diff --git a/README.md b/README.md
index 0890633..b44be02 100644
--- a/README.md
+++ b/README.md
@@ -56,7 +56,10 @@ in it is measured and what is not.
 cutting to a new scene. The Sun gets the real solar-system bodies, moving on JPL's mean orbital
 elements — Standish's for the planets, JPL SSD's satellite table for the moons, the Small-Body
 Database for Ceres, Eris, Haumea and Makemake — and turned by the IAU's rotational elements, Earth
-by the IERS Earth Rotation Angle; other
+by the IERS Earth Rotation Angle; a tidally locked moon's prime meridian (but the Moon's and
+Phobos's) turns at its JPL mean motion and its pole's terms on its node at its JPL node rate, both
+re-phased to the IAU's values on 2025-01-01, and Iapetus's pole follows its orbit normal
+(`lockedToOrbit`), so each keeps its face to its planet from AD 1 to 3000; other
 stars get their confirmed exoplanets. Orbits are drawn as ellipses and bodies are propagated
 along them by a Kepler solver to the date on the map's clock. Under them, a dashed grid marks out
 round distances in AU — 5 AU rings for the solar system, 0.01 AU rings for TRAPPIST-1 — with a
@@ -330,7 +333,7 @@ plugin's own files are kept so it can be listed from a marketplace of its own la
 ## Data credits
 
 Star catalogue: [HYG database](https://github.com/astronexus/HYG-Database) (Hipparcos, Yale
-Bright Star, Gliese) — 68 388 stars within 250 pc. Solar-system orbits: JPL approximate planetary mean elements (Standish), JPL SSD satellite mean elements and the JPL Small-Body Database; rotation: the IAU WGCCRE 2015 report via NAIF's pck00011, and for Earth the IERS Conventions 2010; physical data, and the positions the orbits are checked against: NASA/JPL Horizons. Exoplanets: NASA Exoplanet
+Bright Star, Gliese) — 68 388 stars within 250 pc. Solar-system orbits: JPL approximate planetary mean elements (Standish), JPL SSD satellite mean elements and the JPL Small-Body Database; rotation: the IAU WGCCRE 2015 report via NAIF's pck00011, with a locked moon's W and node terms re-rated to its JPL mean elements and Iapetus's pole carried round its orbit normal, and for Earth the IERS Conventions 2010; physical data, and the positions the orbits are checked against: NASA/JPL Horizons. Exoplanets: NASA Exoplanet
 Archive. Deep-sky objects: [OpenNGC](https://github.com/mattiaverga/OpenNGC). Body and skybox
 imagery: NASA/JPL/USGS public domain and Solar System Scope (CC BY 4.0) — per-file provenance
 is recorded in `src/assets/textures/README.md`.
diff --git a/src/app/features/galaxy-system/system-orbits-renderer.spec.ts b/src/app/features/galaxy-system/system-orbits-renderer.spec.ts
index 333be1e..5dc6f5a 100644
--- a/src/app/features/galaxy-system/system-orbits-renderer.spec.ts
+++ b/src/app/features/galaxy-system/system-orbits-renderer.spec.ts
@@ -923,7 +923,7 @@ describe('locked moons across the clock’s window', () => {
   }
 
   it('keeps Proteus, Miranda, Mimas and Iapetus facing their planets at AD 1 and AD 3000', () => {
-    // Measured: Proteus 2.6 degrees at most over AD 1-3000, Miranda 2.8, Mimas 8.9, Iapetus 16 (9.4
+    // Measured: Proteus 2.6 degrees at most over AD 1-3000, Miranda 2.4, Mimas 8.9, Iapetus 16 (9.4
     // of it the lag of the row its orbit is drawn from). On the IAU's own W and Iapetus's straight
     // pole they were 146, 23, 49 and 87 degrees at AD 1.
     for (const jd of [1721425.5, 2816787.4]) {
@@ -934,4 +934,21 @@ describe('locked moons across the clock’s window', () => {
       expect(Math.abs(facingPlanet('iapetus'))).toBeLessThan(16.5);
     }
   });
+
+  it('keeps the axes of Miranda, Mimas and Iapetus on their drawn orbits’ normals, as a Cassini state holds them, at AD 1, today and AD 3000', () => {
+    // Measured over AD 1-3000: Miranda 0.42 degrees at most, Mimas 0.47, Iapetus 0.74. With their
+    // poles going round at the IAU's node rates, Miranda was 7.6 off at AD 1 and Mimas 2.6; with
+    // Iapetus's pole on its Laplace pole, 8.3 off at every date.
