Aldrin classic Earth-Mars cycler (outbound / up-escalator, 1 synodic)

aldrin-classic-em-k1-outbound · source: literature · validation: V0

Signature

Bodies: E-M
Sequence (canonical): E-M
Sense: outbound
Period: 2.135 yr (1 × E-M synodic)
Cycler period = 1 Earth-Mars synodic period; 2.135 yr is the synodic value used throughout this catalogue (see spec §9). Wikipedia/Hollister tables sometimes quote 2.02 yr for the Aldrin cycler — that is the orbital period of the heliocentric ellipse, NOT the cycler repeat period; the cycler still re-encounters Earth at the synodic cadence via the gravity assist.
Priority date: 1985-10-28

V∞ at encounters

E (#1): 6.50 km/s
Russell 2004 dissertation Table 3.4, cycler 1.0.1.-1 (footnoted as the Aldrin cycler). Rogers/Hughes/Longuski/Aldrin 2012 Table 4 reports V_inf,flyby ranging 5.51-6.55 km/s in the analytic ephemeris model for the 4:3(2)- and 3:2(1)- Aldrin trajectories.
M (#2): 9.70 km/s
Russell 2004 dissertation Table 3.4, cycler 1.0.1.-1 (Aldrin). This is the heliocentric V_inf at Mars in the simplified circular-coplanar model; the Aldrin geometry sacrifices V_inf at Mars to keep V_inf at Earth low and the E->M transit short (146 d).

Orbit elements (heliocentric)

Semi-major axis a: 1.600 AU
Eccentricity e: 0.393
Perihelion: 0.970 AU
Aphelion: 2.230 AU
Inclination: 0.00°

Values per Rogers/Hughes/Longuski/Aldrin 2012 Table 1, attributed there to the Aldrin cycler. Spec.md §9 quotes a≈1.659, e≈0.41, peri≈0.98, apo≈2.34 — those are also literature-cited but appear to come from a different rounding/source convention (possibly an early SAIC presentation or the original Aldrin 1985 talk). See docs/known-cyclers.md 'Outstanding questions' for the discrepancy. M3 test tolerances (±0.01 AU on a, ±0.02 on e) absorb both numbers.

Legs

E → M: 146 d, 0 revs
Earth->Mars outbound transit. Confirmed in multiple sources: Wikipedia (citing McConaghy/Longuski/Byrnes 2002 p. 6), Rogers et al. 2012 (Table 4 STOUR ephemeris ToF: 161-172 d depending on K:L(M) variant — the 146-d value is the circular-coplanar idealization).
M → E: 634 d, 0 revs
REVIEW FIX (2026-05-31): Corrected from 519. The residual arithmetic in the previous draft was flawed. T_cycler (779.8 days) - outbound tof (146 days) = 633.8 days. The cycler completes the remainder of its 2.135-year period on this return leg without breaking into sub-legs, so 634 days is the correct aggregate return ToF for the 1-synodic Aldrin in the simplified model.

Primary citation

Aldrin, B. (1985). Cyclic Trajectory Concepts. SAIC presentation to the Interplanetary Rapid Transit Study Meeting, JPL.

The original presentation is not online; citation per Rogers et al. 2012 ref [8] and Russell 2004 dissertation ref [13]. The first peer-reviewed elaboration is Byrnes/Longuski/Aldrin 1993 (DOI 10.2514/3.25519, see corroborating_sources).

Corroborating sources

Byrnes, D. V. et al. (1993). Cycler Orbit Between Earth and Mars. Journal of Spacecraft and Rockets, Vol. 30, No. 3, pp. 334-336. DOI: 10.2514/3.25519
Friedlander, A. L. et al. (1986). Circulating Transportation Orbits Between Earth and Mars. AIAA/AAS Astrodynamics Conference, Williamsburg VA, AIAA 86-2009-CP. DOI: 10.2514/6.1986-2009
Rogers, B. A. et al. (2012). Preliminary Analysis of Establishing Cycler Trajectories Between Earth and Mars via V-Infinity Leveraging. AIAA/AAS Astrodynamics Specialist Conference, Minneapolis MN, AIAA 2012-4746. DOI: 10.2514/6.2012-4746
Russell, R. P. (2004). Global Search and Optimization for Free-Return Earth-Mars Cyclers. Ph.D. dissertation, University of Texas at Austin, Department of Aerospace Engineering. · link
Russell's dissertation Table 3.4 lists the Aldrin cycler as 'cycler 1.0.1.-1' with V_inf 6.5 (Earth), 9.7 (Mars), E->M time 146 d, Aphelion Ratio 1.47 (=> aphelion 1.47 x 1.52 AU = 2.23 AU).

