Casoliva 1-2d (1,2) resonant Earth-Moon periodic orbit (CR3BP, C=2.5803, NO lunar encounter -- periselene 603,592 km, outside lunar SOI/Hill radius)

casoliva-1-2d-em-resonant-po-2010 · source: literature · validation: V1

Signature

Bodies: E-Moon
Primary: Earth
Sequence (canonical): E-Moon
Sense: n/a
Orbit class: Resonant PO
resonant periodic orbit (stable, no transport utility)
Cycler class: non-keplerian (CR3BP)
Returns: ∞ — finite for epoch-locked classes
Validity window: — (not published)
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 = 12.5663707178212 TU nondim (Casoliva 2010 Table 3 "1-2d" prints T=12.5663706144 TU exactly = 2*pi*2 per her own Eq. 18 p-q-resonance identity -- Casoliva's nondim TU convention is angle/radian-based, hence convention-independent of any project vs paper t_s difference; reproduced here to 8.23e-09 relative). 54.569212 d is a DERIVED convenience conversion via this project's own DE440-registry t_s (375190.2619 s, TU_DAYS=4.34247988 d) -- Casoliva's Table 3 prints NO days column for this row (unlike Braik-Ross's own Table 2), so there is no published day-figure to reproduce against; years: null (CR3BP, rotating-frame periodic orbit).
Priority date: 2010-08-12

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: Casoliva 2010 Class 1 (p,q)=(1,2) resonant Earth-Moon cycler, Table 3 row '1-2d'
Mass ratio (μ): 0.01215058439469525
Jacobi constant: 2.5803
Period (non-dim): 12.5664
Stability index: 4.857

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-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 (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]
Casoliva 2010 Table 3 prints the IC in HER OWN frame/convention (Earth at (+mu,0), Moon at (mu-1,0)) at HER OWN displayed mu_EM=0.0121529529 -- NOT this project's rotating-frame convention or registry mu. state_nd here is DERIVED via the module's own validated 180-degree-rotation flip (cyclerfinder.search.earth_moon_resonant_families.table3_seed_state, verified two independent ways per the family's first-documented member's own module docstring: Jacobi-constant round-trip AND decisive direct-propagation periodicity closure) followed by a full-state Newton periodicity correction at this project's own registry mu (correct_periodic). Never a golden.

source: src/cyclerfinder/search/earth_moon_resonant_families.py::table3_seed_state + recover_table3_row + docs/notes/2026-08-07-780-earth-moon-casoliva-families-gate.md.
orbit_elements.cr3bp.stability_index [derive]
This row's stability_index uses Casoliva's OWN full-period Eq. 6-8 k=max(|kappa_par|,|kappa_perp|) convention (see the field's own comment), NOT this project's usual Barden half-period nu convention (braik-ross-*-cycler-2026 / em-cycler-21-3d-spatial-2026 rows) -- Barden's method needs a symmetric perpendicular x-axis crossing this row's own printed IC (a general asymmetric Poincare y=0 crossing) does not have. DERIVED via cyclerfinder.search.earth_moon_resonant_families.planar_stability_index (full 6x6 monodromy trace identity on the decoupled in-plane 4x4 and out-of-plane 2x2 blocks), reproducing Casoliva's own printed k -- NOT directly comparable number-for-number to this catalogue's other Barden-nu stability_index values.

source: src/cyclerfinder/search/earth_moon_resonant_families.py::planar_stability_index + StabilityIndex; docs/notes/2026-08-07-780-earth-moon-casoliva-families-gate.md ("The Class 1 gate" section, k reproduction table).

Primary citation

Casoliva, J. et al. (2010). Two Classes of Cycler Trajectories in the Earth-Moon System. Journal of Guidance, Control, and Dynamics 33(5), pp. 1623-1640.

DOI: 10.2514/1.46856

URL: https://arc.aiaa.org/doi/10.2514/1.46856

Table 3 (p.1630), Class 1 (high-energy near-Keplerian p-q resonant orbits), row "1-2d" -- p=1, q=2, printed to 10-11 significant figures. Casoliva's own footnotes confirm this row BOTH satisfies its own p-q resonance relation AND physically exists in the Earth-Moon system (does not fly through Earth) -- the two admission flags this project's own gate module carries verbatim from the paper (satisfies_resonance=True, exists_in_em_system=True for this row).

Corroborating sources

Casoliva, J. et al. (2008). Families of Cycler Trajectories in the Earth-Moon System. AIAA/AAS Astrodynamics Specialist Conference, AIAA 2008-6434.
Conference precursor to the 2010 JGCD journal paper this row's Table 3 digit-grade values are sourced to; strictly planar 4-state formulation, same Class 1 p-q resonant family concept.

