Ross/Roberts-Tsoukkas stable Earth-Moon (3,1) prograde cycler (CR3BP)

ross-rt-em-cycler-31-2025 · source: literature · validation: V2

Assumed erratum recorded for this row's source: Table 3 (p. 11), C_(3,1) bound, vs Table 4 (p. 13) Delta-C reconciliation — published so the authors can verify or refute; see errata.

Signature

Bodies: E-Moon
Primary: Earth
Sequence (canonical): E-Moon
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 × E-Moon synodic)
T^stable = 14.78849241668140 TU (Ross Table 3, p. 11) -> 64.305944 d (Table 4, p. 13). Encounter cadence: 3 perigee + 1 perilune pass per period (k1=3, k2=1). Stable window ~750-1,000 km perilune altitude (Delta_p_m 253.70 km; nd perilune radius ~0.00648-0.00713, Fig. 8). years: null (CR3BP, see (1,1) row).
Priority date: 2025-08-01

V∞ at encounters

E (encounter 1): — (not published)
CR3BP periodic orbit: conserved quantity is the Jacobi constant, not V_inf.
Moon (encounter 2): — (not published)
Same — Jacobi-constant model.

CR3BP orbit identity

Family: (3,1) prograde Earth-Moon cycler
Mass ratio (μ): 0.012150584270572
Jacobi constant: 3.1618
Period (non-dim): 14.7885
Stability index: 0.015

Planar CR3BP rotating-frame periodic orbit; Keplerian elements inapplicable. CR3BP identity tuple below.

Orbit view 2.5D ecliptic projection

Not renderable from current data. This is a rotating-frame (CR3BP) 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). The CR3BP identity (Jacobi constant, period, stability) is tabulated above.

model: CR3BP (rotating frame)

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

Definition status

incomplete — core fields missing or known-unknowns tracked below

Known-unknowns (2)

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.state_nd [derive]
No initial-state vector printed in the source (mining note §5). state_nd DERIVED by the fixed-Jacobi corrector, self-consistency-checked; never a golden. (3,1) narrow inner band: reproduced T lands ~2.2e-4 TU from T^stable (results note §1); enforced C and STABLE verdict exact.

source: scripts/cr3bp_ross_reproduce.py; tests/search/test_cr3bp_ross_families.py; 2026 journal version.
orbit_elements.cr3bp.jacobi_max [conflict]
Ross Table 3 C_(3,1) BOUND column = 3.1833333078762 (= C^{u2}_1, the Eq. 8 min) is inconsistent with Table 4: C1 - DeltaC_(3,1) implies C_(3,1) = 3.1756140 (Delta 7.7e-3; mining note §4). The C^stable/C^max/T^stable columns used here are internally consistent and catalogue-grade; only the C_(k1,k2) bound column is inconsistent. Pinned by tests/search/test_cr3bp_ross_families.py::test_data_gap_c31_bound_inconsistency. Re-verify against the 2026 journal.

source: Ross & Roberts-Tsoukkas 2026 journal version.

Primary citation

Ross, S. D. & Roberts-Tsoukkas, M. (2025). Stable, Low-Energy Prograde Earth-Moon Cycler Orbits. AAS/AIAA Astrodynamics Specialist Conference, 2025, paper AAS 25-621.

URL: https://ross.aoe.vt.edu/papers/ross-roberts-tsoukkas-2025-AAS-25-621.pdf

LaTeX preprint 2025-07-17; 2026 journal version exists (re-verify numbering).

Notes

(3,1) stable prograde Earth-Moon cycler, nu=0 midpoint (Delta_p_m 253.70 km, Table 3). Its rotating-frame geometry (3 Earth-realm petals + lunar loop) superficially resembles the Genova/Aldrin 3-petal cycler (genova-aldrin-2015-em-3petal-cycler) but is NOT the same orbit: the Genova/Aldrin 3-petal cycler does not exist in the pure CR3BP (needs solar gravity + station-keeping; reclassified bicircular), whereas (3,1) is a genuine ballistic PCR3BP periodic orbit with a stable window — the first pure-CR3BP 3-petal-geometry catalogue entry. Keep both rows, cross-reference, do not merge (mining note §6). Reproduced in-repo: STABLE (nu=0.01545), independent Radau closure dJ < 1e-12. PCR3BP-only.

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.jacobi_constant: Ross & Roberts-Tsoukkas 2025 Table 3 (p. 11): (3,1) C^stable = 3.161784147013429.
orbit_elements.cr3bp.period_nd: Ross & Roberts-Tsoukkas 2025 Table 3 (p. 11): (3,1) T^stable = 14.78849241668140 TU; Table 4 (p. 13) 64.305944 d.
orbit_elements.cr3bp.basin_widths_km: Ross & Roberts-Tsoukkas 2025 Fig. 8(b) (p. 11): U2 Poincare-inset basin-of-stability widths 23, 195, 155, 146, 92, 227 km along the (3,1) family.