 0.51" for all 101 comparable stars. Five stars resolve to different physical components due to different IAU WGSN name conventions (Menkar, Algedi, Algieba, Albireo, Almach).

All meaningful SEFLG flags are now supported for fixed star calculations: SEFLG_SIDEREAL, SEFLG_J2000, SEFLG_NONUT, SEFLG_XYZ, SEFLG_RADIANS, SEFLG_TRUEPOS, SEFLG_MOSEPH, SEFLG_SPEED3, SEFLG_TOPOCTR.

---

12. Ayanamsha (Sidereal Modes) #

43 ayanamsha systems are supported, matching the full Swiss Ephemeris set.

Formula-based ayanamshas #

Star-based ayanamshas #

Star-based ayanamshas anchor the sidereal zodiac to a specific fixed star. The slightly higher differences reflect different proper motion and precession models:

The IAU 2006 precession model (used by LibEphemeris) is more accurate than the older Lieske (1977) model for computing the precession of the equinox, which directly affects ayanamsha values.

---

13. Eclipses and Occultations #

Solar eclipses #

Calculated using Besselian elements with the full JPL DE ephemeris for Sun and Moon positions. Contact times (C1–C4), path width, central line coordinates, magnitude, and obscuration are computed.

Lunar eclipses #

Full implementation including umbral and penumbral contact times (P1, U1, U2, U3, U4, P4), umbral/penumbral magnitude, gamma parameter, and duration.

Saros and Inex series #

Saros and Inex series numbers are computed from eclipse-to-eclipse relationships using the Saros period (6585.32 days) and Inex period (10571.95 days).

---

14. Rise, Set, and Transit #

Computed using the Bennett (1982) atmospheric refraction formula with configurable atmospheric conditions (pressure, temperature).

---

15. Heliacal Events #

Schaefer (1990) atmospheric visibility model with:

1. Atmospheric extinction: Rayleigh scattering + aerosol + ozone + water vapor
2. Twilight sky brightness: gradient model with moonlight contribution
3. Ptolemaic visibility thresholds: arcus visionis values
4. Contrast threshold: Schaefer model with configurable observer skill levels

Timing precision: <1 day for heliacal rising/setting events.

---

16. Planetary Positions – Measured Precision #

Tested against Swiss Ephemeris at 100+ random dates within DE440 range (1550–2650 CE):

Longitude #

All differences are sub-arcsecond except the Moon (~3 arcseconds), which reflects the different nutation models and COB correction pipelines between the two libraries. Both values are well within the precision of the underlying DE ephemeris.

Latitude #

Velocity #

Source of measured differences #

The differences between LibEphemeris and Swiss Ephemeris are not errors in either library. They arise from intentional methodological choices:

---

17. Photometric Models (Phenomena) #

LibEphemeris implements swe_pheno_ut() / swe_pheno() for computing observable planetary phenomena: phase angle, phase (illuminated fraction), elongation, apparent diameter, and visual magnitude. The photometric models use peer-reviewed formulas from the astronomical literature, validated against astropy and the Astronomical Almanac.

Phase Angle #

The phase angle (Sun-Body-Earth angle) is computed using 3D vector geometry (dot product of geocentric position vectors), which is numerically stable for all configurations including the extremely elongated Sun-Moon-Earth triangle. This avoids the numerical instability of the law-of-cosines approach for bodies at very different distances.

The 4–24" differences for planets arise from the different underlying ephemerides (JPL DE440 vs DE431) and are not correctable.

Visual Magnitude #

LibEphemeris uses Mallama & Hilton (2018) formulas for all planets, published in The Astronomical Journal and adopted by the Astronomical Almanac. These are the current standard for planetary magnitude computation.

Neptune secular brightness variation #

Neptune’s albedo has been increasing since the 1980s due to seasonal atmospheric changes over its 165-year orbital period. LibEphemeris models this with a secular V(1,0) that transitions linearly from -6.89 (pre-1980) to -7.00 (by J2000.0), matching observational data from Lockwood & Thompson (1991) and Sromovsky et al. (2003). This produces exact magnitude agreement across all epochs.

