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

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

Signature

Bodies: E-M
Primary: Sun (default — heliocentric)
Sequence (canonical): E-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: 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.
Fleet size: 4 vehicles
Priority date: 2002-08-05

V∞ at encounters

E (encounter 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 (encounter 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.

Orbit view 2.5D ecliptic projection

spacecraft: idealized coplanar ellipse planets: J2000 osculating ellipse (Standish & Williams Table 1) clock: idealized phase clock (no epoch) orientation: coplanar-idealized (no Ω/ω published — in-plane ellipse) encounters: time-true on the idealized phase clock (real mean motions, phase chosen so the geometry's encounters occur)

Encounter proximity — spacecraft↔planet distance over one period; the dips are the encounters

Earth min 171447 km

Mars min 0.029 AU

Edge-on (X–Z) — i = 0° (coplanar-idealized — flat in this view)

— — planet orbit (true J2000 ellipse) ——— cycler ellipse ○ △ □ encounters (E, M)

Legs (trajectory segments)

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. a/e are the cycler ellipse from Rogers 2012 Table 1.
M → E: (TOF not published)
Return Mars->Earth leg of the 1-synodic U0L1 cycle. ToF not extracted from Rogers 2012 / AIAA 2002-4420; tracked in data_gaps. a/e assumed equal to the outbound arc's cycler ellipse pending the steady-state per-leg decomposition.

Definition status

incomplete — core fields missing or known-unknowns tracked below

Family: U0L1 Earth-Mars 1-synodic high-energy · McConaghy SnLm

Known-unknowns (1)

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[ret-me].tof_days [unknown]
Return M->E leg time-of-flight not tabulated by Rogers 2012; needs the McConaghy 2005 dissertation / AIAA 2002-4420 steady-state cycler decomposition.

source: McConaghy 2005 Purdue PhD AAI3166673 / 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

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.

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

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).