+    for (const jd of [1721425.5, 2460676.5, 2816787.4]) {
+      renderer.update(jd);
+      for (const id of ['miranda', 'mimas', 'iapetus']) {
+        const moon = renderer.members.find((member) => member.id === id)!.marker;
+        const line = moon.parent!.children.find((child) => child.name === 'orbit-line')!;
+        const axis = new THREE.Vector3(0, 1, 0).applyQuaternion(moon.quaternion);
+        const normal = new THREE.Vector3(0, 0, 1).applyQuaternion(line.quaternion);
+        // A line, not a direction: Miranda turns backwards against the IAU's pole.
+        expect((Math.acos(Math.min(1, Math.abs(axis.dot(normal)))) * 180) / Math.PI).toBeLessThan(1);
+      }
+    }
+  });
 });
diff --git a/src/app/shared/models/body.model.ts b/src/app/shared/models/body.model.ts
index aa717c2..50611a6 100644
--- a/src/app/shared/models/body.model.ts
+++ b/src/app/shared/models/body.model.ts
@@ -105,8 +105,9 @@ export interface BodyRecord {
   /**
    * Where the body's pole points and which way its prime meridian faces at any date, from the IAU
    * WGCCRE 2015 report (Archinal et al. 2018) as NAIF's `pck00011.tpc` carries it, but that a locked
-   * moon's W turns at its drawn orbit's rate and Iapetus's pole goes round with its orbit's, so they
-   * keep their faces to their planets over the clock's AD 1 to 3000 (see `lockedToOrbit` in the
+   * moon's W, and its pole's terms on its node, turn at its drawn orbit's rates and Iapetus's pole
+   * goes round with its orbit's, so they keep their faces to their planets, and their poles round
+   * their orbits', over the clock's AD 1 to 3000 (see `lockedToOrbit` in the
    * ETL). Where present it alone sets how the body is drawn, and the ETL checks the period and
    * obliquity above against it. Absent where the report gives none: Hyperion tumbles, and Nereid,
    * Eris, Haumea and Makemake have no model.
diff --git a/src/assets/data/bodies.json b/src/assets/data/bodies.json
index 978b3d1..b6a7305 100644
--- a/src/assets/data/bodies.json
+++ b/src/assets/data/bodies.json
@@ -821,9 +821,8 @@
       "terms": [
         {
           "angleDeg": [
-            121.46893664,
-            660.22803474,
-            0
+            121.49945940952146,
+            660.1059470044942
           ],
           "ra": 3.09217726,
           "dec": 1.83936004,
@@ -831,9 +830,8 @@
         },
         {
           "angleDeg": [
-            231.05028581,
-            660.9912354,
-            0
+            231.2716139683453,
+            660.1059470044942
           ],
           "ra": 0.22980637,
           "dec": 0.1432532,
@@ -841,9 +839,8 @@
         },
         {
           "angleDeg": [
-            251.37314025,
-            1320.50145245,
-            0
+            251.44553184217244,
+            1320.2118940089883
           ],
           "ra": 0.06418655,
           "dec": 0.01911409,
@@ -918,8 +915,8 @@
       "terms": [
         {
           "angleDeg": [
-            283.9,
-            4850.7
+            283.6369874084692,
+            4851.752021563342
           ],
           "ra": 0.094,
           "dec": 0.04,
@@ -983,8 +980,8 @@
       "terms": [
         {
           "angleDeg": [
-            355.8,
-            1191.3
+            355.4537739825443,
+            1192.6848661542538
           ],
           "ra": 1.086,
           "dec": 0.468,
@@ -1066,8 +1063,8 @@
         },
         {
           "angleDeg": [
-            119.9,
-            262.1
+            117.57926275587673,
+            271.38269483015966
           ],
           "ra": 0.431,
           "dec": 0.186,
@@ -1211,8 +1208,8 @@