Moon thin crescent limitation #

For phase angles > 165 degrees (very thin crescents near new moon), the Astronomical Almanac quartic formula diverges from observations. The mean error across all phases is ~0.03 mag; for alpha > 165 degrees it can reach 0.2 mag. This is an inherent limitation of the quartic phase model and affects a narrow range near new moon that is astronomically insignificant (the Moon is unobservable at these phases).

Apparent Diameter #

LibEphemeris uses IAU 2015 equatorial radii for all bodies, which is the standard adopted by the Astronomical Almanac for computing apparent angular diameters.

The equatorial radius is the correct choice for apparent diameter because it represents the maximum cross-section as seen from an external observer. The mean volumetric radius used by Swiss Ephemeris produces systematically smaller diameters (2–3.5% for giant planets). The IAU equatorial values are the standard used in the Astronomical Almanac and professional observatory software.

Swiss Ephemeris comparison #

The differences in pheno_ut between LibEphemeris and Swiss Ephemeris fall into three categories:

1. Irreducible ephemeris differences (phase angle, elongation): 4–24 arcseconds for planets, caused by DE440 vs DE431. These cannot be eliminated and represent the improved accuracy of the newer ephemeris.

2. Intentional methodology differences (apparent diameter): 2–3.5% for giant planets, caused by using IAU equatorial radii vs mean volumetric radii. The IAU values are the professional standard.

3. Equivalent precision (magnitude): < 0.01 mag for all planets except Moon thin crescents and Pluto. Both libraries use similar Mallama 2018 formulas; residual differences are from distance calculations via different ephemerides.

---

18. Minor Bodies #

Strict precision mode (default) #

For major asteroids with strongly perturbed orbits (Chiron, Ceres, Pallas, Juno, Vesta), LibEphemeris requires SPK kernels by default. Simple Keplerian propagation can produce errors of 1–10 degrees for these bodies, which is unacceptable for astrological use.

eph.set_auto_spk_download(True)  # Recommended: automatic SPK from JPL Horizons

SPK kernel precision #

With SPK kernels (downloaded from JPL Horizons), all minor body calculations achieve sub-arcsecond precision matching JPL Horizons exactly.

Trans-Neptunian Objects #

TNOs use Keplerian elements with first-order secular perturbations from Jupiter, Saturn, Uranus, and Neptune (Laplace-Lagrange theory). Typical accuracy: <10° over 50-year spans. For research-grade TNO work, use SPK kernels.

---

19. Thread-safe Context API #

Each EphemerisContext instance has its own isolated state while sharing the expensive ephemeris data across instances. The _CONTEXT_SWAP_LOCK (RLock) ensures thread safety during state operations.

Memory overhead per context: ~1 KB. Ephemeris files (DE440: ~119 MB) are loaded once and shared.

---

20. Comprehensive Precision Audit #

A deep cross-validation audit was performed across all calculation modes and coordinate systems. This section summarizes the findings.

Planetary positions at extreme dates #

Tested all 10 major bodies (Sun through Pluto) at dates spanning 1551–2649 CE (the full DE440 range).

The divergence at extreme dates is driven by Delta-T model differences (Stephenson et al. 2016 vs Espenak & Meeus 2006). The Moon’s rapid motion (~13°/day) amplifies any time-base discrepancy. Outer planets are insensitive due to slow motion and remain within tolerance at all dates.

Fixed stars #

Tested 116 stars at 3 epochs (J2000, J2025, J2100). Proper motions updated to van Leeuwen 2007 (new Hipparcos reduction). All stars independently cross-checked against SIMBAD.

Remaining sub-arcsecond differences are from Skyfield vs Swiss Ephemeris precession/nutation pipeline differences. High proper motion stars (Sirius, Rigil Kentaurus) show largest differences due to annual parallax (not modeled).

House cusps at extreme latitudes #

Tested 7 house systems at latitudes 0°–89°, including the arctic circle (66.56°).

Velocities and speed flags #

Tested all bodies with FLG_SPEED, FLG_SPEED|FLG_EQUATORIAL, and FLG_SPEED|FLG_NONUT at 20 dates.

