About

What is this?

cyclers.space is an open catalogue of planetary cycler trajectories: repeating orbits that periodically encounter two or more bodies without propulsive maneuvers (or with only small course-correction burns). Most are heliocentric — planet-to-planet routes like Earth-Mars — and some are their moon-to-moon cousins inside the Earth-Moon, Jovian, Saturnian, and Uranian systems. Cyclers were proposed in the 1980s by Aldrin and Niehoff as the backbone of a sustainable Earth-Mars transport architecture, and the literature on them is now scattered across four decades of papers, dissertations, and conference proceedings.

There is no single canonical public database. This site exists to be one — generated from a YAML file under version control, with every numerical value traceable to a specific table or page in the cited source.

Reading the diagrams: why do some orbits look pointy?

A question people ask looking at the Earth-Moon panels on the front page: how can the orbit fall back on itself like that, with a sharp corner, when it never runs into anything there? It's a fair thing to notice — a sudden reversal usually means a collision or a maneuver, and neither is happening. The answer is about the camera, not the spacecraft.

The Earth-Moon panels are drawn in the rotating (synodic) frame — a frame of reference that spins together with the Earth-Moon line, so Earth and the Moon both sit still on the page. The spacecraft's real, physical velocity is always smooth; there is no reversal and nothing is encountered at the cusp. But what gets plotted is the spacecraft's motion relative to the rotating frame — its true motion minus the frame's own spin. Wherever the spacecraft's own angular rate around the system momentarily matches the frame's rotation rate, that difference passes through zero and can flip sign, producing a sharp corner in the drawn path even though the underlying trajectory is perfectly smooth in reality.

This is exactly the same, well-known effect as the apparent retrograde motion of Mars or Jupiter seen from Earth: viewed from a moving vantage point (Earth, orbiting the Sun), an outer planet's smooth heliocentric ellipse appears to loop backward, with sharp "stationary points" at each end of the loop. Nothing about Mars's real orbit changes at those points — it's purely an artifact of watching from a moving platform. The cusps in these CR3BP diagrams are the same artifact, one level down: Earth and the Moon are the "fixed" reference instead of the Sun.

Cyclers often (not always) show a cusp near a close lunar or Earth flyby, because that is where the spacecraft's own angular rate changes fastest and so is most likely to cross the frame's rotation rate — but the cusp itself is a frame effect, not evidence that the spacecraft passed close to a body at that exact point. Read the sharp corners as "the camera is spinning," never as "something happened here."

The seven kinds of trajectory

"Cycler" gets used loosely. The catalogue separates seven genuinely different things, because they suit very different missions. The headline distinction: a true cycler repeats forever; two of the others run once; a resonant PO repeats forever but never actually meets the planet it would ferry to; and the two torus kinds aren't a repeating loop at all — see the dedicated section below for why that's a structurally different thing, not just a variant of the other five.

Kind	In plain terms	Good for
Cycler	A heliocentric orbit that re-encounters its planets on a fixed schedule indefinitely — a railway line in space. The vehicle never stops; small taxis ferry crew and cargo on and off at each flyby. The Aldrin cycler is the canonical example (Mars cycler ↗).	A permanent, reusable Earth–Mars transport backbone. You pay to build the railway once; the heavy radiation shielding and habitat ride forever.
Quasi-cycler	Repeats nearly, but only stays closed for a bounded window of real calendar dates before the real-world geometry drifts it apart. The window is listed per entry — the current quasi-cyclers (Uranian moon pairs) hold for roughly eight decades.	A medium-term shuttle when a true ballistic cycler doesn't exist for the planet pair you want.
Precursor	A one-shot trajectory whose only job is to place a vehicle onto a cycler in the first place.	Standing up the railway — the construction train, run once per vehicle.
Tour	A one-shot gravity-assist chain with a final destination — it does not repeat. Most flown missions (Voyager, Cassini, Galileo) are tours.	A single science mission that strings flybys together to reach a target cheaply.
Resonant PO	A stable, strictly periodic resonant (or libration) orbit that repeats forever — but stays far enough from the secondary body that it never actually encounters it, so it ferries nothing. Mathematically a cycler's cousin; operationally a dead end.	Nothing as transport. It is catalogued as a known dynamical structure (e.g. a member of the Antoniadou & Libert 2019 spatial-resonant family), not a usable route.
Torus (connected)	Not a single loop at all — a whole 2-D surface of bounded, never-quite- repeating motion, with a computed departure/arrival connection to and from it (out along the unstable manifold, back along the stable one, to near machine precision).	A confirmed transport node: a reservoir of nearby trajectories plus a demonstrated way on and off it. See quasi-periodic tori below.
Quasi-periodic torus	The same kind of 2-D surface, but with no computed connection yet — an existence/structural discovery, not a demonstrated route.	Not yet usable as transport, but a candidate reservoir worth investigating. See quasi-periodic tori below.