       "terms": [
         {
           "angleDeg": [
-            177.4,
-            -36505.5
+            178.81408536763,
+            -36511.15618661257
           ],
           "ra": 13.56,
           "dec": -1.53,
@@ -1327,8 +1324,8 @@
       "terms": [
         {
           "angleDeg": [
-            300,
-            -7225.9
+            300.02841306210905,
+            -7226.013649136892
           ],
           "ra": 9.66,
           "dec": -1.09,
@@ -1437,8 +1434,8 @@
       "terms": [
         {
           "angleDeg": [
-            345.2,
-            -1016.3
+            342.2970571615749,
+            -1004.6885465505693
           ],
           "ra": 3.1,
           "dec": -0.35,
@@ -1703,8 +1700,8 @@
       "terms": [
         {
           "angleDeg": [
-            102.23,
-            -2024.22
+            103.87516350424971,
+            -2030.8004738534437
           ],
           "ra": 4.41,
           "dec": 4.25,
@@ -1721,8 +1718,8 @@
         },
         {
           "angleDeg": [
-            204.46,
-            -4048.44
+            207.75032700849943,
+            -4061.6009477068874
           ],
           "ra": -0.04,
           "dec": -0.02,
@@ -2028,8 +2025,8 @@
       "terms": [
         {
           "angleDeg": [
-            177.85,
-            52.316
+            177.83706224270992,
+            52.367749612333185
           ],
           "ra": -32.35,
           "dec": 22.55,
@@ -2037,8 +2034,8 @@
         },
         {
           "angleDeg": [
-            355.7,
-            104.632
+            355.67412448541984,
+            104.73549922466637
           ],
           "ra": -6.28,
           "dec": 2.1,
@@ -2046,8 +2043,8 @@
         },
         {
           "angleDeg": [
-            533.55,
-            156.948
+            533.5111867281297,
+            157.10324883699957
           ],
           "ra": -2.08,
           "dec": 0.55,
@@ -2055,8 +2052,8 @@
         },
         {
           "angleDeg": [
-            711.4,
-            209.264
+            711.3482489708397,
+            209.47099844933274
           ],
           "ra": -0.74,
           "dec": 0.16,
@@ -2064,8 +2061,8 @@
         },
         {
           "angleDeg": [
-            889.25,
-            261.58
+            889.1853112135495,
+            261.8387480616659
           ],
           "ra": -0.28,
           "dec": 0.05,
@@ -2073,8 +2070,8 @@
         },
         {
           "angleDeg": [
-            1067.1,
-            313.896
+            1067.0223734562594,
+            314.20649767399914
           ],
           "ra": -0.11,
           "dec": 0.02,
@@ -2082,8 +2079,8 @@
         },
         {
           "angleDeg": [
-            1244.95,
-            366.212
+            1244.8594356989695,
+            366.5742472863323
           ],
           "ra": -0.07,
           "dec": 0.01,
@@ -2091,8 +2088,8 @@
         },
         {
           "angleDeg": [
-            1422.8,
-            418.528
+            1422.6964979416794,
+            418.9419968986655
           ],
           "ra": -0.02,
           "dec": 0,
@@ -2100,8 +2097,8 @@
         },
         {
           "angleDeg": [
-            1600.65,
-            470.844
+            1600.5335601843892,
+            471.30974651099865
           ],
           "ra": -0.01,
           "dec": 0,
@@ -2193,8 +2190,8 @@
         },
         {
           "angleDeg": [
-            142.61,
-            2824.6
+            141.60196187337888,
+            2828.6320421151877
           ],
           "ra": -0.05,
           "dec": -0.04,
diff --git a/tools/etl/build.ts b/tools/etl/build.ts
