McConaghy/Landau/Yam/Longuski two-synodic-period Earth-Mars cycler

mcconaghy-2006-em-k2 · 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: Essentially ballistic · source: mcconaghy-2006
Model assumption: circular-coplanar
Idealised: planets on circles, coplanar ecliptic.
Period: 4.270 yr (2 × E-M synodic)
Two Earth-Mars synodic periods = 2 x 2.135 yr = 4.27 yr.
Priority date: 2003-08-01

V∞ at encounters

E (encounter 1): 4.70 km/s
From the McConaghy 2006 abstract: 'arrival V-infinity magnitudes of 4.7 km/s at Earth and 5.0 km/s at Mars' (circular-coplanar model).
M (encounter 2): 5.00 km/s
From the McConaghy 2006 abstract.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): 2.65
Transit times (days): 153 d, 153 d

Russell 2004 dissertation Table 4.9 row 1 ("4.99 a", footnote a: "documented in Ref. 15", i.e. McConaghy 2002 AIAA 2002-4420 — the precursor paper that became McConaghy 2006 JSR). Russell's parent- cycler list (Table 5.5 and Appendix C) tags row 1 as parent cycler 4.991gG2 (no. 83), and Chapter 5 §5.5 explicitly states "cycler 4.991gG2 (no. 83)... Also known as the 'S1L1' cycler" (dissertation line 7416). The table directly tabulates aphelion = 1.64 AU and V_inf at Earth = 4.99 km/s, V_inf at Mars = 5.10 km/s, t_out = t_in = 150 days, TR = 2.65. Russell does NOT tabulate (a, e, perihelion) directly because the cycler is a piecewise sequence of two generic-return arcs, not a single Keplerian ellipse — each leg has its own (a, e). Only the maximum aphelion is well-defined for the cycler as a whole. Therefore a_au, e, perihelion_au remain null; aphelion_au backfilled from Russell Table 4.9 row 1. The McConaghy 2006 paper itself (DOI 10.2514/1.15215, paywalled at AIAA 403) presumably has higher-precision per-leg orbital elements but is not directly accessible. The 2-decimal Russell values are sufficient for M7 canonical-signature matching.

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)

2031-03-09 V∞ 5.13 / 5.45 km/s
2033-04-17 V∞ 3.19 / 4.72 km/s
2033-05-17 V∞ 4.72 / 3.82 km/s
2035-05-27 V∞ 4.44 / 5.23 km/s
2035-07-26 V∞ 4.56 / 3.09 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: 153 d, 0 revs
Earth->Mars transfer time per McConaghy 2006 abstract: '153-day transfer times between Earth and Mars'. Note Rogers et al. 2012 reports 154-day for the S1L1 variant in the establishment-cycler context; the 153-day value is the cycler's nominal.
M → E: 153 d, 0 revs
Symmetric return leg, same ToF. Per the abstract this cycler is symmetric.
E → E: (TOF not published)
The single intermediate Earth-Earth loop of this 2-synodic ('L1') cycler; fills the remainder of the 4.27-yr period between the two Mars encounters. Multi-rev arc — tof_days / n_revs / branch / (a,e) to be set by the multi-rev Lambert solver.

Free-return arcs (Russell decomposition)

Russell's Earth-to-Earth free-return arcs (spec §16.7.7) — a decomposition distinct from the encounter legs above. A single arc spans what the catalogue models as two or more encounter segments.

Arc type	Resonance	TOF (yr)	Raw descriptor
generic	—	1.4612	g(1.4612,526.02,Ll)
generic	—	2.8096	G(2.8096,651.46,U)

Flyby altitudes (minimal-thrust)

Per-flyby periapsis altitude that delivers each encounter's required turn ballistically, capped at the body's safe flyby floor (200 km for Earth/Mars). A flyby sitting at the floor is bend-binding (it needs the deepest safe pass); higher altitudes are gentler flybys that need less turn. · source: computed-m7

Node	Body	Altitude (km)
1	E	31,746.2
2	M	12,978.8
3	E	26,605.5
4	E	38,988.4
5	M	10,680.7
6	E	22,915.9
7	E	9,768.6
8	M	16,223.4
9	E	27,190.8
10	E	23,834.5
11	M	13,254.7
12	E	25,276.2
13	E	38,006.8
14	M	6,022.5
15	E	21,315.3
16	E	30,873.1
17	M	6,144.3
18	E	22,826.9
19	E	200.3
20	M	20,610.5

Definition status

incomplete — core fields missing or known-unknowns tracked below

Family: S2L1 Earth-Mars 2-synodic (McConaghy 'Notable') · McConaghy SnLm

Known-unknowns (3)

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[loop-ee] [derive]
Intermediate Earth-Earth loop tof_days / n_revs / branch / (a,e) are computable once the in-house multi-rev Lambert solver closes the arc to the published 4.7/5.0 km/s V-infinity; not yet derived.

source: multi-rev Lambert solver
trajectory.segments[out-em].a_au [unknown]
Per-segment (a,e) of the outbound generic-return arc not in the McConaghy 2006 abstract; orbit_elements.a_au/e are null for the same reason (piecewise generic-return arcs, not a single ellipse). Full paper (DOI 10.2514/1.15215, AIAA 403) would have higher-precision per-leg elements.

source: McConaghy/Landau/Yam/Longuski 2006 JSR, DOI 10.2514/1.15215
trajectory.segments[ret-me].a_au [unknown]
Per-segment (a,e) of the symmetric return arc not in the abstract; same source gap as out-em.

source: McConaghy/Landau/Yam/Longuski 2006 JSR, DOI 10.2514/1.15215

Primary citation

McConaghy, T. T. et al. (2006). Notable Two-Synodic-Period Earth-Mars Cycler. Journal of Spacecraft and Rockets, Vol. 43, No. 2, pp. 456-465.

