Case 1 ballistic two-synodic-period Earth-Mars cycler (S2L1 family)

mcconaghy-2005-em-case1 · source: literature · validation: V0

Signature

Bodies: E-M
Sequence (canonical): E-E-M-M
Sense: outbound
Period: 4.270 yr (2 × E-M synodic)
Two Earth-Mars synodic periods = 2 x 2.135 yr = 4.27 yr; consistent with the four-vehicle count in Rogers 2012 Table 1 (one vehicle per outbound/inbound branch x 2 synodic phases).
Priority date: 2002-08-05

V∞ at encounters

E (#1): — (not published)
Steady-state cycling V_inf at Earth not in Rogers 2012 Table 1 (Table 1 gives orbital elements only). Rogers 2012 Table 3 reports the 4:3(2)- establishment-cycler V_inf,flyby = 3.378 km/s (the post-Earth flyby V_inf for the establishment trajectory matching Case 1's orbital elements). McConaghy/Longuski/Byrnes 2002 AIAA 2002-4420 (paywalled at AIAA) is the originating source for the steady-state cycler V_inf; Russell 2004 Table 3.4 does not pair "Case 1" to a Russell-numbered row (only Case 2 = 2.1.1.+2 and Case 3 = 2.3.1.+1 are footnoted).
M (#2): — (not published)
Same — steady-state V_inf at Mars not transcribed by Rogers 2012; awaiting direct access to McConaghy 2005 dissertation or AIAA 2002-4420.

Orbit elements (heliocentric)

Semi-major axis a: 1.220 AU
Eccentricity e: 0.238
Perihelion: 0.930 AU
Aphelion: 1.510 AU
Inclination: 0.00°

Rogers et al. 2012 Table 1: 'Case 1 ... Semi-Major Axis 1.22 AU, Eccentricity 0.238, Aphelion Radius 1.51 AU, Perihelion Radius 0.93 AU' (circular-coplanar model). 0.0 inclination follows from the modelling assumption.

Legs

E → M: 365 d, 0 revs
Rogers 2012 Table 4 (STOUR analytic-ephemeris establishment trajectory) reports TOF = 365 days for the 4:3(2)- Case 1 trajectory. Note this is the establishment-cycler first-leg ToF, not necessarily the steady-state cycler nominal; McConaghy 2005 dissertation would give the steady-state value.

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

First publication of the broad-class enumeration that includes Case 1. The journal version is McConaghy/Longuski 2004 JSR 'Analysis of a Class of Earth-Mars Cycler Trajectories' (DOI 10.2514/1.11939, paywalled). The comprehensive dissertation treatment is McConaghy 2005 Purdue PhD.

Corroborating sources

McConaghy, T. T. (2005). Design and optimization of interplanetary spacecraft trajectories. Ph.D. dissertation, School of Aeronautics and Astronautics, Purdue University; ProQuest / Purdue e-Pubs AAI3166673. · link
Comprehensive dissertation; not directly consulted at ingest (Purdue docs.lib not reachable via WebFetch; ProQuest dissertation full text behind subscription). Cycler chapters subsume the AIAA 2002-4420 broad-class enumeration and the JSR 2004 paper.
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 row 'Case 1' is the source of the orbital elements used here. Table 4 STOUR analytic-ephemeris establishment-cycler entry gives the 365-day Earth-to-Mars time-of-flight; Table 3 genetic-algorithm row 4:3(2)- Case 1 reports V_inf flyby of 3.300-3.378 km/s for the establishment trajectory.

Notes

"Case 1" is the third (alongside Case 2 and Case 3) of the two-synodic- period ballistic cyclers tabulated in McConaghy/Longuski/Byrnes 2002 AIAA 2002-4420 and the Byrnes/McConaghy/Longuski 2002 AIAA 2002-4423 follow-on ("Analysis of Various Two Synodic Period Earth-Mars Cycler Trajectories"). The SnLm classification is S2L1: 2 synodic periods, 1 intermediate Earth-Earth loop between Mars encounters. Russell 2004 Table 3.4 footnotes only Cases 2 (= Russell 2.1.1.+2) and 3 (= Russell 2.3.1.+1) to Byrnes 2002; Case 1 is not footnoted to a specific Russell row in the dissertation excerpt visible from the UT Austin abstract page, but it shares the same generic family. Among the four McConaghy-Byrnes-Longuski 2002 two-synodic-period cyclers, Rogers 2012 §III.A flags Case 2 as having the lowest launch V_inf and shortest 171-day Earth-Mars flight time in the analytic ephemeris (Table 4). Case 1 has the longest first-leg ToF (365 d, Rogers Table 4) — implying the spacecraft completes roughly one full heliocentric orbit before reaching Mars on its first leg, distinguishing it geometrically from Cases 2/3. DATA COMPLETENESS: orbital elements (a, e, peri, apo) populated from Rogers 2012 Table 1. Steady-state cycling V_inf values left null pending direct access to McConaghy 2005 dissertation or the AIAA 2002-4420 / JSR 2004 papers. M7 matching against finder hits can use the orbital-element signature without the V_inf multiset. The 4:3(2)- prefix in Rogers 2012 Tables 3-5 refers to the V_inf-leveraging K:L(M)+/- notation introduced in their Nomenclature table: K = number of Earth orbit revolutions, L = number of spacecraft orbit revolutions, M = spacecraft orbit revolution on which the deep-space maneuver is performed, with +/- denoting flyby before (-) or after (+) perihelion. This is a separate nomenclature from McConaghy's SnLm cycler classification.

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: 'Case 1 ... Semi-Major Axis, AU: 1.22'.
e: Rogers et al. 2012 Table 1: 'Case 1 ... Eccentricity: 0.238'.
perihelion_au: Rogers et al. 2012 Table 1: 'Case 1 ... Perihelion Radius, AU: 0.93'.
aphelion_au: Rogers et al. 2012 Table 1: 'Case 1 ... Aphelion Radius, AU: 1.51'.
legs[0].tof_days: Rogers et al. 2012 Table 4 (STOUR analytic-ephemeris results): row 'Case 1, 4:3(2)-, LD 12/14/2024, TOF 365 days, Periapse 0.946 AU, Apoapse 1.503 AU' — the 365-day TOF for the first leg of the establishment-cycler trajectory that matches the Case 1 cycler orbital elements.
period.years: Period = k * synodic = 2 * 2.135 yr = 4.27 yr; derived from the two-synodic-period family membership confirmed by Rogers 2012 §III.A "various two synodic period cyclers".