Russell-Ocampo cycler 2.1.1.+2 ('Case 2' of Byrnes/McConaghy/Longuski 2002)

russell-ocampo-2.1.1+2-case2 · source: literature · validation: V0

Signature

Bodies: E-M
Primary: Sun (default — heliocentric)
Sequence (canonical): E-E-M-M
Sense: outbound
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: 4.270 yr (2 × E-M synodic)
Maintenance ΔV: 0.008 km/s — near-ballistic (powered nudge)
Priority date: 2002-08-05

V∞ at encounters

E (encounter 1): 4.10 km/s
Russell 2004 dissertation Table 3.4, cycler 2.1.1.+2 (footnoted as 'Case 2' of Byrnes/McConaghy/Longuski 2002): 'Earth v_inf (km/s): 4.1'.
M (encounter 2): 2.00 km/s
Russell 2004 Table 3.4 for 2.1.1.+2: 'Mars v_inf (km/s): 2.0'.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): 0.95
Turn ratio (TR): 1.11
Transit times (days): 207 d

Russell 2004 Table 3.4 reports Aphelion Ratio = 0.95 for cycler 2.1.1.+2, hence aphelion ≈ 0.95 * 1.52 AU = 1.444 AU. Note this is BELOW Mars's semi-major axis: the cycler only reaches Mars when Mars is near its perihelion. Full a, e not directly tabulated in Russell 2004 §3 (those are in the dissertation's Tables 4.x for the more general nπ + generic catalogue).

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no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them).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) ◌ max aphelion ring (sourced)

Not-published gaps (never interpolated):

E → M — segment elements (a, e) not published; no curve drawn.
M → E — segment elements (a, e) not published; no curve drawn.
E → E — segment elements (a, e) not published; no curve drawn.

Real DE440 encounter dates (5)

2031-02-27 V∞ 4.13 / 3.79 km/s
2033-03-18 V∞ 4.13 / 4.17 km/s
2033-05-17 V∞ 3.80 / 3.77 km/s
2035-05-17 V∞ 3.99 / 2.97 km/s
2035-07-26 V∞ 4.20 / 2.72 km/s

Real, verifiable JPL DE440 geometric-match dates (see Launch windows). Positions on the map are idealized; these are the true dates.

Legs (trajectory segments)

E → M: 207 d, 0 revs
Russell 2004 Table 3.4 for 2.1.1.+2: 'Earth->Mars (or aphelion) Time (days): 207'.
M → E: (TOF not published)
Return Mars->Earth leg. Russell 2004 Table 3.4/4.x tabulates only the E->M (or-aphelion) transit time for this row, not the return arc ToF / rev count / per-segment (a,e); tracked in data_gaps.
E → E: (TOF not published)
Intermediate Earth-Earth loop arc(s) that fill the cycler period between Mars encounters (sequence E-E-M-M). Russell's required-geocentric-turn column tabulates 2 Earth flyby(s) for this row, implying 1 intermediate Earth-Earth loop(s). Multi-rev arc(s) — tof_days / n_revs / branch / (a,e) to be set by the multi-rev Lambert solver; represented here as a single structural slot, exact multi-loop topology tracked as uncertain in data_gaps[].

Definition status

incomplete — core fields missing or known-unknowns tracked below

Family: Russell 2-synodic Earth-Mars ballistic · Russell-Ocampo cycler code

Known-unknowns (4)

Values we expect to exist but have not yet filled (distinct from "not applicable"). Tracked per upstream docs/spec.md §16.6.4.

trajectory.segments[ret-me].tof_days [unknown]
Return M->E leg time-of-flight not tabulated by Russell 2004 (Table 3.4/4.x give only the E->M transit time for this row).

source: Russell 2004 dissertation Table 3.4 / 4.x
trajectory.segments[loop-ee] [derive]
Intermediate Earth-Earth loop arc(s) tof_days / n_revs / branch / (a,e) are computable once the multi-rev Lambert solver closes the arc(s) to the published 4.1/2 km/s V-infinity; not yet derived. Russell tabulates only the transit time + aggregate aphelion, not the loop arc(s).

