Case 2 (Byrnes 2002) 5:4(3)- establishment trajectory (Rogers 2015 Table 3, circular-coplanar)

case-2-5-4-3-establishment-cc · source: literature · validation: V0

Signature

Bodies: E-M
Primary: Sun (default — heliocentric)
Sequence (canonical): E-M
Sense: outbound
Orbit class: Precursor
precursor MGA (one-shot insertion into a cycler)
Cycler class: single-ellipse
Returns: 1 — finite for epoch-locked classes
Validity window: — (not published)
Inserts into: Russell-Ocampo cycler 2.1.1.+2 ('Case 2' of Byrnes/McConaghy/Longuski 2002)
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: circular-coplanar
Idealised: planets on circles, coplanar ecliptic.
Period: 4.270 yr (2 × E-M synodic)
K=5 Earth-orbit V-infinity-leveraging establishment timeline.
Maintenance ΔV: 3.500 km/s — near-ballistic (powered nudge)
V_∞ leveraging ΔV (establishment): 0.116 km/s
Source ephemeris: circular-coplanar idealized
Ephemeris model the source states its numbers were computed against.
Priority date: 2015-03-11

V∞ at encounters

E (encounter 1): 2.77 km/s
Rogers 2015 Table 3 row Case 2 '5:4(3)-': V∞ flyby = 2.767 km/s; V∞ launch = 2.013 km/s.
M (encounter 2): — (not published)
Rogers 2015 Table 3 tabulates V∞ launch and V∞ flyby, not a distinct V∞ at Mars.

Orbit elements (heliocentric)

Semi-major axis a: 1.240 AU
Eccentricity e: 0.193
Perihelion: — AU
Aphelion: — AU
Inclination: 0.00°

a/e SOURCED: Rogers 2015 Table 3 (circular-coplanar, post-leveraging). inclination=0 by model definition.

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 216906 km

Mars min 0.162 AU

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

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

Definition status

incomplete — core fields missing or known-unknowns tracked below

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.

launch_epoch [not-applicable]
Rogers 2015 Table 3 is the circular-coplanar idealized GA model (epoch-free by design).

source: Rogers 2015 §3.1.2 (p.118-119) GA model description.

Primary citation

Rogers, B. A. et al. (2015). Establishing cycler trajectories between Earth and Mars. Acta Astronautica 112:114-125 (2015).

DOI: 10.1016/j.actaastro.2015.03.002

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

Notes

Case 2 (Byrnes 2002 — catalogued steady-state as russell-ocampo-2.1.1+2- case2) 5:4(3)- circular-coplanar establishment variant. K=5 Earth-orbit V-infinity-leveraging with maneuver on 3rd s/c orbit before line of apsides. Admitted under v4.7 scope as orbit_class=precursor_mga (wave 2, 2026-06-17).

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: Rogers 2015 Table 3 row Case 2 '5:4(3)-': V∞ flyby = 2.767 km/s.
v_infinity_leveraging_dv_kms: Rogers 2015 Table 3: ΔV_DSM = 0.116 km/s.
delta_v_kms: Rogers 2015 Table 3: ΔV_total = 3.500 km/s.
flyby_mechanics[0].min_altitude_km: Rogers 2015 Table 3: h_flyby = 422 km.
orbit_elements.a_au: Rogers 2015 Table 3: a = 1.24 AU.
orbit_elements.e: Rogers 2015 Table 3: e = 0.193.