Computed Earth-Venus two-working-body ballistic cycler ev4-4 (k = 4, both planets bend)

earth-venus-two-working-body-cycler-ev4-4-2026 · source: this-project · validation: V1 · candidate

Signature

Bodies: E-V
Primary: Sun
Sequence (canonical): V-V-V-E-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: 6.395 yr (4 × E-V synodic)
DERIVED (this project): 4 Earth-Venus synodic periods = 2335.778 d in the ideal model (Venus period 0.61520 yr, Earth 1 yr).
Source ephemeris: ideal circular-coplanar model; real-ephemeris patched-conic rung (d) on Standish J2000 mean elements and on DE440 (blend to lambda 1, closure dV; the DE440 shoot)
Ephemeris model the source states its numbers were computed against.
Priority date: 2026-10-08

V∞ at encounters

E (encounter 1): 6.83 km/s
DERIVED (this project, ideal-model zero; data/973_ev/k4_gauntlet.json). Earth turns 38.32 / 0.00 / 38.32 deg; largest demanded/available ratio 0.557 at the 200-km floor.
V (encounter 2): 4.04 km/s
DERIVED (this project). Venus turns 68.45 / 8.40 / 76.86 deg; largest ratio 0.779 at the 300-km floor (required altitude 6,077 km).

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 730.5 d, 730.5 d, 245.574 d, 324.484 d, 224.702 d, 80.018 d

Multi-arc. Distance from the Sun 0.496-1.168 AU (extents, 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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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 (2)

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 AT THE BEST EPOCH, WINDOW-DEPENDENT. Standish: ballistic and gate-passing at 5 of 5 epochs (0 fail, 0 not reached), turn deficit 0 per 7 cycles at the passing epochs (strictly ballistic by construction). DE440 blend (no shoot; 6.18/6.24 reading): reaches lambda 1 at 5/5 with the minimax gate passing at 5/5; mid-course closure dV per 7 cycles at the best epoch 43.3 m/s (low-maintenance; the Earth legs are an UPPER BOUND, DE440's Earth carries the lunar reflex), of which the Venus legs plus turn deficit 5.3 m/s (essentially-ballistic); range over the reached epochs 43.3-51.1 m/s.

source: docs/notes/2026-10-11-1025-ev-realeph-rung-d.md secs. 6, 5a; data/1025_ev_realeph/summary.json; data/1025_ev_writeback_v1.json; band thresholds: docs/notes/2026-06-22-dv-band-definitions.md and cyclerfinder.verify.dv_band_acceptance
validation_level [unknown]
DE440 ballistic closure untested in effect: the DE440 shoot found no gate-passing closure for this member (0 pass, 1 fail, 4 no closure of 5 epochs; best shoot residual 0.0039, the worst junction component, where 0.001 means a 1-m/s V_inf mismatch or a 1-km miss). The shoot route cannot judge a full-rev Earth-Venus chain on DE440: its control ev-A fails with both the free and the anchored shoot (steps 1 and 1b). The negative is conditional on the formulation (restart defect, date guard; backlog, low priority, owner 2026-10-11).

source: docs/notes/2026-10-11-1025-ev-realeph-rung-d.md secs. 8, 9.3, 9.5; data/1025_ev_realeph/de440_shoot/

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). ev4-4 carries n:m full-revolution returns other than 1:1, outside those itineraries; structurally, no k = 4 or k = 5 one-visit structure equals an H&M orbit or a sub-period of one (data/973_ev/hm1970_subperiod_check.json; docs/notes/2026-10-07-973-two-working-body-k-extension.md secs. 2.2, 6.5).

Notes

Member ev4-4 of the Earth-Venus two-working-body set: both planets bend; k = 4 (2335.778 d, 6.395 yr); structure k4|RE/2:3|RE/2:3|LE>V/0s|LV>V/1l|RV/1:1|LV>E/0s. Ideal-model Lambert-leg starts 325.344596, 570.918575, 1120.104121 d (model epoch: both planets at angle 0 at t = 0). Worst demanded/available turn ratio 0.779. Enumeration, gauntlet and screens: docs/notes/2026-10-07-973-two-working-body-k-extension.md secs. 13-14. Family: the same two-working-body Earth-Venus class as ev-A (earth-venus-two-working-body-cycler-eva-2026) and ev-B (earth-venus-two-working-body-cycler-evb-2026): both planets bend, with returns outside the Hollister-Menning FR/SY itineraries. ev-C (earth-venus-venus-hosted-cycler-evc-2026) is a different architecture (Earth massless). Shares its transfer and Venus block with ev4-6 and ev4-7: identical ideal-model V_inf and identical real-ephemeris dates at every epoch; the members differ only in their Earth full-rev returns (docs/notes/2026-10-11-1025-ev-realeph-rung-d.md sec. 8). (direction-dependent tilted-circle flag) does not apply: the screen status is "pass". V1 evidence (data/1025_ev_writeback_v1.json): lamberthub <= 9.5e-09 m/s on every Lambert leg; DOP853 re-fly 3.5e-04 km, gate passes on the integrated vectors. Real-ephemeris standing (rung (d), docs/notes/2026-10-11-1025-ev-realeph-rung-d.md; chains of 3 cycles = 19.2 yr; route controls Hollister 1H, ev-A and ev-B reproduce): - Standish J2000 mean elements: 5/5 PASS. JD 2462829.8 PASS (route S1, worst 0.919, re-fly 6.1e-04 km); JD 2465172.6 PASS (route S1, worst 0.945, re-fly 7.8e-04 km); JD 2467500.4 PASS (route S1, worst 0.981, re-fly 8.6e-04 km); JD 2469842.1 PASS (route S1, worst 0.830, re-fly 7.1e-04 km); JD 2472176.4 PASS (route S1, worst 0.774, re-fly 6.9e-04 km). Band at the best epoch: strictly-ballistic (turn deficit 5.0e-09 m/s per 7 cycles, numerical zero). - DE440 blend (lambda 1, minimax directions, no shoot): JD 2462829.6 gate pass 0.920, closure E/V 15.5/4.6 m/s per chain; JD 2465172.5 gate pass 0.946, closure E/V 16.3/2.8 m/s per chain; JD 2467500.2 gate pass 0.979, closure E/V 16.3/2.3 m/s per chain; JD 2469841.8 gate pass 0.831, closure E/V 18.4/3.6 m/s per chain; JD 2472176.2 gate pass 0.772, closure E/V 18.0/3.6 m/s per chain. - DE440 shoot (sec. 8): no gate-passing closure; the route cannot judge, see data_gaps. Literature: literature_check v3-A1 returns "not-found" (necessary, not sufficient; data/1025_litcheck_973_members.json). The Hollister/H&M anchor is excluded on return types. Human prior-art reading: docs/notes/2026-10-08-1025-literature-step.md sec. 5 (the ev-A/ev-B search, docs/notes/2026-10-07-942-evAB-prior-art-search.md, applies; no new search was run). OWNER DECISION 2026-10-11: candidate-novel V1 under option "(a) 10 rows, Standish >= 4/5", attributed to Hollister 1969 and Hollister & Menning 1970. Wording: "first computed", never "new class".