S1L1 ballistic two-synodic-period Earth-Mars cycler

s1l1-2syn-em-cpom · source: literature · validation: V0

Signature

Bodies: E-M
Sequence (canonical): E-E-M-M
Sense: outbound
Period: 4.270 yr (2 × E-M synodic)
Priority date: 2002-08-05

V∞ at encounters

E (#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.
M (#2): 3.05 km/s
Per spec.md §9 — the published 2-synodic E-M cycler V_inf at Mars.

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

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.

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]).

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.