source: multi-rev Lambert solver; Russell 2004 Table 3.4/4.x leg descriptors
trajectory.segments [uncertain]
Segment topology is provisional. sequence_canonical E-E-M-M is the lex-min canonical form; the actual cycle has 2 Earth flyby(s) (Russell required-geocentric-turn column) implying 1 intermediate Earth-Earth loop(s) over the 4.27-yr period. Only a single representative loop-ee slot is materialised here; the full multi-loop decomposition must be verified against Russell 2004 / closed by the solver.

source: Russell 2004 dissertation Table 3.4 / 4.x; multi-rev Lambert solver
trajectory.segments[out-em].a_au [unknown]
Per-segment (a,e) of the outbound transit arc not tabulated by Russell 2004 (orbit_elements.a_au/e are null for the same reason — only the aggregate aphelion ratio is published).

source: Russell 2004 dissertation Table 3.4 / 4.x leg descriptors

Primary citation

Byrnes, D. V. et al. (2002). Analysis of Various Two Synodic Period Earth-Mars Cycler Trajectories. AIAA/AAS Astrodynamics Specialist Conference, Monterey CA, AIAA 2002-4423.

DOI: 10.2514/6.2002-4423

URL: https://arc.aiaa.org/doi/10.2514/6.2002-4423

orbit source Russell 2004, Table 3.4 orbit fidelity circular-coplanar V∞ source Russell 2004, Table 3.4 V∞ fidelity circular-coplanar

Corroborating sources

Russell, R. P. (2004). Global Search and Optimization for Free-Return Earth-Mars Cyclers. Ph.D. dissertation, UT Austin. · link

Notes

Russell explicitly footnotes this entry in Table 3.4 with "d: 'Case 2' cycler described by Byrnes et al [16]" — so attribution belongs to Byrnes/ McConaghy/Longuski 2002. Rogers et al. 2012 also calls it "Case 2" and reports it as having the lowest V_inf_launch (2.522 km/s) and a 171-day Earth-Mars flight time in the analytic ephemeris (Table 4). Russell 2004 Table 3.4 classifies this cycler under the wider ARMIN=0.9 / TRMIN=0.85 "ballistic" net rather than the strict AR>=1.0 AND TR>=1.0 criterion. Strictly, this cycler is near-ballistic: AR=0.95, TR=1.11; the gravity-assist deflection at Mars is short of fully ballistic (aphelion just under Mars's circular-orbit radius) and requires a small powered nudge. The `trajectory_regime: ballistic` field is retained because Russell and the cycler literature group it with the ballistic family; consumers doing powered-flyby DV accounting should still compute the residual.

Source quotes (per-field provenance)

Every numerical value in this entry traces to a verbatim or paraphrased quote from a cited source.

delta_v_kms: Derived from Russell 2004's tabulated AR / TR via the M2 powered-flyby surrogate (src/cyclerfinder/core/flyby.py): ΔV ≈ (V∞_E + V∞_M) × max(0, 1 − TR) + (1 − AR) × (V∞_E + V∞_M) × 0.025 [AR-correction term active only when AR < 1]. Upper bound; biases near-ballistic entries toward 'requires nudge'. Strict-ballistic rows (AR ≥ 1 AND TR ≥ 1) give ΔV = 0 exactly. AR/TR primary values: Russell 2004 Table 3.4, row 2.1.1.+2.
vinf_kms_at_encounters[0].vinf_kms: Russell 2004 Table 3.4, row 2.1.1.+2.
vinf_kms_at_encounters[1].vinf_kms: Russell 2004 Table 3.4, row 2.1.1.+2.
legs[0].tof_days: Russell 2004 Table 3.4, row 2.1.1.+2: Earth->Mars 207 days.
aphelion_au: Russell 2004 Table 3.4 row 2.1.1.+2: Aphelion Ratio 0.95 (his definition: ratio to 1.52 AU = Mars's circular-orbit a). aphelion = 0.95 * 1.52 = 1.444 AU.