Sanchez Net 2022 EM near-ballistic Earth-Mars cycler (Fig. 2b Cycler 2)

sanchez-net-2022-em-cycler2 · source: literature · validation: V0

Signature

Bodies: E-M
Primary: Sun (default — heliocentric)
Sequence (canonical): E-E-E-M
Sense: outbound
Orbit class: Cycler
strict cycler (infinite returns)
Cycler class: multi-arc
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: analytic-ephemeris
Mid-fidelity: real eccentricity / inclination retained; not full N-body.
Period: 7.870 yr (4 × E-M synodic)
Period between the two Mars visits (events 2→5) is 2875 days = 7.87 yr. The Fig. 2b caption states '8 years between Mars 1 and 2' (rounded). Nearest synodic-integer k=4 (4 × 2.135 yr ≈ 8.54 yr) is the best-fit integer, though the actual period is ~8% shorter.
Maintenance ΔV: 0.007 km/s — near-ballistic (powered nudge)
Priority date: 2022-05-01

V∞ at encounters

M (encounter 1): 6.47 km/s
SOURCED: Sanchez Net 2022 Fig. 2b event 2 (Mars flyby 12/19/2037): v∞ = 6.466 km/s.
E (encounter 2): 3.09 km/s
SOURCED: Sanchez Net 2022 Fig. 2b event 3 (Earth flyby 10/10/2040): v∞ = 3.090 km/s. Δv = 7 m/s near-ballistic maneuver at this event.
E (encounter 3): 5.29 km/s
SOURCED: Sanchez Net 2022 Fig. 2b event 4 (Earth flyby, date not given in Fig. 2b): v∞ = 5.285 km/s. Date is absent from Fig. 2b — see data_gaps[].
M (encounter 4): 6.87 km/s
SOURCED: Sanchez Net 2022 Fig. 2b event 5 (Mars flyby 11/02/2045): v∞ = 6.871 km/s. Δv = 6 m/s near-ballistic maneuver at this event.
E (encounter 5): 5.72 km/s
SOURCED: Sanchez Net 2022 Fig. 2b event 6 (Earth flyby 08/24/2048): v∞ = 5.721 km/s. Caption annotation: Dec. = 20.8 degrees.

Cycle-level identity (multi-arc invariants)

Aphelion ratio (AR): —
Turn ratio (TR): —
Transit times (days): 1447 d, 1026 d

Multi-arc patched-conic: each arc is a separate heliocentric ellipse. No single (a,e,i) characterises the full trajectory. Launch declination not given in Fig. 2b (event 6 declination Dec. = 20.8 deg is a different encounter). No per-arc orbital elements are tabulated in the paper.

Orbit view 2.5D ecliptic projection

spacecraft: analytic-ephemeris (real e/i retained) planets: J2000 osculating ellipse (Standish & Williams Table 1) orientation: coplanar-idealized (no Ω/ω published — in-plane ellipse)

3D view not available for multi-arc trajectories yet. The 3D system can now render a numerically-sampled polyline (n-body or multi-arc), but no sampled trajectory is published for this row — each leg is a separate ellipse with honest gaps where elements are unpublished (the 2D view above shows them). The button will appear here once a sampled path is exported for this trajectory; we never interpolate one from the catalogue's per-leg (a, e).

— — planet orbit (true J2000 ellipse)

Not-published gaps (never interpolated):

E → M — segment elements (a, e) not published; no curve drawn.
M → E — segment elements (a, e) not published; no curve drawn.
E → E — segment elements (a, e) not published; no curve drawn.
E → M — segment elements (a, e) not published; no curve drawn.
M → E — segment elements (a, e) not published; no curve drawn.
E → E — segment elements (a, e) not published; no curve drawn.

