Casoliva 7-3b (7,3) resonant Earth-Moon cycler (CR3BP, C=1.0688, genuine lunar encounter periselene 13,210 km)

casoliva-7-3b-em-cycler-2010 · source: literature · validation: V1

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 = 18.8496322021155 TU nondim (Casoliva 2010 Table 3 "7-3b" prints T=18.8495559215 TU exactly = 2*pi*3 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 4.05e-06 relative). 81.854149 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)=(7,3) resonant Earth-Moon cycler, Table 3 row '7-3b'
Mass ratio (μ): 0.01215058439469525
Jacobi constant: 1.0687
Period (non-dim): 18.8496
Stability index: 57.356

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 "7-3b" -- p=7, q=3, 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 "7-3b" -- (7,3) p-q resonant near-Keplerian Earth-Moon periodic orbit at C_J=1.0688, T=2*pi*3 TU (UNSTABLE, k=57.3519). 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=4.37e-05, period_rel_err=4.05e-06, jacobi_rel_err=1.00e-04, k_rel_err=7.35e-05), AND an independent Radau integrator cross-check passes (radau_djacobi=1.59e-12). 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 = cycler: Casoliva's own printed periselene r_pM=13210.0 km sits WELL INSIDE the lunar sphere of influence (66182.9 km, patched-conic SOI=a*(m2/m1)^(2/5) at this project's own registry mu) and Hill radius (61524.1 km) -- an independent DERIVE cross-check (dense propagation of the corrected orbit over one full period) confirms 13269.2 km. A genuine lunar flyby every period, satisfying cycler's own defining 'transports between encounters' property (data/README.md schema v4.7). 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 8.40e-11. Independent Radau integrator cross-check (crosscheck_periodic) passes, preserving Jacobi to dJ=1.59e-12 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 13269.2 km and min Earth distance 15933.2 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 "7-3b", C_J column = 1.0687623900.
orbit_elements.cr3bp.period_nd: Casoliva 2010 Table 3 (p.1630) row "7-3b", T column = 18.8495559215 TU (=2*pi*3 exactly, her own Eq. 18).
orbit_elements.cr3bp.stability_index: Casoliva 2010 Table 3 (p.1630) row "7-3b", k column = 57.3519357466 (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 "7-3b", r_pM column = 0.0343651369 LU (13210.0 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 schema v4.7 cycler definition ('transports between encounters') + this row's own casoliva_periselene_km/DERIVE cross-check, both well inside the lunar SOI/Hill radius.