Notes

The "outbound" / "up escalator" branch. Aldrin's original concept includes a complementary "inbound" / "down escalator" cycler that is the time-mirror image (short Mars->Earth, long Earth->Mars). Per Russell 2004 dissertation section 3.8: "Due to symmetry, the energy properties for inbound and outbound cyclers are identical." The inbound cycler is separately catalogued as `aldrin-classic-em-k1-inbound` so the search validates both directional geometries; M7 will collapse them under one identity at the matching stage via signature canonicalisation. Russell 2004 dissertation section 3.8 footnote 'c' explicitly identifies cycler 1.0.1.-1 in Table 3.4 as "Aldrin cycler". This is the only entry in the dissertation explicitly labelled Aldrin. Spec §9 anchor values (a≈1.659, e≈0.41, peri≈0.98, apo≈2.34, E->M 146 d) vs. the Rogers 2012 / Russell 2004 / Wikipedia values (a=1.60, e=0.393, peri=0.97, apo=2.23, E->M 146 d): the discrepancy is real but the test tolerances in docs/phases/m3-model-construct/plan.md §4.3 (TOL_A_AU=0.01, TOL_E=0.02, TOL_PERI_AU=0.02, TOL_APO_AU=0.02) are too tight to absorb the gap between the two value sets. M3 implementers MUST reconcile this before the gate test passes — either widen tolerances or pick the value set that matches the construction the code actually produces from the M1 circular-coplanar ephemeris (which uses sma_E=1.00000261, sma_M=1.52371034). See docs/known-cyclers.md "Outstanding questions" §A. Russell 2004 Table 3.4 classifies this cycler under the wider ARMIN=0.9 / TRMIN=0.85 "ballistic" net rather than the strict AR>=1.0 AND TR>=1.0 criterion. Strictly, this cycler is near-ballistic: AR=1.47, TR=0.86; the gravity-assist deflection at Mars is short of fully ballistic and requires a small powered nudge. The `trajectory_regime: ballistic` field is retained because Russell and the cycler literature group it with the ballistic family; consumers doing powered-flyby DV accounting should still compute the residual.

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 'Orbital elements and number of vehicles for selected cycler trajectories': "Aldrin Cycler ... Semi-Major Axis, AU: 1.60". Same value derivable from Russell 2004 Table 3.4 (Aldrin = cycler 1.0.1.-1) via Aphelion Ratio 1.47 and the geometry.
e: Rogers et al. 2012, Table 1: "Aldrin Cycler ... Eccentricity: 0.393". Consistent with Wikipedia's quotation of the same value, attributed there to "Byrnes, Longuski & Aldrin 1993, pp. 334-335" [9].
perihelion_au: Rogers et al. 2012, Table 1: "Aldrin Cycler ... Perihelion Radius, AU: 0.97".
aphelion_au: Rogers et al. 2012, Table 1: "Aldrin Cycler ... Aphelion Radius, AU: 2.23". Russell 2004 Table 3.4 lists Aphelion Ratio 1.47 for cycler 1.0.1.-1, giving aphelion = 1.47 x 1.52 AU = 2.23 AU.
inclination_deg: Inclination 0 is the modelling assumption (circular-coplanar) used in the original Aldrin 1985 derivation and all subsequent reproductions in §9 of Russell 2004 and §III.A of Rogers 2012. Real-ephemeris versions (Rogers 2012 Table 4 STOUR results) inherit Mars' ~1.85° inclination; that is an M6 concern, not M3.
vinf_kms_at_encounters[0].vinf_kms: Russell 2004 Table 3.4 row for cycler 1.0.1.-1: "Earth v_inf (km/s): 6.5".
vinf_kms_at_encounters[1].vinf_kms: Russell 2004 Table 3.4 row for cycler 1.0.1.-1: "Mars v_inf (km/s): 9.7".
legs[0].tof_days: Russell 2004 Table 3.4 row for cycler 1.0.1.-1: "Earth->Mars Time (days): 146". Also Wikipedia 'Mars cycler': "travels from Earth to Mars in 146 days (4.8 months)" citing McConaghy/Longuski/Byrnes 2002 p. 6 [5].
legs[1].tof_days: Derived mathematically from synodic period minus outbound transit time: T_cycler (≈779.8 d) − tof_E→M (146 d) = 633.8 d ≈ 634 d. See leg note for the 2026-05-31 review fix that replaced the previously published 519 d.
period.years: "Earth-Mars synodic 2.135 yr" — spec.md §9; also used as the Aldrin cycler repeat in Wikipedia and McConaghy/Longuski/Byrnes 2002 p. 6.