Computed Earth-Venus two-working-body ballistic cycler ev-A (k = 2, generic Venus return)

earth-venus-two-working-body-cycler-eva-2026 · source: this-project · validation: V2 · candidate

Signature

Bodies: E-V
Primary: Sun
Sequence (canonical): V-V-V-E
Sense: n/a
Orbit class: Cycler
strict cycler (infinite returns)
Cycler class: multi-arc
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: circular-coplanar
Idealised: planets on circles, coplanar ecliptic.
Period: 3.198 yr (2 × E-V synodic)
DERIVED (this project): 2 Earth-Venus synodic periods = 1167.889 d (ideal model).
Source ephemeris: ideal circular-coplanar model; real-ephemeris patched-conic rung on Standish J2000 mean elements; DE440 closure measure
Ephemeris model the source states its numbers were computed against.
Priority date: 2026-10-06

V∞ at encounters

E (encounter 1): 4.89 km/s
DERIVED (this project, ideal-model zero; data/942_cell_ev_gauntlet.json). Earth turn 31.76 deg, ratio 0.347.
V (encounter 2): 10.36 km/s
DERIVED (this project). Venus turns 6.57 / 21.60 / 15.03 deg, worst ratio 0.574 (required altitude 7,061 km).

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 175.575 d, 224.702 d, 592.036 d, 175.575 d

Multi-arc. Distance from the Sun 0.512-1.243 AU (all legs, the Venus full-rev included).

Orbit view 2.5D ecliptic projection

spacecraft: idealized coplanar ellipse planets: J2000 osculating ellipse (Standish & Williams Table 1) orientation: coplanar-idealized (no Ω/ω published — in-plane ellipse)

3D view not available for multi-arc trajectories yet. The 3D system can now render a numerically-sampled polyline (n-body or multi-arc), but no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them). The button will appear here once a sampled path is exported for this trajectory; we never interpolate one from the catalogue's per-leg (a, e).

— — planet orbit (true J2000 ellipse)

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.

trajectory_regime [uncertain]
On DE440 (astropy Earth, not the Earth-Moon barycentre) no gate-passing ballistic member was found: NEAR-BALLISTIC, 1.56-2.53 m/s of mid-course correction per 16-yr chain from the gate-passing minimax solution (6.25). The chain-tool shoot at today's settings (restarts 0.03/0.05 rad; step 1, 2026-10-11) closes ballistic 5-cycle chains at all 5 epochs, but every closure fails the gate at Venus: best epoch JD 2467763.3, worst ratio 1.117, required periapsis 627 km below the surface (927 km below the 300-km floor). With the anchored shoot (6.48 method; step 1b) the ballistic chain at JD 2462508.0 passes the gate for 1-3 cycles (6.4 yr; worst 0.757, lowest required periapsis altitude 3,109 km) and violates the Venus floor from 4 cycles on; at JD 2464843.6 it passes for 1 cycle only. Limits: the 1-3-cycle closures were not independently re-flown; one epoch; below the 5-cycle criterion.

source: data/942_evAB_de440_closure_dv.json; results note 6.24-6.25; docs/notes/2026-10-11-1025-ev-realeph-rung-d.md secs. 9.3, 9.5; data/1025_ev_realeph/control_1057/, control_1057b/

Primary citation

No primary citation recorded; see the provenance tags below.

orbit fidelity circular-coplanar V∞ fidelity circular-coplanar

Corroborating sources

Hollister, W. M. (1969). Periodic Orbits for Interplanetary Flight. Journal of Spacecraft and Rockets 6(4):366-369. DOI: 10.2514/3.29664
CLASS source: the Earth-Venus two-working-body periodic orbits (orbits I-III).
Hollister, W. M. & Menning, M. D. (1970). Periodic Swing-By Orbits between Earth and Venus. Journal of Spacecraft and Rockets 7(10):1193-1199. DOI: 10.2514/3.30134
CLASS and METHOD source: 15 orbits built from full-revolution (FR) and symmetric (SY) returns only (Menning 1968 App. A-1). Menning 1968 (pp.41-42) estimates 'a minimum of 1024' FR/SY orbits and names half-revolution and order variations, not computed. ev-A carries a GENERIC Venus return (1-rev, 2.63 Venus periods), which is neither FR nor SY.

Notes

First computed Earth-Venus two-working-body ballistic cycler with a generic Venus return (both planets bend), k = 2 (1167.889 d). Legs: - E->V; - a Venus 1:1 full-rev; - a Venus 1-rev high return of 592.0 d (2.63 Venus periods). This is neither Menning's full-revolution return nor his symmetric return, which lasts between one and two planet periods; - V->E. Ideal-model Lambert-leg starts 583.944387, 984.221555, 1576.257792 d. Results note 6.12, 6.23, 6.25; owner summary sec. 2.4. Real-ephemeris standing: - Standish J2000 mean elements (direct route, 5 cycles = 16 yr): ballistic and gate-passing at 5/5 epochs (worst 0.579-0.580; re-fly <= 1.9e-3 km, the Venus full-revs included). Route validated by D1 (Hollister 1H) and the H&M endpoint orbits. - DE440 (owner-required statement): NEAR-BALLISTIC. - No gate-passing ballistic DE440 member was found. - From the minimax solution, the full-rev legs need 1.56-2.53 m/s of mid-course correction per 16-yr chain (max 0.91 m/s per leg; induced arrival |V_inf| change <= 1.70 m/s) (results note 6.24-6.25, data/942_evAB_de440_closure_dv.json). - DE440 shoot (2026-10-11): at today's restarts every 5-cycle closure fails the gate at Venus (best worst ratio 1.117, periapsis 627 km below the surface); the anchored shoot passes for 1-3 cycles at one epoch only (see data_gaps). - screen (data/973_screen_942_ev.json): passes. ev-A is not among the 9 ev gate-passers flagged "direction-dependent". V2-ballistic (spec §14 owner amendment 2026-10-08, same-phase drift wording of 2026-10-11; docs/notes/2026-10-08-1007-v2-ballistic-chain-campaign.md secs. 8.11, 8.13-8.14): PASS at 5 of 5 Standish epochs, 10 continuous cycles each (32 yr; L = 5; first and last cycle excluded). - Junction continuity <= 1.8e-12 km/s; gate worst 0.580; re-fly <= 1.9e-3 km. - Same-phase drift: dates 0.65-1.53 d against an 8.74-d band; |V_inf| 0.013-0.043 km/s against 0.49. - Slope diagnostics (handed to V3): dates -0.07 to +0.32 d per cycle; |V_inf| +0.0009 to +0.0127 km/s per cycle. - Positive control: Hollister-Menning 1970 orbit 1 from its printed dates passes. - V2 is on Standish mean elements. On DE440 the row stays near-ballistic (see above and data_gaps). Literature: - Scripted gate (literature_check v2,; data/942_943_litcheck_scope.json): NOT-FOUND (necessary, not sufficient). - The Hollister/H&M anchor (scope: two working bodies, FR/SY returns) is excluded by return-types (ev-A's generic return). - The grounded Hughes et al. 2014 anchor (one-shot free returns, mga-tour) is excluded by topology. - Human searches: docs/notes/2026-10-07-942-evAB-prior-art-search.md (OpenAlex citers of H&M 1970 and Hollister 1969, 14 queries, NTRS, arXiv, web), results note 6.52 (Minovitch 1963) and 6.53 (Hollister 1963). No collision. - Owner ruling 2026-10-07: candidate-novel, attributed to Hollister 1969 and Hollister & Menning 1970 (nearest published class: FR/SY).