Legs (trajectory segments)

E → M: 1447 d, 0 revs
Earth launch to first Mars flyby. ToF derived from Fig. 2b dates.
M → E: 1026 d, 0 revs
First Mars flyby to Earth flyby. ToF derived from Fig. 2b dates. ANOMALY: 1026 days (~33.5 months) exceeds the paper's own <12-month (batch-1) ME transit bound stated in §III.A (p. 863). This is the observed value from Fig. 2b; the discrepancy is recorded as a data_gap. Δv = 7 m/s near-ballistic maneuver at the arriving Earth flyby.
E → E: (TOF not published)
Earth-to-Earth arc between event 3 and event 4. ToF unknown: event 4 date is absent from Fig. 2b.
E → M: (TOF not published)
Earth flyby (event 4) to second Mars flyby (event 5). ToF unknown: event 4 date is absent from Fig. 2b. Δv = 6 m/s near-ballistic maneuver at event 5 Mars flyby.
M → E: 1026 d, 0 revs
Second Mars flyby to Earth flyby. ToF derived from Fig. 2b dates. Note: same duration (1026 days) as me-leg1 — consistent with repeating cycle structure.
E → E: 26 d, 0 revs
Earth-to-Earth arc between events 6 and 7 (end of 3-cycle trajectory). ToF derived from Fig. 2b dates. Event 7 has no v∞ value in Fig. 2b.

Definition status

incomplete — core fields missing or known-unknowns tracked below

Family: Sanchez Net 2022 EM near-ballistic Earth-Mars cycler set · Sanchez Net EM patched-conic

Known-unknowns (9)

Values we expect to exist but have not yet filled (distinct from "not applicable"). Tracked per upstream docs/spec.md §16.6.4.

orbit_elements [unknown]
Per-arc and aggregate (a,e,i) not published in Sanchez Net 2022. This is a patched-conic real-date trajectory from JPL STAR; orbital elements for each arc are not tabulated. Do not compute from launch conditions.

source: Sanchez Net et al. 2022, JSR 59(3):861-870, DOI 10.2514/1.A35091
trajectory.segments[ee-leg1].tof_days [unknown]
Event 4 date is absent from Fig. 2b. The Earth flyby (event 4, v∞ = 5.285 km/s, alt 7560 km) has no date printed in the figure at available resolution. ToF for ee-leg1 (event 3 → event 4) and em-leg2 (event 4 → event 5) cannot be derived.

source: Sanchez Net 2022 Fig. 2b event 4
trajectory.segments[em-leg2].tof_days [unknown]
Depends on event-4 date which is absent from Fig. 2b. See data_gap for ee-leg1.

source: Sanchez Net 2022 Fig. 2b event 4
trajectory.maneuvers[em-leg2->me-leg2].periapsis_alt_km [unknown]
Altitude at event 5 Mars flyby (11/02/2045) not legible from Fig. 2b at available resolution.

source: Sanchez Net 2022 Fig. 2b event 5
trajectory.maneuvers[me-leg2->ee-leg2].periapsis_alt_km [unknown]
Altitude at event 6 Earth flyby (08/24/2048) not given in Fig. 2b.

source: Sanchez Net 2022 Fig. 2b event 6
vinf_kms_at_encounters[event7] [unknown]
Event 7 (Earth 09/19/2048) has no v∞ value in Fig. 2b. The event is listed (date only) at the end of the 3-cycle trajectory. v∞ is not recoverable from this figure.

source: Sanchez Net 2022 Fig. 2b event 7
trajectory.segments[me-leg1].tof_days [anomaly]
ANOMALY: me-leg1 (Mars 12/19/2037 to Earth 10/10/2040) = 1026 days (~33.5 months, ~2.81 yr). This exceeds the paper's own batch-1 constraint of <12 months per ME leg (Sanchez Net 2022 §III.A, p. 863). The value is sourced directly from Fig. 2b dates and is not a computation error. Possible explanations: (1) this cycler was selected from batch-2 (<18 months) or an unconstrained run, not batch-1; (2) the annotation is for a different sub-trajectory phase; (3) figure-reading error (unlikely given clear date stamps). Do NOT discard — record as anomaly for future investigation.

source: Sanchez Net 2022 Fig. 2b events 2-3; §III.A p. 863 for batch-1 bound
trajectory.segments[*].n_revs [unknown]
Revolution counts for each segment arc not tabulated; derivable from patched-conic propagation but not published.

