Computed Pluto-Charon stable (5,1) prograde CR3BP cycler (known-class member, Ross-RT 2026 (k1,k2) cycler class; family+mu never computed in the source)

pc-cycler-51-2026 · source: this-project · validation: V1 · known-class

Signature

Bodies: Pluto-Charon
Primary: Pluto
Sequence (canonical): Pluto-Charon
Sense: n/a
Orbit class: Cycler
strict cycler (infinite returns)
Cycler class: non-keplerian (CR3BP)
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: cr3bp
CR3BP — Jacobi-constant-conserved; signature not patched-conic comparable.
Period: — yr (1 × Pluto-Charon synodic)
T = 24.305715846918527 TU (DERIVED from the fixed-hc C-sweep's nu=0 midpoint, independently re-found by the family's first-documented member's own brentq on nu(C) to 1.2e-13 in C). 1 TU = T_s/(2*pi) = 87855.80656569646 s (satellites.py: Charon a=19600 km, GM_system=975.5 km^3/s^2). T in days: 24.305715846918527 * 87855.80656569646 / 86400 = 24.7153 d (DERIVED) = 3.868 Charon orbital periods. Encounter cadence: 5 Pluto + 1 Charon passes per period (k1=5, k2=1). years: null (CR3BP, rotating-frame periodic orbit, no heliocentric synodic-multiple convention applies).
Priority date: 2026-08-11

V∞ at encounters

Pluto (encounter 1): — (not published)
CR3BP periodic orbit: conserved quantity is the Jacobi constant (C=3.167935964707404 DERIVED), not patched-conic V_inf. Pluto-Charon rotating frame.
Charon (encounter 2): — (not published)
Same -- Jacobi-constant model. Charon is the secondary (mu=0.10876 = GM_Charon/GM_system). Exactly ONE Charon close approach per period (k2=1), verified by local-minima count on a dense one-period propagation: minima at 10739 / 14319 / 745.5 / 14319 / 10739 km from Charon centre.

CR3BP orbit identity

Family: (5,1) prograde CR3BP cycler (Pluto-Charon, mu=0.10876473603280369)
Mass ratio (μ): 0.10876473603280369
Jacobi constant: 3.1679
Period (non-dim): 24.3057
Stability index: 0.000

Planar CR3BP rotating-frame periodic orbit in the Pluto-Charon system; Keplerian elements inapplicable.

Orbit view 2.5D ecliptic projection

Not renderable from current data. This is a rotating-frame (CR3BP-family — CR3BP, CCR4BP, or CRNBP) periodic or quasi-periodic orbit. A faithful render requires numerical propagation of the synodic-frame state, which the catalogue does not yet publish as a sampled path — so no stand-in ellipse is drawn (drawing a heliocentric ellipse here would misrepresent the dynamics). Whatever identity fields the model supports (Jacobi constant, period, stability — not all apply to every model in this family; see "Model assumption" above) are tabulated above.

model: CR3BP (rotating frame)

3D view not available for rotating-frame (CR3BP-family) orbits.

Definition status

incomplete — core fields missing or known-unknowns tracked below

Known-unknowns (1)

Values we expect to exist but have not yet filled (distinct from "not applicable"). Tracked per upstream docs/spec.md §16.6.4.

orbit_elements.cr3bp [derive]
All CR3BP IC values (jacobi_constant, period_nd, stability_index, state_nd) are DERIVED from the fixed-hc C-sweep along the (5,1) branch at mu=0.10876473603280369, seeded from the grid seed (x0=-0.6685146994, C=3.05) and independently re-derived end-to-end. No published IC exists for this family at any mass ratio: Ross & Roberts-Tsoukkas 2026 computes only (1,1),(3,1),(3,2),(3,3) and never at mu~0.1087. Crosschecks: independent Radau closure <1e-6 with dJ=7.9e-13; independent full-period monodromy nu agreeing with Barden nu to 3e-7.

source: data/found/810_pc51_fixed_hc_sweep/{sweep_up,sweep_down,sweep_window,gates}.jsonl; tests/scripts/test_run_810_pc_51_fixed_hc.py; docs/notes/2026-08-12-836-pc-51-adjudication.md.

Primary citation

undefined et al. (0). . .

Corroborating sources

Ross, S. D. & Roberts-Tsoukkas, M. (2026). Stable Ballistic Prograde Cyclers in the Three-Body Problem. arXiv preprint arXiv:2606.29189. · link
CLASS source only -- this paper supplies NO (5,1) family and NO Pluto-Charon member, so it cannot be first_published for this row. Grounded against the artifact on 2026-08-12 (arXiv HTML + PDF of v2, 10 Jul 2026): the paper computes (1,1),(3,3),(3,2),(3,1) only, at mu in {0.001, 0.012150584270572, 0.1, 0.3, 0.5} (Sun-Jupiter, Earth-Moon, and three abstract mu); the strings "Pluto" and "Charon" and any k1=5 family appear nowhere in it. Its conjecture -- "We conjecture that saddle-center birth is universal among cycler families, suggesting that stable cyclers are a generic feature of three-body dynamics", with "every cycler family contains a subfamily that is linearly stable to both planar and out-of-plane perturbations" -- is what this member CONFIRMS at a family+mu the authors never computed. TITLE NOTE: the title above is the one printed on page 1 of the arXiv PDF. The arXiv listing metadata renders it as "Stable Families of Ballistic Prograde Cyclers in the Restricted Three-Body Problem", and the ~6 sibling rows citing this paper carry a third, paraphrased string ("Families of Stable Prograde Cycler Orbits in the Circular Restricted Three-Body Problem") that matches neither. Those rows also cite v1 while the live paper is v2. is registered to reconcile all of them at once; not fixed here (concurrent sessions are editing catalogue.yaml).

