CODE Catalogue: Comet Orbit Dynamics

• CODE Catalogue is a curated dynamical database of long-period comets, providing five orbital evolution snapshots and detailed uncertainty estimates through Monte Carlo simulations.
• It employs a uniform orbit determination method with both gravitational and non-gravitational models, carefully capturing the impacts of water- and CO-sublimation forces.
• The catalogue supports comprehensive studies on comet origins, dynamical status, and the effects of Galactic tide plus stellar perturbations on Oort Cloud objects.

Searching arXiv for the cited catalogue papers and the cometary CODE updates to ground the article in the literature. CODE, the Catalogue of Cometary Orbits and their Dynamical Evolution, is a curated dynamical database of long-period comets (LPCs), especially Oort Cloud and Oort spike objects, designed to provide not only osculating orbits but also the original, future, previous, and next stages of a comet’s trajectory together with uncertainty information and dynamical classification (Królikowska et al., 2020). Its distinguishing feature is that it treats comet cataloguing as a long-baseline orbital-evolution problem rather than as a static list of orbital elements: the catalogue links a comet’s observed apparition to its inferred motion before planetary entry and after planetary exit, and in later versions it does so in both a Galactic-tide-only model and a Galactic-plus-stellar-perturber model (Królikowska et al., 2023, Dybczyński et al., 28 Aug 2025).

1. Historical development and scope

The original 2020 release announced a catalogue containing data for 277 LPCs, described as almost 300 LPCs discovered before 2018, with emphasis on comets having original semimajor axis greater than 10,000 au for a purely gravitational orbit; these were identified as Oort spike comets (Królikowska et al., 2020). The catalogue was intended to be nearly complete for LPCs discovered in 1885–2017 satisfying that criterion, apart from a small set of about twenty Oort-spike comets with $q<3.1$ au discovered in 2013–2017 that were still absent at that stage (Królikowska et al., 2020).

The 2023 update described a broader and nearly complete sample of Oort spike comets discovered through January 2021. At that point, CODE contained 312 LPCs with 766 sets of orbits, including 258 Oort Cloud comets, and explicitly added the complete sample of 29 Oort Cloud comets discovered in 2018, 2019, 2020, and January 2021, plus 4 other LPCs from the same period (Królikowska et al., 2023).

The 2025 update expanded the database further to 983 orbital solutions for 369 comets with full uncertainty estimates and dynamical classifications. It stated that the catalogue covers nearly all comets with original semi-major axes exceeding 10,000 au and discovered before 2022, as well as all LPCs discovered beyond 10 au from the Sun during this period, and over 80% of the known LPCs with perihelion distances beyond 7 au (Dybczyński et al., 28 Aug 2025).

Version	Scope stated in the paper	Size
2020 (Królikowska et al., 2020)	LPCs discovered before 2018; nearly complete for 1885–2017 Oort-spike sample	277 LPCs
2023 (Królikowska et al., 2023)	Nearly complete sample of Oort spike comets through January 2021	312 LPCs; 766 orbit sets
2025 (Dybczyński et al., 28 Aug 2025)	Nearly all relevant pre-2022 Oort-Cloud/LPC cases, plus all LPCs discovered beyond 10 au	369 comets; 983 solutions

This progression shows that CODE evolved from a standardized Oort-spike catalogue into a more general-purpose, dynamically homogeneous LPC database. A plausible implication is that its scientific role shifted from cataloguing a specific dynamical population to supporting broader inference on comet origin, dynamical age, and outer-Solar-System structure.

2. Orbital architecture and the five-stage representation

A central design feature of CODE is that it stores each comet in five snapshots of orbital evolution: previous, original, observed, future, and next (Królikowska et al., 2020). These five stages are arranged so as to cover three successive passages through the perihelion: the perihelion before the observed apparition, the observed perihelion, and the subsequent perihelion.

In the 2020 definition, the observed snapshot is the osculating heliocentric orbit determined from positional observations near the center of the observed data arc, typically near perihelion. The original and future snapshots are obtained by propagating the motion to 250 au from the Sun, where planetary perturbations are negligible and the orbit is considered in the barycentric frame. The previous and next snapshots are obtained by propagating farther backward and forward under Galactic and stellar perturbations, to the previous and next perihelion respectively; for hyperbolic or extremely elongated cases, the stopping point is instead the escape limit of 120,000 au (Królikowska et al., 2020).

Stage	Meaning in CODE	Dynamical context
Previous	Orbit at previous perihelion, or at 120,000 au in special cases	Long-term backward evolution
Original	Orbit at 250 au before strong planetary perturbations	Barycentric pre-entry state
Observed	Osculating orbit from the observed arc	Near-apparition state
Future	Orbit at 250 au after planetary perturbations	Barycentric post-exit state
Next	Orbit at next perihelion, or at 120,000 au in special cases	Long-term forward evolution

From the 2023 update onward, the previous and next stages are supplied in two variants: one including the full Galactic tide only, and another including the full Galactic tide + all known stellar perturbers (Królikowska et al., 2023). The 2025 update states that these are exposed in the interface as previous, next and previous_g, next_g (Dybczyński et al., 28 Aug 2025). This dual representation is methodologically important because it isolates the contribution of stellar encounters to long-term orbital history.

