← Catalogue

S1L1 ballistic two-synodic-period Earth-Mars cycler

s1l1-2syn-em-cpom · 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

single-ellipse

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)

Priority date

2002-08-05

V∞ at encounters

E (encounter 1)

5.65 km/s

Per spec.md §9 and corroborating sources, the S1L1 ballistic two-synodic-period cycler has 'low V-infinity at Earth and Mars (5.65 and 3.05 km/s, respectively)'. This is the spec-anchored M5 milestone value. PROVENANCE (updated, 2026-06-19): the spec-9 value is now CORROBORATED as within the published real-ephemeris envelope of Byrnes-McConaghy-Longuski 2002 ('Analysis of Various Two Synodic Period Earth-Mars Cycler Trajectories', AIAA/AAS Monterey Aug 2002) — its Case-3 (S1L1-B near-twin) real-eph table spans Earth v∞ 4.15–7.44 km/s, which CONTAINS 5.65. The McConaghy S1L1-B literal pair is 4.7 km/s (the resonant near-twin). Earlier caveat retained for history: not literal-matched in Patel 2019 (3.657 km/s flyby) / McConaghy 2006; the Byrnes 2002 envelope is the first published source to bracket the spec value. See data_gaps[] entry.

M (encounter 2)

3.05 km/s

Per spec.md §9 — the published 2-synodic E-M cycler V_inf at Mars. PROVENANCE (updated, 2026-06-19): the spec-9 value 3.05 is now CORROBORATED as within the published real-ephemeris envelope of Byrnes-McConaghy-Longuski 2002 (AIAA/AAS Monterey Aug 2002) — its Case-3 (S1L1-B near-twin) real-eph table spans Mars v∞ 2.97–7.83 km/s, which CONTAINS 3.05 (at the low edge). The McConaghy S1L1-B literal Mars pair is 5.0 km/s. Earlier caveat retained for history: not literal-matched in any prior mined source (Patel 2019 no Mars v∞; McConaghy 2006 abstract 5.0; Sanchez Net 2022 5.2–7.3). The Byrnes 2002 envelope is the first published source to bracket the spec value. See data_gaps[] entry.

Orbit elements (heliocentric)

Semi-major axis a

1.300 AU

Eccentricity e

0.257

Perihelion

0.970 AU

Aphelion

1.640 AU

Inclination

0.00°

Per Rogers et al. 2012 Table 1, the S1L1 cycler has these orbital elements (4 vehicles, circular-coplanar). NB Rogers 2012 reports V_inf values at the 4:3(2)- Aldrin establishment epoch (2.04 km/s launch, 3.51 km/s flyby — Table 3) which differ from the steady-state S1L1 cycling V_inf of 5.65/3.05 quoted elsewhere; the difference is the V-infinity leveraging maneuver context vs. nominal cycler operation.

Legs (trajectory segments)

• E → M: 154 d, 0 revs
  Per Mistree/Kornfeld 2019 (cited via search) and Spreen et al. 2020 'Design Considerations for an Earth-Mars Cycler Spacecraft Using the S1L1 Cycler': 'a nominal 154-day trajectory'. NB Russell 2004 Table 4.9 has the McConaghy 2006 'notable' variant at t_out=150 d; the 154-d figure is for the S1L1 specifically.
• M → E: (TOF not published)
  PROVISIONAL / likely mismodelled: there is no defined direct Mars->Earth leg in the S1L1 architecture. In the McConaghy/Longuski/Byrnes nomenclature S and L denote consecutive Earth-to-Earth resonant intervals, not Earth<->Mars transits; Mars is a flyby target of opportunity on the outbound arc. A single S1L1 vehicle gives one-way fast transit only — the crewed return uses a mirrored companion cycler (conjugate L1S1). This segment should be replaced by the S1/L1 Earth-to-Earth resonant intervals; see data_gaps.
• E → E: (TOF not published)
  The single intermediate Earth-Earth loop that gives S1L1 its 'L1'; fills the remainder of the ~1559.86-d (2-synodic) period. Multi-rev arc — n_revs/branch to be set by the multi-rev Lambert solver.

Definition status

incomplete — core fields missing or known-unknowns tracked below

Family: S1L1 Earth-Mars 2-synodic · McConaghy SnLm

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.