Quasi-periodic tori: a reservoir, not (yet) a route

A strict cycler is one closed loop: a periodic orbit with a repeating, alternating sequence of close encounters with named bodies (Earth→Mars→Earth→Mars, say) — that sequence is exactly what the catalogue's own sequence_canonical field records. A quasi-periodic invariant torus is structurally different. Instead of one closed loop, the trajectory is confined to a 2-D toroidal surface in phase space, built from two independent, generally-incommensurate oscillation frequencies. It never exactly repeats — but it never leaves that surface either. There is no alternating-encounter sequence to state, so these rows carry sequence_canonical: null.

The catalogue's example is the Jupiter-Europa 3:4 torus: built by inflating the Jupiter-Europa 3:4 exterior resonant periodic orbit outward into a torus, locked to the real Io-Europa-Ganymede Laplace resonance. Io and Ganymede are never closely approached — across all ten tested real-ephemeris epochs (2000–2083) at the entry's best torus point, the closest either moon ever comes is a few hundred thousand kilometres, far outside any sphere of influence. They are felt only as gravitational perturbers on the base Jupiter-Europa dynamics, never encountered.

Why it's useful in a cycler-like way, despite not being one

Two properties carry over from the cycler idea even though the object itself isn't a cycler:

It's a reservoir, not a single curve. Being a whole 2-D surface means every point on it is a slightly different member of the same family — the same concept real libration-point missions already exploit: a spacecraft flies a nearby quasi-halo torus member rather than the exact halo orbit, picking whichever phase best suits its transfer window. The same freedom is available here.
Confirmed real-ephemeris persistence. The idealized torus does not survive real-ephemeris propagation everywhere — most of the surface genuinely diverges (a naive reference point drifts to a ~3.7×10⁵ km gap, comparable to Ganymede's own orbital radius). But at one torus point, all ten tested real epochs land in a recurring narrow near-miss window — position gaps of roughly 500–2,000 km against a pre-declared 5,000 km gate, confirmed genuine against both a positive control (a known-good ~1.75×10⁻² km case) and a known-divergent negative case, not integrator noise. That recurring, bounded-drift behaviour is the direct analogue of a cycler's own "low station-keeping cost" property — a spacecraft could plausibly loiter near this structure for extended real time with small maintenance needs.

What's still missing: a computed connection

A cycler's real value isn't just that it persists — it's persistence plus a usable arrival/departure connection. This torus row explicitly has no computed manifold connection: orbit_class=quasi_periodic_torus was chosen, rather than the sibling torus_homoclinic class below, specifically because no departure/arrival route has been computed for this object. It is catalogued as a pure existence/structural discovery, not a demonstrated transport route. Whether that connection can eventually be computed is an open, actively-investigated question — this page reflects the object's current state, not a claim about where that investigation will land.

The closely-related case that does have a connection

The sibling class's own example, the Uranus-Umbriel 1:2 torus (Titania-forced), is the same kind of object — a quasi-periodic invariant torus, also with sequence_canonical: null — but with a computed connection: it departs along the torus's own unstable manifold and returns along its stable manifold, closing to near machine precision (idealized position gap ~5.7×10⁻¹⁰ km, cross-checked against an independent integrator to within ~1.1×10⁻⁷ km). That combination — a persistent reservoir plus a demonstrated way on and off it — is what earns it the torus_homoclinic class instead of quasi_periodic_torus. It's the honest contrast for reading the Jupiter-Europa torus: structurally the same kind of object, one computed connection short of the same transport-node status.

Ballistic, powered, and the maintenance-ΔV bands

The most useful thing to know about a cycler is how much propulsion the railway itself needs to keep running — its maintenance ΔV (a speed change, in metres or kilometres per second; the currency of spaceflight). This is separate from what the taxis spend getting on and off. A cycler is called ballistic if, in the idealised model, it needs no deterministic engine burns to stay on schedule (the planets' gravity does all the steering), and powered if it needs regular burns.