index 5cf738c..e6f20ba 100644
--- a/tools/etl/build.ts
+++ b/tools/etl/build.ts
@@ -1,6 +1,6 @@
 import { statSync } from 'node:fs';
 
-import { BodyRecord, OrbitalElements } from '../../src/app/shared/models/body.model';
+import { BodyRecord, OrbitalElements, RotationalElements } from '../../src/app/shared/models/body.model';
 import { eclipticToEquatorial, laplacePlaneToEquatorial, raDecToUnitVector } from '../../src/app/shared/astro/coordinates';
 import { meanElementsAt, positionAtEpoch } from '../../src/app/shared/astro/kepler';
 import { orientationAt } from '../../src/app/shared/astro/rotational-elements';
@@ -257,7 +257,7 @@ const MAX_OBLIQUITY_OFFSET_DEG = 0.1;
  *
  * Measured on this catalogue: at most 5.36 degrees (Titan) but for three. The Moon 7.62, at AD 1:
  * its longitude swings 6.3 either way with its eccentricity, Horizons' too, and W's quadratic, the
- * tidal slowing its orbit here does not carry, adds 0.75 by then. Mimas 8.94: about 6.3 off on
+ * tidal slowing its orbit here does not carry, adds 0.75 by then. Mimas 8.89: about 6.3 off on
  * average because the IAU's W and JPL's mean longitude disagree, and swung 2.3 either way (2e) by
  * its eccentricity. None of that is Mimas: its measured physical libration is 0.84 degrees
  * (Tajeddine et al. 2014, Science 346, 322), and W carries none; Horizons, on the same W against its
@@ -269,6 +269,22 @@ const MAX_OBLIQUITY_OFFSET_DEG = 0.1;
  */
 const MAX_SUB_PLANET_LONGITUDE_DEG = 7;
 const SUB_PLANET_CEILINGS_DEG: Record<string, number> = { moon: 8, mimas: 9.5, iapetus: 16.5 };
+/**
+ * How far a locked moon's spin axis may lean from the normal of the orbit it is drawn going round,
+ * over the same dates. A locked moon sits in a Cassini state, its axis on its orbit normal as the
+ * node carries both round the Laplace pole, and the IAU's pole goes round on a term of the node's
+ * angle; at the rate the IAU's source had for it and not the drawn orbit's, Miranda's axis was 7.89
+ * degrees off at AD 9 and Mimas's 2.63, and an Iapetus pole left on the Laplace pole is 8.30 off at
+ * every date (see `lockedToOrbit`).
+ *
+ * Measured on this catalogue: at most 0.97 degrees (Tethys, whose IAU pole sits 0.69 from its orbit
+ * normal today; Titan 0.94, whose pole the IAU holds still while its node turns in 705 years) but
+ * for four. The Moon 6.98, its real 6.7-degree tilt to its orbit. Phobos 1.81 and Deimos 1.74, and
+ * Proteus 1.09: their IAU poles nod with Mars's and Neptune's precessing poles, the Laplace poles
+ * their orbits are drawn round are fixed.
+ */
+const MAX_AXIS_FROM_ORBIT_DEG = 1;
+const AXIS_FROM_ORBIT_CEILINGS_DEG: Record<string, number> = { moon: 7.1, phobos: 2, deimos: 2, proteus: 1.2 };
 /** The clock's window, AD 1 to 3000 (`CLOCK_WINDOW` in `time.store.ts`), as Julian dates. */
 const CLOCK_START_JD = Date.parse('0001-01-01T00:00Z') / 86400000 + 2440587.5;
 const CLOCK_END_JD = Date.parse('3000-01-01T00:00Z') / 86400000 + 2440587.5;
@@ -279,6 +295,19 @@ function angleBetweenDeg(a: { x: number; y: number; z: number }, b: { x: number;
   return (Math.acos(Math.min(1, Math.max(-1, cosine))) * 180) / Math.PI;
 }
 
+/** Degrees between a body's spin axis — its IAU pole, turned over where W runs backwards — and the normal of the orbit it is drawn going round, at a TDB date. */
+function axisFromOrbitDeg(body: BodyRecord, rotation: RotationalElements, jd: number): number {
+  const pole = orientationAt(rotation, jd);
+  const pointing = raDecToUnitVector(pole.poleRaDeg / 15, pole.poleDecDeg);
+  const sense = Math.sign(rotation.primeMeridianDeg[1]);