• vinf_kms_at_encounters [unverified-provenance]
  The 5.65/3.05 km/s pair traces only to spec.md §9 and could NOT be corroborated in any mined primary source. Patel 2019 (which cites McConaghy 2006 throughout) gives Earth flyby v∞ 3.657 km/s and NO Mars v∞ in the circular-coplanar model. The near-ballistic real-date regime (Sanchez Net 2022, JSR 59(3):861-870) gives Mars v∞ 5.2–7.3 km/s and Earth 3.6–5.7 km/s — none matching 5.65/3.05. McConaghy 2006 JSR 43(2):456-465 abstract gives ≈4.7 km/s Earth / 5.0 km/s Mars for the real-ephemeris case. The values are retained in place (not overwritten) pending access to the McConaghy 2006 full text.
  source: McConaghy 2006 JSR 43(2):456-465 full text
• trajectory.segments[ret-me] [uncertain]
  No direct Mars->Earth leg ToF exists to extract: it is undefined by construction. The S/L labels denote Earth-to-Earth resonant intervals (S1 short, L1 long), not Earth<->Mars transits; Mars is a flyby target of opportunity on the outbound arc, and the crewed return uses a mirrored conjugate L1S1 cycler. The fix is to re-model the post-Mars arc as the S1/L1 Earth-to-Earth resonant intervals, not to back-fill a return ToF. NB the day-count breakdown of S1 vs L1 is not reconciled against a single citation and must not be invented.
  source: McConaghy/Longuski/Byrnes 2002, AIAA 2002-4420; nomenclature: McConaghy/Russell/Longuski 2005
• trajectory.segments[loop-ee] [derive]
  Intermediate Earth-Earth loop tof_days / n_revs / branch are computable once the in-house multi-rev Lambert solver closes the arc to the published 5.65/3.05 km/s V-infinity; not yet derived.
  source: multi-rev Lambert solver
• trajectory.segments [uncertain]
  Segment topology is provisional AND the current 3-segment E->M / M->E / E-loop skeleton is structurally wrong: it posits a direct Mars->Earth leg that the S1L1 nomenclature does not define. Correct model: outbound E->M (~154 d) with a ballistic Mars flyby, then the S1 (short) and L1 (long) Earth-to-Earth resonant intervals carry the vehicle back to its next Earth flyby to repeat. Re-derive the S1/L1 interval ToF / n_revs / branch from the in-house multi-rev Lambert solver constrained to the published 5.65/3.05 km/s V-infinity; do not invent interval day-counts. probe work showed the naive 3-leg fixed-154-d structure does not close ballistically, consistent with the mismodelled return leg.
  source: McConaghy/Longuski/Byrnes 2002, AIAA 2002-4420

Primary citation

McConaghy, T. T. et al. (2002). Analysis of a Broad Class of Earth-Mars Cycler Trajectories. AIAA/AAS Astrodynamics Specialist Conference, Monterey CA, AIAA 2002-4420.

DOI: 10.2514/6.2002-4420

S1L1 nomenclature originates with McConaghy/Russell/Longuski's standard nomenclature paper (ref [25] in Russell 2004); the S1L1 cycler itself is one entry in the broader class catalogued by McConaghy/Longuski/Byrnes 2002 (Russell 2004 ref [17]).

orbit source Rogers et al. 2012, Table 1 orbit fidelity circular-coplanar V∞ source McConaghy et al. 2002 V∞ fidelity circular-coplanar

Corroborating sources

• McConaghy, T. T. et al. (2005). Towards a Standard Nomenclature for Earth-Mars Cycler Trajectories. Journal of Spacecraft and Rockets (in press as of Russell 2004 ref [25]).
• Spreen, C. & et al. (2020). Design Considerations for an Earth-Mars Cycler Spacecraft Using the S1L1 Cycler. Journal of Spacecraft and Rockets. DOI: 10.2514/1.A35160
  Modern design study using the S1L1 cycler; reports 154-d nominal Earth-Mars transfer time.
• Rogers, B. A. et al. (2012). Preliminary Analysis of Establishing Cycler Trajectories Between Earth and Mars via V-Infinity Leveraging. AIAA 2012-4746. DOI: 10.2514/6.2012-4746
  Table 1 of this paper has the S1L1 orbital elements row used here.

Notes

The "S1L1" name follows the standard Earth-Mars cycler nomenclature proposed by McConaghy/Russell/Longuski (Russell 2004 dissertation ref [25]): "S" = (number of synodic periods in cycler) preceded by S, "L" = number of intermediate Earth-Earth loops, and the trailing 1's encode the leg types. This is the cycler the spec §9 M5 milestone references with V_inf = "5.65 km/s (E), 3.05 km/s (M)". It is NOT the same as the McConaghy 2006 "Notable" cycler (which has V_inf 4.7/5.0); both are two-synodic E-M cyclers with one intermediate Earth encounter, but they belong to different families in the McConaghy/Longuski/Byrnes 2002 (AIAA 2002-4420) broad-class taxonomy. Rogers et al. 2012 Table 1's S1L1 entry shows (a, e, peri, apo) = (1.30, 0.257, 0.97, 1.64) which gives aphelion comfortably inside Mars's aphelion of ~1.67 AU only marginally — implying the Mars encounter happens near the cycler's aphelion. This matches the low V_inf at Mars (3.05 km/s): the cycler "catches up" to Mars near its slowest point in its heliocentric motion.

Source quotes (per-field provenance)

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

a_au

Rogers et al. 2012, Table 1: 'S1L1... Semi-Major Axis, AU: 1.30'.

e

Rogers et al. 2012, Table 1: 'S1L1... Eccentricity: 0.257'.

perihelion_au

Rogers et al. 2012, Table 1: 'S1L1... Perihelion Radius, AU: 0.97'.

aphelion_au

Rogers et al. 2012, Table 1: 'S1L1... Aphelion Radius, AU: 1.64'.

vinf_kms_at_encounters[0].vinf_kms

Spec.md §9: "Published 2-synodic E-M V_inf | ≈ 5.65 km/s (E), 3.05 km/s (M)". Corroborated by web search snippets attributing these to the S1L1 cycler ('A cycler that repeats every two synodic periods has a low V-infinity at Earth and Mars (5.65 and 3.05 km/s, respectively)').

vinf_kms_at_encounters[1].vinf_kms

Spec.md §9 (same as above).

legs[0].tof_days

Search result: "The S1L1 cycler is designed to transfer a crew of six from Earth to Mars on a nominal 154-day trajectory." — multiple secondary sources citing Spreen et al. 2020 (DOI 10.2514/1.A35160).

period.years

Period = 2 x 2.135 = 4.27 yr; derived from cycler being two-synodic.