Glossary

Acronyms and conventions that appear across the empyrean docs. Linked from the cookbook pages where the term first shows up.

Astrodynamics

STM

State Transition Matrix $\Phi(t, t_0) = \partial \mathbf{x}(t) / \partial \mathbf{x}_0$. 6×6 in this codebase. Maps state-space perturbations from the initial epoch $t_0$ to a target time $t$. Linear-order covariance map: $\Sigma_t = \Phi \Sigma_0 \Phi^\top$. See :class:~empyrean.StateSensitivities.

STT

State Transition Tensor — the second-order analogue of the STM, $\Psi_{k,ab}(t, t_0) = \partial^2 x_k / \partial x_{0,a}\, \partial x_{0,b}$. 6×6×6. Required for Park-Scheeres second-order Gaussian covariance and $\kappa$. See :class:~empyrean.StateSensitivities.

IOD

Initial Orbit Determination — the first-pass orbit fit from sparse astrometry that seeds differential correction. empyrean uses Herget’s method (range-search variant) by default.

DC

Differential Correction — the iterative least-squares orbit fit that refines the IOD seed with the full astrometric arc.

CA

Close Approach — a local minimum in the planet-relative distance along a propagated trajectory. Detected per-body by villeneuve’s event-detection layer.

VA

Virtual Asteroid — a sample drawn from the orbit-uncertainty distribution. A VA sample is the population the :class:~empyrean.MonteCarlo and :class:~empyrean.SigmaPoint uncertainty methods sweep across.

IP

Impact Probability — the probability that a sampled or analytically propagated state vector intersects an Earth-equivalent target. Reported by :func:~empyrean.compute_impact_probabilities under multiple uncertainty methods.

B-plane

The encounter plane perpendicular to the hyperbolic excess velocity vector at a planetary close approach. Coordinates $(B \cdot T,\, B \cdot R)$ in the Öpik / Valsecchi frame are the canonical reporting convention.

Keyhole

A small region in the B-plane that, if traversed, leads to an impact at the next encounter (resonant return). Keyhole detection feeds into multi-encounter IP rolldowns.

κ (kappa)

Local nonlinearity diagnostic on a propagated chain — a scalar measure of how much the second-order STT contribution would shift the propagated mean relative to the linear map at each output epoch. Useful as a qualitative flag for which epochs are safely-linear vs need a sample-based check. See :meth:~empyrean.StateSensitivities.kappa.

EIH

Einstein-Infeld-Hoffmann — the post-Newtonian general-relativity correction to N-body equations of motion. Included in ForceModelTier.Basic and above.

J2-J4

The first three Earth gravitational zonal harmonic coefficients. Included in ForceModelTier.Standard.

Marsden non-grav

The Marsden / Sekanina non-gravitational force model — radial, transverse, and normal accelerations $(A_1, A_2, A_3)$ modulated by a heliocentric distance-dependent function $g(r)$. Used to model Yarkovsky for asteroids and outgassing for comets. See :class:~empyrean.NonGravParams.

Yarkovsky effect

Anisotropic thermal re-radiation that produces a small but measurable secular force on the orbit of a small body. Modelled via the Marsden $A_2$ coefficient.

ADES

Astrometry Data Exchange Standard — the MPC-blessed astrometric observation format. Read with :func:~empyrean.read_ades; query with :func:~empyrean.query_observations.

PSV

Pipe-Separated Values — the canonical ADES file format on disk.

Reference frames and bodies

ICRF

International Celestial Reference Frame — the fundamental quasi-inertial reference frame for astronomy. Equivalent to J2000 equatorial coordinates at the milliarcsecond level.

EclipticJ2000

Mean ecliptic and equinox of J2000.0 — the integration frame in villeneuve / empyrean. The default frame on propagation output.

ITRF93

International Terrestrial Reference Frame (1993 realisation) — Earth-fixed, rotates with the Earth. Used for ground-station coordinate vectors.

NAIF ID

JPL’s integer identifier for Solar System bodies (e.g. 10 = Sun, 399 = Earth, 301 = Moon). Used in the :class:~empyrean.Origin enum and body_filter_naif arguments.

SSB

Solar System Barycenter — NAIF body 0. The integration origin in villeneuve / empyrean.

SPK

Spacecraft and Planetary Kernel — JPL’s binary file format for ephemerides. See :doc:../cookbook/data-setup.

BPC

Binary PCK (planetary-constants kernel) — the kernel format for Earth-orientation, Moon-orientation, and other body-fixed-frame rotations.

GM

Gravitational parameter $\mu = G M$. The gm_de440.tpc text-PCK file ships bundled in the wheel.

DE440

JPL Development Ephemeris 440 — the planetary ephemeris empyrean integrates against. Pulled in via the naif-de440 PyPI package.

SB441

JPL’s small-body mass perturber ephemeris family — released paired with DE441 but used here alongside DE440. The 16-asteroid “N16” cut is what ForceModelTier.Standard integrates against.

EOP

Earth Orientation Parameters — drives ITRF93 ↔ ICRF and the Earth-fixed surface-station vectors. Pulled in via the naif-eop-* PyPI packages.

Time scales

MJD

Modified Julian Date — JD - 2400000.5. The convention used everywhere in empyrean for raw time-as-float values.

TDB

Barycentric Dynamical Time — the time scale of the integration and the default scale on every Epochs / MJD value at the API boundary unless explicitly converted.

UTC

Coordinated Universal Time — leap-second-aware civil time. Convert in / out via :meth:~empyrean.Epochs.to_utc / :meth:~empyrean.Epochs.from_iso.

TT

Terrestrial Time — TDB to within milliseconds for most uses; the Earth-orientation kernels (BPCs) are built on TT.

TAI

International Atomic Time — TAI = UTC + leap seconds.

Observation models

Vereš et al. weighting

The standard astrometric uncertainty model for MPC observations (Vereš et al. 2017). Combines a per-station floor with a per-catalog systematic. Driven by :class:~empyrean.ODConfig defaults.

Cook’s distance

Per-observation influence diagnostic — measures how much the fit moves when a single observation is removed. Reported in :class:~empyrean.ObservationResults. $D_i \gtrsim 1$ is typically a flag for review.

Leverage

Per-observation diagonal of the projection matrix — bounded in $[0, 2]$. High-leverage observations sit at the edges of the arc and disproportionately constrain the fit; their residuals can be misleadingly small even when they’re driving the solution.

Adaptive rejection

The Carpino / Milani / Chesley 2003 rejection scheme — uses a $\chi^2$ threshold modulated by per-observation information loss. Default in :class:~empyrean.ODConfig.