Notes

Pluto-Charon (mu=0.10876473603280369 = 106.1/975.5, satellites.py) stable (5,1) prograde CR3BP cycler -- 5 Pluto loops and 1 Charon loop per period. Found (2026-08-11) by re-sweeping the genuine prograde (5,1) grid seed with the half-crossing index held FIXED at hc=5 through the whole C-sweep (the (3,2) positive-control convention), instead of the `hc=None` auto-redetection that had silently walked the branch onto an unrelated (4,0) family and produced the false negative. Independently re-derived end-to-end (2026-08-12) and admitted at V1. The family's ONE stable window across the whole swept extent C in [2.90, 3.24604] is C in [3.167773862, 3.168099844] -- width 3.26e-4, a NARROW window on a fragile branch (dx0/dC ~ 2.5; a plain fixed-dC=0.005 sweep jumps off it at the first step). Below the window the family continues to C=2.90 with nu rising monotonically; above it the branch terminates at a measured fold at C=3.24603516. the apparent second nu sign change near C=3.2440 was re-walked at dc=5e-5 and probed at dc=2e-6 and is real-eigenvalue sign FLICKER at |nu| >= 2.33, not a second stable window. NARROW CHARON CLEARANCE -- recorded caveat, adjudicated explicitly. The closest approach to Charon is 745.5244 km from centre against a 606.0 km radius (Nimmo 2017, the gate's sourced value): it CLEARS, but by only 139.52 km, i.e. 1.230 Charon radii from centre. confirmed this figure is EXACT rather than a sampling artifact: the minimum sits at t = T/2, the orbit's second perpendicular x-axis crossing (|y|=1.6e-11, xdot=0), and Charon sits on the x-axis at (1-mu, 0), so the closest approach is the single coordinate difference |x(T/2) - (1-mu)| = 0.0380369589206897 nd. Brent local minimization on dense output agrees with the sampled minimum to 1.9e-9 km across two integrators (DOP853, Radau) and rtol/atol from 1e-11 to 1e-13. The margin cannot be traded for stability: across the ENTIRE |nu|<1 window the clearance only varies 744.54-746.49 km (altitude 138.5-140.5 km), so no member of the stable window has a materially better margin. This is an IDEAL point-mass CR3BP figure; a real mission would care. Honest caveats: Charon's non-sphericity, the CR3BP circular-orbit idealization (true PC eccentricity ~0.0022), and no ephemeris/solar perturbation. Distinguished from the Antiope precedent, which REJECTED candidates passing 30-38 km BELOW the secondary's surface: this member is 139.5 km ABOVE it, a categorically different regime, and the gate passes on the sourced radius with margin 0. Physical cross-check: C(L1) = 3.62101825776712 (computed) vs Jbara 2025 (arXiv:2510.13479) independently-published C_L1 ~ 3.6210 at mu~0.109 -- MATCH; and C = 3.16794 < C(L1), so the L1 gateway is OPEN at this energy, which a cycler passing between Pluto and Charon requires. NOT CLAIMED NOVEL. The live literature gate (search/literature_check.py signature: primary=Pluto, sequence=(Charon), resonances=("5:1"), topology_label={repeated-moon}) was re-run live on 2026-08-12 and returned not-found -- necessary-not-sufficient per [[feedback_literature_novelty_check_baseline]]. Closest prior art grounded against source: Ross & Roberts-Tsoukkas 2026 (see corroborating_sources). Also surfaced and DISTINGUISHED: Jbara 2025 (arXiv:2510.13479) is Pluto-Charon CR3BP but studies zero-velocity structures, Lagrange-point instability and tadpole/horseshoe chaos -- no cyclers, no periodic-orbit families, no winding numbers, nothing near C=3.168; Antoniadou & Libert 2018 (arXiv:1805.00288, CMDA) studies 5/1 MEAN-MOTION resonant periodic orbits of a massless body about a star in a star+giant-planet system (mu~1e-3), not cyclers encountering both primaries, and never at mu~0.109. JPL SSD Three-Body Periodic Orbits catalog does not index Pluto-Charon at all, so jpl_family_check cannot adjudicate this row. MODEL: pure planar CR3BP (PCR3BP). No ephemeris, no solar perturbation.

Source quotes (per-field provenance)

Every numerical value in this entry traces to a verbatim or paraphrased quote from a cited source.

orbit_elements.cr3bp.mass_ratio: satellites.py (repo): Charon GM=106.1 km^3/s^2 / Pluto-system GM=975.5 km^3/s^2 = 0.10876473603280369.
orbit_elements.cr3bp.lunit_km: satellites.py (repo): Charon a=19600.0 km (semi-major axis, CR3BP unit length = P1-P2 distance).