Heliocentric and barycentric modes #

Note: Barycentric Sun shows large angular differences (~100"+) at dates when the Sun is near the Solar System Barycenter (distance ~0.001 AU). This is a geometric amplification effect, not a precision issue – the Cartesian positions agree to <0.000001 AU.

Sidereal mode and ayanamshas #

Tested Lahiri, Raman, Krishnamurti, and Fagan/Bradley ayanamshas.

Delta-T #

LibEphemeris uses the more recent Stephenson, Morrison & Hohenkerk (2016) model. For the modern era where observed data exists, both libraries agree to sub-second precision.

Ecliptic obliquity and nutation #

Sub-milliarcsecond agreement across all tested dates (1800–2200). Both libraries implement IAU 2006/2000A correctly.

SEFLG_MOSEPH behavior #

When SEFLG_MOSEPH (flag value 4) is passed, Swiss Ephemeris falls back to the Moshier semi-analytical ephemeris. LibEphemeris accepts this flag for API compatibility but always uses JPL DE440. The resulting differences (typically <0.2" for modern dates) reflect the lower precision of the Moshier ephemeris, not a bug in either library.

---

See Also #

• Swiss Ephemeris Comparison — Exhaustive comparison between libephemeris and pyswisseph, including measured precision tables, known differences with detailed explanations, bugs found and fixed, and API signature differences. Based on 1,619 automated tests covering all 87 swe_* functions.

---

References #

1. Park, R.S. et al. (2021). “The JPL Planetary and Lunar Ephemerides DE440 and DE441.” Astronomical Journal, 161(3), 105.
2. Capitaine, N. et al. (2003). “Expressions for IAU 2000 precession quantities.” Astronomy & Astrophysics, 412, 567-586.
3. Mathews, P.M. et al. (2002). “Modeling of nutation-precession: New nutation series for nonrigid Earth.” Journal of Geophysical Research, 107(B4).
4. Capitaine, N. et al. (2005). “IAU 2006 precession.” Highlights of Astronomy, 14, 474-475.
5. Lieske, J.H. (1998). “Galilean Satellites of Jupiter. Theory E5.” Astronomy & Astrophysics Supplement, 129, 205-217.
6. Vienne, A. & Duriez, L. (1995). “TASS1.6: Ephemerides of the major Saturnian satellites.” Astronomy & Astrophysics, 297, 588-605.
7. Jacobson, R.A. (2009). “The orbits of the Neptunian satellites.” Astronomical Journal, 137, 4322-4329.
8. Brozovic, M. & Jacobson, R.A. (2024). “The orbits of the Pluto system.” Planetary Science Journal.
9. Stephenson, F.R., Morrison, L.V. & Hohenkerk, C.Y. (2016). “Measurement of the Earth’s rotation: 720 BC to AD 2015.” Proceedings of the Royal Society A, 472, 20160404.
10. Meeus, J. (1998). Astronomical Algorithms, 2nd edition. Willmann-Bell.
11. Moshier, S.L. (1992). “Comparison of a 7000-year lunar ephemeris with analytical theory.” Astronomy & Astrophysics, 262, 613-616.
12. Schaefer, B.E. (1990). “Telescopic limiting magnitudes.” Publications of the Astronomical Society of the Pacific, 102, 212-229.
13. IERS Conventions (2010). IERS Technical Note No. 36, ed. Petit, G. & Luzum, B.
14. ESA (1997). The Hipparcos and Tycho Catalogues. ESA SP-1200.
15. Mallama, A. & Hilton, J.L. (2018). “Computing Apparent Planetary Magnitudes for The Astronomical Almanac.” Astronomy and Computing, 25, 10-24.
16. Lockwood, G.W. & Thompson, D.T. (1991). “Solar cycle chromospheric variations and photometric variability of Neptune.” Nature, 349, 593-594.
17. Sromovsky, L.A. et al. (2003). “Episodic bright and dark spots on Uranus.” Icarus, 163, 256-261.
18. IAU (2015). “IAU 2015 Resolution B3: Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties.” IAU General Assembly, Honolulu.