Measured over a standard 7-cycle stretch in a realistic ephemeris, at the best launch date, catalogue cyclers sort into bands. Real published numbers:

Band	Maintenance ΔV	Real example	What it means for a mission
Strictly ballistic	< 1 m/s / 7 cycles	Liang 2024 CGE — ~1×10⁻⁷ m/s per cycle in a SPICE ephemeris	Essentially free to run. The dream case: the railway costs nothing to keep on rails (in the gravity model). Best possible reusable backbone.
Essentially ballistic	< 10 m/s / 7 cycles	S1L1 Earth–Mars — ~10 m/s over a 30-yr repeat (McConaghy 2006)	A few seconds of engine burn per decade — a thimble of propellant. A very practical permanent Earth–Mars line.
Low-maintenance	< 300 m/s / 7 cycles	Russell-Ocampo 2006 parent cyclers — the paper's census puts 74 of them in this band (these catalogue rows are not yet individually banded)	Modest upkeep — a small solar-electric thruster topped up at each rendezvous keeps it going. Still a reusable backbone.
Powered (Aldrin-type)	≥ 300 m/s — typically ~1.5–2 km/s every 15 years	Aldrin cycler — three burns on 3 of every 7 orbits (Friedlander 1986; Byrnes-Aldrin 1993; Rauwolf 2002)	The vehicle needs real propulsion and refuelling. You accept that cost in exchange for shorter, lower-energy crossings. Suits a smaller fleet where transit time matters more than fuel.
Low-thrust / SEP	same burns, flown with ion engines	SEP Aldrin — ~3 tonnes of xenon over 15 yr, refuelled at each pass (Rauwolf 2002)	Trades chemical fuel for high-efficiency electric propulsion: ~4% of the vehicle mass in propellant instead of ~38%.

The Earth–Moon cyclers sit in their own regime — e.g. the Genova-Aldrin 3-petal needs ~20–62 m/s per ~26-day lunar cycle (≈39 m/s/month) in a full ephemeris: a short-period line is inherently more demanding to hold than a slow Earth–Mars one.

Is any cycler truly free, forever? No — and here's the honest part.

The word "ballistic" describes an idealised model, not a promise of perpetual free flight. In a simplified solar system (circular, flat planetary orbits) a ballistic cycler is an exact repeating orbit needing zero engine burns. The real solar system is messier, and no cycler is genuinely zero-ΔV for all time. Three things always cost something:

Gravity that doesn't quite repeat (the big one). Real planets have slightly elliptical, tilted orbits whose periods aren't exact whole-number ratios, and the Moon and other planets tug as well. The geometry never lines up perfectly twice, so the schedule needs periodic correction. This is exactly what the 10–300 m/s figures in the table above are — the price of the model's idealisation meeting reality.
Sunlight pushing on the vehicle. Solar radiation pressure — photons from the Sun striking the spacecraft — is a small but relentless force that slowly changes the orbit and must be trimmed out. (This is the dominant non-gravitational effect; the actual solar wind of particles is far weaker but acts the same way.) A big, lightweight habitat with lots of surface area feels this more.
You never launch perfectly. Injection and navigation errors mean every real cycler also carries a budget of small trajectory-correction maneuvers — what Friedlander's 1986 paper called "navigation targeting maneuvers," needed even for the otherwise-ballistic VISIT cyclers.

So the honest reading of the table: a strictly-ballistic cycler's ~10⁻⁷ m/s is its deterministic gravitational residual in the model — a flown mission would still add a (small) station-keeping budget for sunlight and navigation on top. "Ballistic" means the railway needs no engine to exist in the maths, not that a real vehicle on it never fires a thruster. The bands are best read as how big that budget is — and they span seven orders of magnitude, which is why different cyclers suit genuinely different missions.

Sources for the bands. The <1 / <10 / <300 m/s-per-7-cycle tier census: Russell & Ocampo, J. Guid. Control Dyn. 29(2), 2006 (doi:10.2514/1.13652 ↗). Ballistic floor & the ~200–300 m/s "correctable-to-ballistic" boundary, corroborated independently across three systems: Friedlander, Niehoff, Byrnes & Longuski 1986 (VISIT "free orbit"); McConaghy, Landau, Yam & Longuski, JSR 43(2), 2006 — S1L1 ~10 m/s (doi:10.2514/1.15215 ↗); Liang et al., JGCD 2024 — CGE ~10⁻⁷ m/s/cycle (doi:10.2514/1.G008387 ↗). Powered Aldrin maintenance: Byrnes, Longuski & Aldrin, JSR 30(3), 1993 (doi:10.2514/3.25519 ↗); SEP execution: Rauwolf, Friedlander & Nock, AIAA 2002-5046. Every per-row number in the catalogue traces to a specific table/page in its cited source — click any example above to open that row's full provenance.

