Schwaniger 1963 retrograde (counter-rotation) cislunar symmetric periodic free return, Earth-Moon CR3BP (perigee 6555 km = 177 km altitude, periselene about 2200 km, T = 26.06 d)

schwaniger-1963-em-cislunar-retrograde-periodic-free-return · source: literature · validation: V0 · reproduction

Signature

Bodies: E-Moon
Primary: Earth
Sequence (canonical): E-Moon
Sense: n/a
Orbit class: Cycler
strict cycler (infinite returns)
Cycler class: non-keplerian (CR3BP)
Trajectory regime: ballistic
Maintenance ΔV band: unclassified
Model assumption: cr3bp
CR3BP — Jacobi-constant-conserved; signature not patched-conic comparable.
Period: — yr (1 × E-Moon synodic)
T = 6.001502749598107 TU at the registry mu (625.47 h = 26.061 d, t_s = 375190.26 s). One perigee and one perilune per period. Schwaniger prints "about 650 hours" (p.6, read off Fig. 11); the 3.8% difference is within the graph-reading precision of the source. Not a lunar-synodic multiple (the sidereal month is 27.32 d = 6.2832 TU).
Maintenance ΔV: 0 km/s — strict ballistic
Priority date: 1963-06-01

V∞ at encounters

E (encounter 1): — (not published)
CR3BP periodic orbit: the conserved quantity is the Jacobi constant. Perigee speed 10,959.95 m/s Earth-relative inertial (10,977.42 m/s rotating frame) at r = 6555 km.
Moon (encounter 2): — (not published)
CR3BP periodic orbit; Jacobi-constant model. Periselene 2202.64 km from the Moon's centre at the start state.

CR3BP orbit identity

Family: Schwaniger 1963 counter-rotation cislunar symmetric free return of the first kind (Miele image theorem), periodic member (perigee on the Earth-Moon line, sec. III.E)
Mass ratio (μ): 0.01215058439469525
Jacobi constant: 1.0854
Period (non-dim): 6.0015
Stability index: 262.652

Planar CR3BP rotating-frame periodic orbit, symmetric about the Earth-Moon line (two perpendicular x-axis crossings: periselene at t = 0, perigee at T/2).

Orbit view 2.5D ecliptic projection

Not renderable from current data. This is a rotating-frame (CR3BP-family — CR3BP, CCR4BP, or CRNBP) periodic or quasi-periodic orbit. A faithful render requires numerical propagation of the synodic-frame state, which the catalogue does not yet publish as a sampled path — so no stand-in ellipse is drawn (drawing a heliocentric ellipse here would misrepresent the dynamics). Whatever identity fields the model supports (Jacobi constant, period, stability — not all apply to every model in this family; see "Model assumption" above) are tabulated above.

model: CR3BP (rotating frame)

3D view not available for rotating-frame (CR3BP-family) orbits.

Definition status

incomplete — core fields missing or known-unknowns tracked below

Known-unknowns (3)

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.cr3bp.mass_ratio [unknown]
Schwaniger 1963 states no mass ratio, distance or GM. The row uses the registry mu; the digest's mu = 0.012150 and mu = 1/81.30 give 2202.5 km / 625.47 h and 2229.8 km / 625.4 h. The paper's 'about 2150 km / about 650 h' are graph readings.
vinf_kms_at_encounters [conflict]
Schwaniger Fig. 9 injection speeds at 1938 km periselenum sit about 64 m/s below the digest's reproduction (constant offset, after allowing for the 2 omega r rotating/inertial split); times and longitudes match. A speed convention the report does not state. Unresolved.
orbit_elements.cr3bp.perigee_km [not-applicable]
Perigee 176.9 km altitude is below this project's 200-km Earth floor (PLANETS['E'].safe_alt_km); not a both-floors cycler-class member under the gate. Floors govern this project's novelty claims, not literature rows: the published orbit is recorded as published (lead ruling 2026-10-07).

Primary citation

Schwaniger, A. J. (1963). Trajectories in the Earth-Moon Space with Symmetrical Free Return Properties. NASA TN D-1833 (Lunar Flight Study Series Vol. 5), NASA Marshall Space Flight Center, June 1963.

URL: https://ntrs.nasa.gov/citations/19630007117

Sec. III.E (p.6-7): cross-plotting Fig. 15 gives "one cislunar case... counter-rotational injection at 180 degrees longitude and periselenum radius of about 2150 km", period "about 650 hours or about one month" (Fig. 11). Summary (p.7): "a periodic trajectory which approaches the moon at about 2150 km radius approximately once each month." No initial conditions printed.

Notes

Reproduced with the project corrector (cyclerfinder.search.cr3bp_periodic. correct_symmetric_fixed_jacobi, plain DOP853 rtol = atol = 1e-12 in physical time, no regularisation) plus a secant on C for the perigee condition r1(T/2) = 6555 km. Full-period closure 8.5e-7 km / 3.7e-7 m/s (plain); the Moon-centred KS propagator (core.cr3bp_ks) and the Sundman r1*r2 propagator (core.cr3bp_regularized) re-close it to 1.1e-5 km and 8.7e-6 km. The KS transition matrix gives b_h within 3e-8 of the plain one. det M = 1 - 2.3e-8; the trivial eigenvalue pair is recovered at 0.99914 / 1.00086. Positive control for CR3BP correctors and for any corrector regularised at both primaries (R4): tests/core/test_970_schwaniger_control.py. It is a WEAK regularisation control: the plain integrator already handles the 177 km perigee and 465 km perilune. The C = 1.09727 quoted in the digest-era summaries (with the mu(1-mu) term) belongs to the 6-digit rounded initial state, a neighbouring member with perigee 6560 km; the 6555 km member reproduced here has C = 1.0854167 (1.0974197 with mu(1-mu)). Not a duplicate: no catalogue Earth-Moon row has C near 1.085 with T near 6.0 (digest grep inventory). NOT the arenstorf-em-figure8-1963 orbit and must not fill that row's nulls. Literature novelty check deferred to (not needed for a literature row).

Source quotes (per-field provenance)

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

orbit_elements.cr3bp.periselene_km: Schwaniger 1963 sec. III.E (p.6-7): 'one cislunar case is a periodic orbit which has counter-rotational injection at 180 degrees longitude and periselenum radius of about 2150 km.'
period: Schwaniger 1963 sec. III.E: 'From the curve in Figure 11, the period is ascertained to be about 650 hours or about one month.'
orbit_elements.cr3bp.perigee_km: Schwaniger 1963 sec. II.C: 'injection (and, therefore, reentry) is assumed to occur at 100 nautical mile altitude or 6555 km radius from the earth's center with horizontal path angle.'