Computed Earth-Venus two-working-body ballistic cycler ev-B (k = 3, Venus 3:2 full-rev return)

earth-venus-two-working-body-cycler-evb-2026 · source: this-project · validation: V1 · candidate

Signature

Bodies: E-V
Primary: Sun
Sequence (canonical): V-V-V-E-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: 4.796 yr (3 × E-V synodic)
DERIVED (this project): 3 Earth-Venus synodic periods = 1751.833 d in the ideal model (Venus period 0.61520 yr, Earth 1 yr).
Source ephemeris: ideal circular-coplanar model; real-ephemeris patched-conic rung on Standish J2000 mean elements
Ephemeris model the source states its numbers were computed against.
Priority date: 2026-10-06

V∞ at encounters

E (encounter 1): 8.01 km/s
DERIVED (this project, ideal-model zero; data/942_cell_ev_gauntlet.json). Earth turn 2 x 21.81 deg, ratio 0.375.
V (encounter 2): 10.93 km/s
DERIVED (this project). Venus turns 23.49 / 14.23 / 9.26 deg, worst ratio 0.673 (required altitude 4,584 km).

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 365.25 d, 50.096 d, 506.998 d, 674.105 d, 155.384 d

Multi-arc. Distance from the Sun 0.610-1.686 AU (all legs, the full-revs 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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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]
BAND FLAGGED (owner decision 2026-10-08): strictly ballistic at the best window; window-dependent. 2 of 5 Standish epochs are ballistic (0 and 3); epoch 1 closes for 3 cycles only; epochs 2 and 4 need 346-981 m/s per 7 cycles (beyond-bend price, minimax full-rev directions, upper-bound style).

source: docs/notes/2026-10-05-942-943-two-working-body-generator.md 6.55b, 6.57a; data/942_dv_band.json; data/942_evB_ramp/

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: orbits built from full-revolution (FR, 1:1) and symmetric (SY) returns only (Menning 1968 App. A-1). ev-B carries a Venus 3:2 full-revolution return and a generic 1-rev Venus return, outside those itineraries.

Notes

First computed Earth-Venus two-working-body ballistic cycler of this structure (both planets bend), k = 3 (1751.833 d). Legs: an Earth 1:1 full-rev, E->V (50.1 d), a Venus 1-rev low return (507.0 d), a Venus 3:2 full-rev (674.1 d) and V->E (155.4 d). Ideal-model Lambert-leg starts 547.596902, 597.693177, 1778.796557 d. Results note 6.12, 6.23, 6.55-6.57a; owner summary sec. 2.5. V1 evidence (data/942_943_writeback_v1.json): lamberthub <= 6.3e-10 m/s on every Lambert leg; DOP853 re-fly 2.2e-3 km, gate passes on the integrated vectors. Real-ephemeris standing (Standish J2000 mean elements, 4 cycles = 19.2 yr), BAND FLAGGED: - ballistic and gate-passing at 2 of 5 epochs (JD 2463054.0, worst 0.933; JD 2470059.7, worst 0.757), dV 0 per 7 cycles: strictly ballistic at the best window; - epoch JD 2465390.1: closes and passes the gate for 3 cycles only (k = 2 worst 0.914, k = 3 0.875; the 4-cycle solve does not converge) (6.55b); - epochs JD 2467728.3 and 2472400.0: converge but fail the gate (worst 1.092 and 1.034). The turn-deficit price is 981.4 and 345.7 m/s per 7 cycles (beyond-bend; Oberth periapsis 2392.4 and 813.7), with minimax full-rev directions: upper-bound style (6.57a, data/942_dv_band.json). - Method: 6.55a ramp continuation with the epoch-0 positive control passing (6.55b). V2-ballistic (final wording of 2026-10-11; docs/notes/2026-10-08-1007-v2-ballistic- chain-campaign.md secs. 8.14, 8.17): NOT JUDGEABLE at 10 cycles. - Its geometric repeat at the owner's 0.02-rev tolerance is L = 49 (residual 0.0201 rev at L = 5), so V2 needs >= 98 cycles (470 yr); no such chain exists. - The 10-cycle run of sec. 8.14 used a hard-coded L = 5, which the rule does not allow. - ev-B's V1 standing for V2 purposes rests on the GATE FAILURE alone: at 10 cycles the gate fails or is indeterminate at 3 of 5 epochs (worst 1.011, 1.019, 0.999), and there is no 10-cycle chain at the 4th. The row stays V1. Literature: - Scripted gate: literature_check v2/v3-A1 returns NOT-FOUND (necessary, not sufficient; data/942_943_litcheck_scope.json). The Hollister/H&M anchor is excluded by return types (the Venus 3:2 and generic returns). - Human searches: docs/notes/2026-10-07-942-evAB-prior-art-search.md, results note 6.52-6.53; no collision. The VESTA web concept's "1752-d Earth-Venus cycle" (no sources) shares the period only (its E->V leg is 109 d against 50.1 d). - OWNER DECISION 2026-10-08: candidate-novel V1, band flagged as above, attributed to Hollister 1969 and Hollister & Menning 1970.