3. Orbit determination, nongravitational modeling, and multiple solutions

CODE uses a uniform orbit-determination procedure for its osculating solutions, with consistent data-selection and weighting choices emphasized as essential for statistical studies of the Oort spike maximum, that is, the distribution of original reciprocal semimajor axes $1/a$ (Królikowska et al., 2020). The catalogue is not limited to one orbit per comet. For many objects it contains several acceptable solutions, differing by force model, data subset, or both (Królikowska et al., 2020, Królikowska et al., 2023).

For about one third of the LPCs in the 2020 catalogue, detectable non-gravitational (NG) accelerations were found, and in the subsample with $q<3.1$ au NG solutions were found for more than 60% of objects (Królikowska et al., 2020). The 2025 update similarly states that more than 40% of all LPCs in CODE show detectable residual trends, rising to over 60% for small-perihelion comets with $q<3.35$ au (Dybczyński et al., 28 Aug 2025). When NG effects are significant, CODE stores both an NG solution and, for comparison, a purely gravitational solution.

The standard NG acceleration model follows the Marsden et al. formalism,

$$F_i = A_i\,g(r), \qquad A_i=\mathrm{const\ for}\ i=1,2,3,$$

with

$g(r)=\alpha (r/r_0)^m\left[1+(r/r_0)^n\right]^k,$

where $F_1,F_2,F_3$ are the radial, transverse, and normal components of the NG acceleration (Królikowska et al., 2020). CODE uses both a water-sublimation law and a CO-sublimation law, and in some cases a more specialized force model or a fourth NG parameter representing a time shift of the $g(r)$ maximum relative to perihelion, allowing asymmetric NG solutions (Królikowska et al., 2020). The 2023 update adds that CODE may also use subsolar-point water sublimation, again in symmetric or asymmetric form (Królikowska et al., 2023).

Multiple solutions are also generated from different observational subsets: the entire data arc, pre-perihelion data only, post-perihelion data only, or sometimes only data at large heliocentric distance (Królikowska et al., 2020, Królikowska et al., 2023). This is especially relevant when outbursts, splitting, or disintegration make a single constant-NG model inadequate. The 2023 paper is explicit that the preferred orbit is ordinarily the NG orbit, or the GR orbit if NG effects are not detectable, and that it is derived from the longest possible data arc, except in unusual cases such as disintegrating comets (Królikowska et al., 2023). The same paper also stresses that the preferred orbit is not always best for dynamical-history studies. This is a substantive methodological caution rather than a minor implementation detail.

4. Monte Carlo propagation, perturbation models, and uncertainty reporting

To construct the original and future orbits, CODE generates a swarm of 5001 virtual comets (VCs), including the nominal orbit, by a Monte Carlo method and integrates them backward and forward until each reaches 250 au (Królikowska et al., 2020). For the previous and next stages, the same swarms are propagated farther under the action of the Galactic potential and perturbations from nearby stars (Królikowska et al., 2020). The 2025 update reiterates that CODE uses full Monte Carlo virtual-comet swarms and notes that dynamical classification propagates the nominal orbit together with 5000 additional VCs (Dybczyński et al., 28 Aug 2025).

In the 2020 release, the stellar-perturber model used a list of 643 stars or stellar systems that may pass within 4 pc of the Sun during the relevant time intervals (Królikowska et al., 2020). The 2023 and 2025 updates replaced this with the StePPeD database of potential stellar perturbers, built from Gaia-era astrometry and radial velocities; the 2023 paper identifies the latest version it mentions as StePPeD v3.3, released on 2023 June 28 (Królikowska et al., 2023). The introduction of separate Galactic-only and Galactic-plus-stellar variants reflects the authors’ judgment that stellar-encounter data remain materially uncertain.

CODE also formalizes the distinction between returning, escaping, and hyperbolic virtual comets. For hyperbolic or extremely elongated elliptic orbits, 120,000 au is adopted as an escape limit; VCs not going beyond this are counted as returning, while those that do are escaping, with hyperbolic cases counted separately (Królikowska et al., 2020). The catalogue records, for previous and next orbits, the number of returning $[R]$, escaping $[E]$, and hyperbolic $1/a$0 VCs, which group contains the nominal orbit, and statistics of reciprocal semimajor axis, aphelion distance, and time interval to perihelion (Królikowska et al., 2020).