DOI: 10.2514/1.15215

URL: https://arc.aiaa.org/doi/10.2514/1.15215

orbit source Russell 2004, Tables 4.9 / 4.13 orbit fidelity circular-coplanar V∞ source McConaghy et al. 2006 V∞ fidelity circular-coplanar

Corroborating sources

McConaghy, T. T. et al. (2003). Two-Synodic-Period Earth-Mars Cyclers with Intermediate Earth Encounter. AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 03-509.
Conference precursor to the 2006 JSR paper. Russell 2004 dissertation cites this as ref [15].

Notes

Spec.md §9 anchors the M5 milestone to "5.65 km/s (E), 3.05 km/s (M)" for the published 2-synodic E-M cycler. Those numbers do NOT match the McConaghy 2006 abstract's "4.7 km/s at Earth and 5.0 km/s at Mars". Resolution: the 5.65 / 3.05 pair corresponds to a DIFFERENT 2-synodic cycler — specifically the S1L1 cycler popularised by Aldrin Enterprises' CPOM (Cycling Pathways to Occupy Mars) studies; see the next entry `s1l1-2syn-em-cpom`. Both are 2-synodic, both have one intermediate Earth encounter, but they are different family members. M5 should test against the S1L1 numbers per the spec. Russell 2004 dissertation Table 4.9 lists five ballistic 2-synodic cyclers; the McConaghy 2006 'notable' one is the first row (V_inf,E=4.99, V_inf,M=5.10, t_out=t_in=150d, aphelion 1.64 AU, TR=2.65, leg descriptor "g(1.4612,526.02,Ll) G(2.8096,651.46,U)" — two generic- return arcs of 1.46 yr and 2.81 yr respectively, summing to the 4.27-yr 2-synodic period). The row carries footnote 'a' = "documented in Ref. 15", referring to McConaghy/Longuski/Byrnes AIAA 2002-4420. Russell's parent-cycler list tags this row as 4.991gG2 no. 83 (dissertation lines 7416, 8008, 8600). Russell's V_inf values (4.99/5.10) differ from McConaghy 2006's (4.7/5.0) by ~0.3 km/s at Earth and ~0.1 km/s at Mars; the most plausible explanation is that McConaghy 2006 reports realistic-ephemeris optimised values whereas Russell Table 4.9 reports the circular-coplanar simple-model values, not pure rounding. Both are valid characterisations of the same underlying ballistic cycler; M7 matching tolerances should be wide enough (~0.5 km/s on V_inf, ~10 d on ToF) to collapse them under the canonical signature. The Russell entry for this cycler is catalogued separately as `russell-ch4-4.991gG2` with the circular-coplanar values + Russell- convention attribution. M7 should collapse the two via the canonical signature (V_inf multiset + ToF + period rounded to whole-number days).

Source quotes (per-field provenance)

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

vinf_kms_at_encounters[0].vinf_kms: McConaghy et al. 2006 abstract (quoted via search.arc.aiaa.org/doi/10.2514/1.15215 and corroborated by McConaghy 2006 Request PDF on ResearchGate): "In a circular-coplanar model it requires no propulsive maneuvers, has 153-day transfer times between Earth and Mars, and has arrival V-infinity magnitudes of 4.7 km/s at Earth and 5.0 km/s at Mars."
vinf_kms_at_encounters[1].vinf_kms: McConaghy et al. 2006 abstract: "...4.7 km/s at Earth and 5.0 km/s at Mars."
legs[0].tof_days: McConaghy et al. 2006 abstract: "153-day transfer times between Earth and Mars".
legs[1].tof_days: McConaghy et al. 2006 abstract: same 153-day value implied by symmetry ('transfer times between Earth and Mars' — plural, both directions).
period.years: Period = 2 x synodic = 2 x 2.135 = 4.27 yr; derived value not quoted as such in McConaghy 2006 (the abstract says "every two synodic periods").
orbit_elements.aphelion_au: Russell 2004 dissertation Table 4.9 (page 127), row 1 of 5 rows. Header column "aphel. (AU)" lists 1.64 for this row. The row is tagged with footnote 'a' = "documented in Ref. 15" (McConaghy et al. AIAA 2002-4420). Russell Chapter 5 (line 7416 of pdftotext extraction from /tmp/russell-2004.txt) explicitly identifies this row as "cycler 4.991gG2 (no. 83)... Also known as the 'S1L1' cycler". Note: Russell's "aphelion" column means the maximum orbit aphelion across both legs; the cycler is not a single Keplerian ellipse but a piecewise sequence of two generic-return arcs.