Validation levels (V0–V5)

Each entry carries a validation level, drawn from the §14 gauntlet of the upstream cyclers project — the highest gate it has mechanically passed. The level is back-filled upstream from recorded test evidence, never aspirationally: a row is promoted off V0 only when an in-repo, teeth-bearing test earns it. Most entries are V0 (literature-sourced, not yet independently re-derived): 339 at V0, 6 at V4, 2 at V3, 8 at V2, 44 at V1. Higher levels populate as the finder's cross-validation gauntlet (the Forge pipeline) closes loops on each entry.

Level	Meaning
V0	Internal consistency: hard constraints met, V∞ preserved across each flyby, idealized closure residual within tolerance. (Literature-sourced rows that have not been re-derived also sit at this floor.)
V1	Solver cross-check: every leg re-solved with lamberthub (izzo + gooding) agreeing under 1e-3 m/s, and the full trajectory re-propagated with the Kepler propagator meeting planet positions.
V2	Multi-lap periodicity (class-split, §14). V2-ballistic: ≥3 continuous laps with bounded drift in the dynamic rotating frame of the row's defining model. V2-powered: ≥3 cycles where every planned encounter is met under documented maintenance, with bounded intra-cycle drift-vs-plan.
V3	Ephemeris realisation: phase-matched to a real launch window; ephemeris-mode horizon TCM over 3–5 laps (~20–30 yr) bounded within the ΔV budget.
V4	High-fidelity external: an independent codebase + ephemeris (e.g. GMAT) reproduces the trajectory and maintenance ΔV.
V5	Novelty + expert review: misses catalogue and literature, human-reviewed, ideally independently reproduced.

How we search

The companion cyclers project runs a multi-stage automated pipeline — the Forge — to find, score, and verify candidate trajectories. Every candidate that makes it into the catalogue has passed the V0–V5 gauntlet described above; the pipeline is designed to reproduce published results before trusting its own discoveries, and a clean negative (no cycler found in a region) is treated as a valid, reportable result.

Orbit generation (the "genome" correctors)

The pipeline maintains a family of numerical correctors that each know how to close a particular class of orbit:

Planar and 3-D periodic-orbit differential correctors — the standard multiple-shooting monodromy-based correctors used in CR3BP families.
BCR4BP genome — extends the search into the bicircular restricted four-body problem (Sun–Earth–Moon) for orbits that live in the coupled three-body regime.
Quasi-periodic 2-torus (GMOS) genome — targets invariant 2-tori around the libration-point periodic orbits, admitting trajectories that are bounded but not strictly periodic.
Tulip-orbit genome — period-multiplying and family-switching corrector for trajectories that visit more than one unstable orbit before returning, analogous to the "petal" families seen in rotating-frame plots.
Asymmetric-branch corrector — handles orbits that break the Jacobi-symmetry of the standard formulation, needed for certain Venus–Earth–Mars configurations.
Heteroclinic-cycle corrector — finds closed chains of invariant-manifold connections between two or more unstable periodic orbits (a "periodic-up-to-rotation" closure). This corrector was validated against the computer-assisted proof of Wilczak & Zgliczyński for the Sun–Jupiter–Oterma system.

Candidate ranking (the accessibility scorer stack)

Before spending computation on full correction, candidates are ranked by a multi-layer scorer that estimates the cost of reaching one orbit from another:

Neural reachability prefilter — a fast learned classifier that screens out geometrically unreachable pairings before any deterministic solver is invoked.
Energy-preserving and impulsive reachable-set scorers — analytic bounds on ΔV based on Jacobi-constant level sets and impulsive maneuver geometry.
Resonant-manifold heteroclinic scorer — measures how closely the unstable manifold of the departure orbit approaches the stable manifold of the target, using resonant-passage intersections in phase space.
FTLE (chaos-field) scorer — uses finite-time Lyapunov exponent maps of the transfer region to flag chaotic corridors that are likely to yield low-cost connections.
Lobe-overlap graph scorer — applies lobe-dynamics accounting to estimate the phase-space volume exchanged between the two orbit families per synodic period.