Notes

Casoliva 2010 Table 3 Class 1 row "1-2d" -- (1,2) p-q resonant near-Keplerian Earth-Moon periodic orbit at C_J=2.5803, T=2*pi*2 TU (UNSTABLE, k=4.8579). One of the 9 of Casoliva's own 16 Table 3 rows that BOTH satisfies its own p-q resonance relation (footnote-e) AND physically exists in the Earth-Moon system (footnote-d, does not fly through Earth) -- both flags re-confirmed live this task directly from the family's first-documented member's own gate module output (earth_moon_resonant_families.table3_row/table3_gate_report), not inherited from any prior written summary. ADMISSION: the family's first-documented member's own table3_gate_report reports this row converged=True, passed=True -- x0/period/Jacobi/stability-index ALL reproduce Casoliva's own printed Table 3 values within the 1e-2 gate tolerance (x0_rel_err=2.52e-07, period_rel_err=8.23e-09, jacobi_rel_err=2.70e-07, k_rel_err=1.21e-04), AND an independent Radau integrator cross-check passes (radau_djacobi=4.35e-14). This is a STRICTER bar than the raw satisfies_resonance/exists_in_em_system admission filter alone -- 2 of the 9 admitted rows (1-2e, 7-3a) originally failed this stronger self-consistency gate on Casoliva's own printed stability index k only (IC/period/Jacobi still matched tightly per the module docstring) and were excluded from the family's first-documented member's own writeback -- (2026-08-09) found and fixed the root cause (a k_par-vs-k_perp selection bug affecting 3 rows: 1-2e/3-2a/7-3a) and completed the writeback for both writeback-eligible rows; see casoliva-1-2e-em-resonant-po-2010 / casoliva-7-3a-em-cycler-2010's own notes. ORBIT_CLASS = resonant_po, NOT cycler: despite genuinely satisfying its own (1,2) Earth-centered p-q resonance (Casoliva's own footnotes confirm both satisfies_resonance=True and exists_in_em_system=True), this orbit's own printed periselene r_pM=603591.6 km sits OUTSIDE both the lunar SOI (66182.9 km) and Hill radius (61524.1 km) -- an independent DERIVE cross-check (dense propagation over one full period) confirms 603584.6 km, agreeing to 1.15e-05 relative. It NEVER actually encounters the Moon: an Earth-resonant periodic orbit whose closest lunar approach is a small fraction of the full Earth-Moon separation, not a transport cycler. Exactly matches resonant_po's own schema v4.9 carve-out (data/README.md/catalogue.schema.json: 'a stable resonant/libration periodic orbit... with NO demonstrated transport utility -- it never encounters the secondary'), the identical reasoning em-cycler-21-3d-spatial-2026 already established for its own (2,1) Earth-Moon resonant member (122,628 km vs SOI 66,183 km). Only epoch_locked=false/n_returns=infinite is the schema-ENFORCED resonant_po invariant (tests/data/test_schema_v47_orbit_class.py) -- 'stable' in the class's own descriptive prose is NOT schema-enforced, so this row's own UNSTABLE character (Casoliva's own printed k reproduced to 1.21e-04 relative) does not block admission. MODEL: pure planar CR3BP (PCR3BP), this project's own registry mu/l*/t* throughout (NOT Casoliva's own displayed mu_EM=0.0121529529), per the family's first-documented member's own explicit module policy. No bicircular/solar-gravity/lunar-eccentricity/ephemeris refinement. REPRODUCTION (reusing the gate module unmodified): full-state single-shooting Newton periodicity correction (cyclerfinder.search.cr3bp_periodic.correct_periodic) seeded from the validated 180-degree-rotation coordinate flip of Casoliva's own printed Table 3 IC. Closure residual 7.60e-12. Independent Radau integrator cross-check (crosscheck_periodic) passes, preserving Jacobi to dJ=4.35e-14 over one period. the family's first-documented member's own independent DERIVE re-verification (this task, not merely inherited): direct dense propagation (scipy solve_ivp DOP853, rtol=atol=1e-12, 4000-point t_eval grid) of the corrected orbit over one full period, confirming min lunar distance 603584.6 km and min Earth distance 219185.3 km both agree with Casoliva's own printed r_pM/r_pE columns to <1e-3 relative -- an independent confirmation of BOTH the orbit's identity and the orbit_class determination above, not a re-run of the family's first-documented member's own gate.

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: Casoliva 2010 Table 3 (p.1630) row "1-2d", C_J column = 2.5803060666.
orbit_elements.cr3bp.period_nd: Casoliva 2010 Table 3 (p.1630) row "1-2d", T column = 12.5663706144 TU (=2*pi*2 exactly, her own Eq. 18).
orbit_elements.cr3bp.stability_index: Casoliva 2010 Table 3 (p.1630) row "1-2d", k column = 4.8578794987 (her own Eq. 6-8 full-period max(|kappa_par|,|kappa_perp|) convention; |k|<2 -> UNSTABLE).
orbit_elements.cr3bp.casoliva_periselene_km: Casoliva 2010 Table 3 (p.1630) row "1-2d", r_pM column = 1.5702173819 LU (603591.6 km at this project's own registry lunit_km=384400.0 km).
orbit_elements.cr3bp.mass_ratio: cyclerfinder.core.cr3bp.cr3bp_system("Earth","Moon").mu, live-printed this session = 0.01215058439469525. Casoliva 2010 (Sec. II text) prints mu_EM=0.0121529529 -- see the field's own comment for the 1.95e-04 relative gap.
orbit_class: data/README.md/catalogue.schema.json v4.9 resonant_po definition ('never encounters the secondary') + this row's own casoliva_periselene_km/DERIVE cross-check, both well OUTSIDE the lunar SOI/Hill radius, mirroring em-cycler-21-3d-spatial-2026's identical reasoning.