Russell-Ocampo cycler 4.7.1.-3 (4-synodic)

russell-ocampo-4.7.1-3 · source: literature · validation: V0

Signature

Bodies: E-M
Sequence (canonical): E-E-M-M
Sense: outbound
Period: 8.540 yr (4 × E-M synodic)
4 x Earth-Mars synodic period (2.135 yr) per Russell 2004 dissertation §3.8 row 4.7.1.-3; n_flybys = 4.
Priority date: 2003-02-09

V∞ at encounters

E (#1): 4.30 km/s
Russell 2004 dissertation Table 3.4 row 4.7.1.-3: Earth v_inf = 4.3 km/s.
M (#2): 6.80 km/s
Russell 2004 dissertation Table 3.4 row 4.7.1.-3: Mars v_inf = 6.8 km/s.

Orbit elements (heliocentric)

Semi-major axis a: — AU
Eccentricity e: —
Perihelion: — AU
Aphelion: 1.824 AU
Inclination: 0.00°

Aphelion derived from Russell 2004 Table 3.4 Aphelion Ratio AR = 1.2 x 1.52 AU (his §3.3 Mars reference radius) = 1.824 AU. Other elements (a, e, perihelion) not directly tabulated in Table 3.4.

Legs

E → M: 163 d, 0 revs
Russell 2004 dissertation Table 3.4 row 4.7.1.-3: Earth->Mars (or aphelion) time = 163 days.

Primary citation

Russell, R. P. & Ocampo, C. A. (2005). Geometric Analysis of Free-Return Trajectories Following a Gravity-Assisted Flyby. Journal of Spacecraft and Rockets, Vol. 42, No. 1, pp. 138-152.

DOI: 10.2514/1.5571

URL: https://arc.aiaa.org/doi/abs/10.2514/1.5571

Peer-reviewed venue for the 24-ballistic cycler catalogue (geometric analysis branch). The conference precursor (Russell/Ocampo AAS 03-145, Feb 2003) establishes priority.

Corroborating sources

Russell, R. P. & Ocampo, C. A. (2004). Systematic Method for Constructing Earth-Mars Cyclers Using Free-Return Trajectories. Journal of Guidance, Control, and Dynamics, Vol. 27, No. 3, pp. 321-335. DOI: 10.2514/1.1011
The companion JGCD paper that introduced the free-return construction method.
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
Table 3.4 row 4.7.1.-3: AR=1.2, TR=1.38, E->M days=163, V_inf,E=4.3, V_inf,M=6.8, 4 flyby turning angles [72, 72, 72, 72] deg. Strictly ballistic by Russell footnotes a/b (AR>=1 AND TR>=1).

Notes

Strictly ballistic per Russell's Table 3.4 footnotes a and b: AR=1.2 >= 1 means the cycler reaches Mars without a powered maneuver; TR=1.38 >= 1 means all required Earth flybys are physically attainable above the 200 km minimum altitude. 4-synodic period. 4 required Earth flybys (turning angles [72, 72, 72, 72] deg per Russell Table 3.4 last column). Note Russell's nomenclature: the trailing negative index (-3) denotes the lower-energy Lambert branch of the generic-return solution.

Source quotes (per-field provenance)

Every numerical value in this entry traces to a verbatim or paraphrased quote from a cited source.

vinf_kms_at_encounters[0].vinf_kms: Russell 2004 dissertation Table 3.4 row 4.7.1.-3: Earth v_inf (km/s) = 4.3.
vinf_kms_at_encounters[1].vinf_kms: Russell 2004 dissertation Table 3.4 row 4.7.1.-3: Mars v_inf (km/s) = 6.8.
legs[0].tof_days: Russell 2004 dissertation Table 3.4 row 4.7.1.-3: Earth->Mars (or aphelion) Time (days) = 163.
aphelion_au: Russell 2004 dissertation Table 3.4 row 4.7.1.-3: Aphelion Ratio = 1.2 (Russell's §3.3 ratio to 1.52 AU = Mars sma); aphelion = 1.2 x 1.52 AU = 1.824 AU.
period.years: 4 x Earth-Mars synodic 2.135 yr = 8.54 yr; Russell 2004 §3.3 fixes synodic geometry on 1.875-yr Mars period (=15-yr alignment); 2.135 yr matches spec.md §9.