Ephemeris grounding

For mission-heritage entries, the pipeline extracts V∞ directly from NASA SPICE / JPL Horizons ephemerides at the documented flyby epochs. Flown trajectories checked this way include Voyager 1 & 2, Pioneer 10 & 11, Galileo (VEEGA), Cassini (VVEJGA), Juno, Mariner 10, and BepiColombo. Matching a new candidate's V∞ sequence against these benchmarks is one of the first things the pipeline does when a literature entry is loaded.

Work in progress

Several search campaigns are actively running or planned:

Cross-system cycler search (in progress). We are building a search that chains Sun–Earth libration-point manifolds with Earth–Moon manifolds ("patched CR3BP", in the spirit of the "Shoot the Moon" low-energy transfer literature) to look for a trajectory that closes periodically across both regimes. No published closed cross-system cycler exists; this is a genuinely open question, and a clean negative is a valid outcome.
Earth–Mars multi-arc closer (planned). A dedicated multi-arc trajectory closer that joins patched-conic legs at a Mars gravity-assist to validate the Aldrin and SnLm families at higher fidelity.
BCR4BP refinement and petal-plot visualisation (planned). Candidate cross-system cycles will be lifted into the BCR4BP for higher-fidelity continuation, and rotating-frame rosette ("petal") plots will be added to catalogue entries where the corrector converges.

The literature-novelty check (spec §16.5) is a hard gate: no trajectory is labelled novel until it has been searched against the published record and found absent. A row's relationship to that record is recorded as its our_status (spec §16.4), which takes one of three values. A literal computed copy of a single published orbit is a known-reproduction; the original authors keep the credit. A computed member of a published class — not a literal copy of any one published orbit, yet not novel because the class is already known — is a known-class-member; for example our 3D out-of-plane (2,1) Earth-Moon resonant periodic orbit is a member of the spatial-resonant family of Antoniadou & Libert (2019). A trajectory absent from the published record is a candidate-novel.

Three kinds of result are easy to mis-file as "already known". Since September 2026 the catalogue treats each as candidate-novel, still subject to the literature gate, and each carries a duty to credit its source. First, a trajectory in a class the original authors deliberately left out of their search on practicality grounds: for example Jones, Hernandez and Jesick (2017) searched Venus-Earth-Mars triple cyclers only at one and two synodic periods with at most six flybys, so a three-synodic member found later is new work that cites their method. A stated scope exclusion says what was not searched; it is not a computation. Second, a published architecture applied at a planetary system its authors never treated: Russell and Strange (2009) built one-working-moon cyclers at Jupiter and Saturn; a member at Uranus or Neptune credits them and must explain what was re-applied and what changed physically (the flyby moon, the passive target, the bend regime). Third, an orbit whose type a theorem guarantees to exist, such as periodic orbits accumulating on a homoclinic connection: the theorem says orbits of that kind exist, but it does not supply the orbit, its period, or whether it actually passes inside a moon's sphere of influence. Such an orbit is candidate-novel only if it belongs to no published family; the entry cites the theorem and the source of the parent orbit, and the claim is worded "first computed", never "first predicted". By contrast, a quasi-periodic torus that merely describes the neighbourhood of an already-published orbit stays a known-class-member. In every case a literal match against a published orbit or family is checked first and always wins: published beats novel.

Attribution policy

For every entry, attribution goes to the earliest published source. Later elaborations, corroborations, or re-tabulations are listed as corroborating sources. If this project's finder later re-derives a literature cycler, the entry is tagged as a known-reproduction; the original authors keep the credit. This rule mirrors spec §16.4.

If you find an attribution error, please open an issue on the site repo.

How to contribute corrections

The catalogue's single source of truth is data/catalogue.yaml in the upstream cyclers repo (this site keeps no editable copy — it fetches that file at build time). Open a pull request there with the change, including the verbatim quote and source identifier (page, table, equation number, DOI) for every modified numerical value. Bare numbers without provenance are not accepted. For site-rendering problems (broken layout, wrong label, viz bugs), use the cyclers.space repo instead.

Data flow

The site is a static build of the upstream YAML catalogue: every build starts by syncing the latest catalogue.yaml from the cyclers repo, and the launch-windows dataset is refreshed by a weekly job against the real JPL DE440 ephemeris. The site has no backend and no analytics; JavaScript is limited to small opt-in islands — the catalogue filter/sort controls and the click-to-load 3D orbit viewers.