The uncertainty summaries are distribution-aware. In the 2020 design, if a parameter distribution is close to Gaussian, CODE reports the mean and standard deviation; otherwise it reports the 10th, 50th (median), and 90th percentiles (Królikowska et al., 2020). The 2023 update places stronger emphasis on the decile representation, noting that previous/next-orbit distributions are often non-Gaussian and are therefore given as the 10th percentile, median, and 90th percentile (Królikowska et al., 2023).

5. Dynamical status, perihelion history, and the role of stellar perturbations

The scientific core of CODE is the inference of a comet’s dynamical status from its earlier orbital history. In the 2020 catalogue, the previous-perihelion summary includes the fraction of VCs with perihelion distance smaller than 10 au, between 10 and 20 au, and greater than 20 au; for the previous orbit, these bins are interpreted respectively as dynamically old, uncertain status, and dynamically new (Królikowska et al., 2020). The 2025 update makes the same logic explicit as thresholds on $1/a$1:

$1/a$2

$1/a$3

$1/a$4

(Dybczyński et al., 28 Aug 2025).

A recurring conclusion of the later papers is that $1/a$5 alone is not enough to determine whether a comet is dynamically new (Dybczyński et al., 28 Aug 2025). The 2025 update proposes a better approximate proxy only when $1/a$6 cannot be computed: use

$1/a$7

as a rough criterion for a dynamically new comet, provided stellar perturbations are included (Dybczyński et al., 28 Aug 2025). The same paper explicitly cautions against relying on the older $1/a$8 au$1/a$9 cutoff as a universal boundary.

The importance of stellar perturbations is one of the strongest quantitative results in the 2025 update. For 222 comets with fully returning swarms in both force models, the median $q<3.1$0 is 6.9 au without stars and 59.0 au with stars (Dybczyński et al., 28 Aug 2025). For the subset with $q<3.1$1 au$q<3.1$2, comprising 118 comets, the median $q<3.1$3 changes from 12.7 au without stars to 643.1 au with stars (Dybczyński et al., 28 Aug 2025). Within that subset, using the $q<3.1$4 au threshold, 115 comets become dynamically new when stars are included, 0 are dynamically old, and 3 are uncertain; without stellar perturbations, only 36 would have been classed as dynamically new (Dybczyński et al., 28 Aug 2025). This result directly supports the catalogue’s later two-variant design.

Specific objects illustrate the classification logic. In the 2020 paper, the preferred solution for C/2002 T7 LINEAR yields a previous perihelion distance of about 150 au, placing it outside the planetary region and therefore identifying it as dynamically new (Królikowska et al., 2020). The 2023 update shows how dynamical inference can remain sensitive to NG law and data treatment in objects such as C/2015 O1 (PanSTARRS), for which different acceptable solutions yield different $q<3.1$5 values, even if the broad dynamical interpretation remains comparable (Królikowska et al., 2023).

6. Interfaces, scientific uses, and limitations

CODE is designed for both inspection and statistical analysis. The 2020 paper describes two public interfaces: Browse, which lists comets and by default shows one preferred orbit per comet, and Search, which allows filtering by nearly all orbital and observational parameters, with results downloadable in full precision together with uncertainties (Królikowska et al., 2020). The 2023 update notes an interface restriction: the Search option works only with previous and next orbits obtained from the full dynamical model including both stars and Galactic tide (Królikowska et al., 2023).

The catalogue is intended to support studies of the origins and evolution of LPCs and the Oort Cloud, analyses of how NG effects alter osculating and original orbits, investigations of the $q<3.1$6 distribution and the Oort spike, classification of comets as dynamically new or old, and examination of the effects of Galactic tides and stellar encounters on past and future trajectories (Królikowska et al., 2020). The 2025 update adds that CODE is meant to support the study of the 6D distribution of orbital elements relevant to the outer Solar System (Dybczyński et al., 28 Aug 2025).

The papers also state several limitations. The catalogue reflects the current state of knowledge and can change if new positional data become available or if old data are re-reduced with better star catalogues (Królikowska et al., 2020). The 2020 release was still missing some small-perihelion Oort-spike comets from 2013–2017 (Królikowska et al., 2020), although the 2025 update later reports that it added a complete sample of 24 LPCs discovered in 2013–2017 with $q<3.1$7 au (Dybczyński et al., 28 Aug 2025). Previous and next orbits depend on the adopted stellar-perturber list, and the 2023 paper cites HD 7977 as an example of a potentially strong perturber whose Gaia data remain inconclusive (Królikowska et al., 2023). The 2020 paper also notes that original and future orbits might be slightly affected by unmodeled influences, including a hypothetical Planet Nine (Królikowska et al., 2020).

These caveats do not reduce the catalogue to a provisional ephemeris list. Rather, they define its character as a living dynamical atlas whose principal scientific value lies in the combination of standardized orbit determination, alternative physical models, uncertainty propagation through virtual-comet swarms, and explicit tracking of how Galactic and stellar perturbations reshape LPC histories over Myr timescales (Królikowska et al., 2020, Dybczyński et al., 28 Aug 2025).