U0L1 high-energy zero-loop one-synodic Earth-Mars cycler

mcconaghy-2005-em-u0l1 · source: literature · validation: V0

Signature

Bodies: E-M
Sequence (canonical): E-M
Sense: outbound
Period: 2.140 yr (1 × E-M synodic)
One synodic = 2.135 yr (Earth-Mars synodic period) — k=1 from S=1 in SnLm. Rogers 2012 Table 1 lists U0L1 as having 4 vehicles, consistent with a 1-synodic outbound + inbound x 2 phasing.
Priority date: 2002-08-05

V∞ at encounters

E (#1): — (not published)
Steady-state V_inf at Earth not in Rogers 2012 Table 1. Rogers Table 3 gives V_inf,flyby = 9.801-12.634 km/s for the establishment-cycler 4:3(2)-, 3:2(1)- and 2:1(1)- variants targeting U0L1's orbital elements — substantially higher than the Aldrin cycler's ~5.7 km/s at Earth, reflecting U0L1's high-energy aphelion-3.2-AU orbit (well beyond Mars).
M (#2): — (not published)
Same — steady-state cycling V_inf at Mars not transcribed by Rogers 2012. McConaghy 2005 dissertation is the awaiting source.

Orbit elements (heliocentric)

Semi-major axis a: 2.050 AU
Eccentricity e: 0.563
Perihelion: 0.900 AU
Aphelion: 3.200 AU
Inclination: 0.00°

Rogers et al. 2012 Table 1: 'U0L1 ... Semi-Major Axis 2.05 AU, Eccentricity 0.563, Aphelion Radius 3.20 AU, Perihelion Radius 0.90 AU' (circular-coplanar). U0L1 is the highest-aphelion ballistic Earth-Mars cycler in Rogers' Table 1 — well beyond the asteroid belt's inner edge.

Legs

E → M: 97 d, 0 revs
Rogers 2012 Table 4 (STOUR analytic-ephemeris) row 'U0L1 ... 3:2(1)- ... LD 11/25/2025, TOF 97 days' — the establishment-cycler first-leg ToF. The fast 97-d ToF reflects the high-energy orbit's rapid heliocentric crossing from Earth to Mars; the high V_inf at Mars (8.049 km/s per Rogers Table 4) is the price of the fast transit.

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

The U0L1 cycler is one of the SnLm members enumerated in this broad-class paper (with S=1, L=0 in McConaghy's SnLm notation; the 'U' prefix denotes the up-escalator branch). 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 treatment is McConaghy 2005 Purdue PhD dissertation.

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
Not directly consulted at ingest (Purdue docs.lib not reachable via WebFetch). Cycler chapters subsume the AIAA 2002-4420 broad-class enumeration including U0L1.
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 'U0L1' is the source of the orbital elements used here. Tables 2, 3, 4, 5, 6 give establishment-cycler analysis for U0L1: direct DV from LEO 8.052 km/s, V_inf,flyby 9.801-12.634 km/s, propellant mass savings 45.8 mt via V_inf leveraging.

Notes

U0L1 is the high-energy outlier in Rogers 2012 Table 1's enumeration of established cyclers. In McConaghy's SnLm cycler nomenclature (Russell 2004 dissertation ref [25] McConaghy/Russell/Longuski 2005 JSR "Towards a Standard Nomenclature for Earth-Mars Cycler Trajectories"), the "U" prefix is the up-escalator branch indicator; "0L1" indicates zero intermediate Earth-Earth loops and one synodic period to repeat. U0L1 is the most propulsion-expensive of the cyclers in Rogers 2012 Table 2 (direct LEO DV 8.052 km/s) but also enjoys the largest absolute mass savings from V_inf leveraging (45.8 mt per Rogers Table 6) — a useful test case for V_inf leveraging studies but not a practical candidate for crewed Earth-Mars transit. DATA COMPLETENESS: orbital elements populated from Rogers 2012 Table 1; steady-state cycling V_inf at Earth/Mars left null pending direct access to McConaghy 2005 dissertation or AIAA 2002-4420. M7 matching against finder hits in the high-aphelion (>3 AU) regime can use the orbital-element signature. DISTINGUISHED FROM S1L1: both are one-synodic Earth-Mars cyclers with no intermediate Earth-Mars-Earth loops in the SnLm sense, but S1L1 has L=1 (one intermediate Earth-Earth loop) and aphelion ~1.64 AU just inside Mars's orbit, whereas U0L1 has L=0 (zero intermediate Earth loops) and aphelion 3.20 AU far beyond Mars. The "U" prefix distinguishes the up-escalator (outbound-to-Mars) branch from the down-escalator (inbound-to-Earth) branch on the same family.

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: 'U0L1 ... Semi-Major Axis, AU: 2.05'.
e: Rogers et al. 2012 Table 1: 'U0L1 ... Eccentricity: 0.563'.
perihelion_au: Rogers et al. 2012 Table 1: 'U0L1 ... Perihelion Radius, AU: 0.90'.
aphelion_au: Rogers et al. 2012 Table 1: 'U0L1 ... Aphelion Radius, AU: 3.20'.
legs[0].tof_days: Rogers et al. 2012 Table 4 (STOUR analytic-ephemeris results): row 'U0L1, 3:2(1)-, LD 11/25/2025, TOF 97 days, Periapse 0.960 AU, Apoapse 3.189 AU, V_inf,launch 3.702 km/s, V_inf,flyby 8.049 km/s, h_flyby 6,633 km'. The 97-day TOF is the establishment-cycler first-leg ToF.
period.years: Period = k * synodic = 1 * 2.135 yr = 2.14 yr; derived from S=1 in the SnLm classification. Consistent with the 4-vehicle manifest in Rogers 2012 Table 1 (outbound + inbound x 2 phases).