source: Sanchez Net et al. 2022, JSR 59(3):861-870
trajectory.epoch_tzero [unverified-provenance]
The epoch is given as a Gregorian calendar date from Fig. 2b; exact UTC/TDB offset and MJD equivalent are not published. epoch_tzero is set to the ISO-8601 date string (2034-01-02) as a best approximation.

source: Sanchez Net 2022 Fig. 2b event 1

Primary citation

Sanchez Net, M. et al. (2022). Cycler Orbits and Solar System Pony Express. Journal of Spacecraft and Rockets, Vol. 59, No. 3, pp. 861-870, May-June 2022.

DOI: 10.2514/1.A35091

Fig. 2b (p. 862) provides the event list, dates, v∞ values, altitudes, and Δv for Cycler 2 ('8 years between Mars 1 and 2'). The trajectory was generated by the JPL STAR patched-conic tool with unoptimised per-flyby Δv ≤ 10 m/s.

Notes

Sanchez Net 2022 Fig. 2b Cycler 2. Near-ballistic EM Earth-Mars cycler from the JPL STAR patched-conic enumeration. Launch: 01/02/2034, C∞ = 10.7 km²/s² (v∞ ≈ 3.27 km/s) — sourced from Fig. 2b caption. Two Mars visits over ~15 years (events 2, 5). Max unoptimised Δv = 7 m/s (event 3). The trajectory uses real-date ephemeris (analytic- ephemeris model). Period between Mars visits (events 2→5): 2875 days = 7.87 yr. Caption states "8 years between Mars 1 and 2" (rounded). The macro label "EM" (Sanchez Net §III.A) describes one Mars visit per cycle; the actual encounter sequence (E→M→E→E→M→E→E) has two intermediate Earth flybys per cycle, giving sequence_canonical "E-E-E-M" (lex-min 4-node cycle). ANOMALY: The first ME transit (events 2→3, Dec 2037→Oct 2040) is 1026 days (~33.5 months, ~2.81 yr). This exceeds the paper's own batch-1 bound of <12 months per ME leg (§III.A, p. 863). This is the observed Fig. 2b value; the discrepancy is recorded as a data_gap anomaly and NOT discarded — it may indicate this cycler was from a different batch or an anomalous trajectory in the STAR database. The identical ME duration reappears at events 5→6 (1026 days), suggesting the value is internally consistent even if it violates the stated batch-1 bound. V∞ multiset (from Fig. 2b, per encounter): Earth encounters 3.090, 5.285, 5.721 km/s; Mars encounters 6.466, 6.871 km/s. Launch v∞ ≈ 3.27 km/s (C∞ = 10.7 km²/s²).

Source quotes (per-field provenance)

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

delta_v_kms: Sanchez Net 2022 Fig. 2b event 3: '7 m/s' (near-ballistic maneuver at Earth flyby 10/10/2040).
period.years: Sanchez Net 2022 Fig. 2b caption: '8 years between Mars 1 and 2'. Events 2 (12/19/2037) to 5 (11/02/2045) = 2875 days = 7.87 yr.
vinf_kms_at_encounters[M/6.466]: Sanchez Net 2022 Fig. 2b event 2 (Mars flyby 12/19/2037): v∞ = 6.466 km/s.
vinf_kms_at_encounters[E/3.090]: Sanchez Net 2022 Fig. 2b event 3 (Earth flyby 10/10/2040): v∞ = 3.090 km/s.
vinf_kms_at_encounters[E/5.285]: Sanchez Net 2022 Fig. 2b event 4 (Earth flyby, date absent): v∞ = 5.285 km/s.
vinf_kms_at_encounters[M/6.871]: Sanchez Net 2022 Fig. 2b event 5 (Mars flyby 11/02/2045): v∞ = 6.871 km/s.
vinf_kms_at_encounters[E/5.721]: Sanchez Net 2022 Fig. 2b event 6 (Earth flyby 08/24/2048): v∞ = 5.721 km/s.