+  const axis = { x: sense * pointing.x, y: sense * pointing.y, z: sense * pointing.z };
+  const { inclinationDeg, longitudeOfAscendingNodeDeg } = meanElementsAt(body.orbit, body.rates, jd);
+  const tilt = inclinationDeg * DEG_TO_RAD;
+  const node = longitudeOfAscendingNodeDeg * DEG_TO_RAD;
+  const normal = { x: Math.sin(tilt) * Math.sin(node), y: -Math.sin(tilt) * Math.cos(node), z: Math.cos(tilt) };
+  return angleBetweenDeg(axis, body.laplacePole ? laplacePlaneToEquatorial(normal, body.laplacePole) : eclipticToEquatorial(normal));
+}
+
 function validateBodies(bodies: BodyRecord[], horizonsOrbits: Map<string, OrbitalElements>, horizonsTracks: Map<string, TrackPoint[]>): void {
   assertCondition(bodies.length > 0, 'No solar-system bodies were produced.');
 
@@ -364,14 +393,7 @@ function validateBodies(bodies: BodyRecord[], horizonsOrbits: Map<string, Orbita
         spins.push(`${body.id} day ${dayOffset.toExponential(1)}`);
       }
       if (body.obliquityDeg !== undefined) {
-        const pole = orientationAt(rotation, horizons!.epochJd);
-        const pointing = raDecToUnitVector(pole.poleRaDeg / 15, pole.poleDecDeg);
-        const axis = { x: Math.sign(rate) * pointing.x, y: Math.sign(rate) * pointing.y, z: Math.sign(rate) * pointing.z };
-        const { inclinationDeg, longitudeOfAscendingNodeDeg } = meanElementsAt(body.orbit, body.rates, horizons!.epochJd);
-        const tilt = inclinationDeg * DEG_TO_RAD;
-        const node = longitudeOfAscendingNodeDeg * DEG_TO_RAD;
-        const normal = { x: Math.sin(tilt) * Math.sin(node), y: -Math.sin(tilt) * Math.cos(node), z: Math.cos(tilt) };
-        const obliquity = angleBetweenDeg(axis, body.laplacePole ? laplacePlaneToEquatorial(normal, body.laplacePole) : eclipticToEquatorial(normal));
+        const obliquity = axisFromOrbitDeg(body, rotation, horizons!.epochJd);
         assertCondition(
           Math.abs(obliquity - body.obliquityDeg) <= MAX_OBLIQUITY_OFFSET_DEG,
           `${body.name}'s IAU spin axis is ${obliquity.toFixed(3)} degrees from its orbit's pole, where ${body.id === 'pluto' ? 'its IAU pole' : 'Horizons'} gives an obliquity of ${body.obliquityDeg} (at most ${MAX_OBLIQUITY_OFFSET_DEG} apart expected) — the pole or the sense of W was read wrongly.`
@@ -406,6 +428,13 @@ function validateBodies(bodies: BodyRecord[], horizonsOrbits: Map<string, Orbita
           `Moon ${body.id} turns its face up to ${worst.toFixed(2)} degrees from its planet between AD 1 and 3000 (at most ${ceiling} expected) — its orbit and its W disagree.`
         );
         spins.push(`${body.id} faces ${worst.toFixed(2)}`);
+        const axisCeiling = AXIS_FROM_ORBIT_CEILINGS_DEG[body.id] ?? MAX_AXIS_FROM_ORBIT_DEG;
+        const worstAxis = Math.max(...LOCK_DATES_JD.map((jd) => axisFromOrbitDeg(body, rotation!, jd)));
+        assertCondition(
+          worstAxis <= axisCeiling,
+          `Moon ${body.id}'s spin axis leans up to ${worstAxis.toFixed(2)} degrees from its orbit's normal between AD 1 and 3000 (at most ${axisCeiling} expected) — its pole does not go round with its node.`
+        );
+        spins.push(`${body.id} axis ${worstAxis.toFixed(2)}`);
       }
       if (body.massRatio !== undefined) {
         // The pair's barycentre, which the planet's elements place, must lie outside the planet —
diff --git a/tools/etl/lib/locked-spin.ts b/tools/etl/lib/locked-spin.ts
index 2f85ac4..82de187 100644
--- a/tools/etl/lib/locked-spin.ts
+++ b/tools/etl/lib/locked-spin.ts
@@ -21,6 +21,16 @@ const MAX_LOCKED_RATE_OFFSET = 1e-5;
 /** Harmonics of the node's angle that carry a pole round its orbit's; see {@link lockedToOrbit}. */
 const POLE_HARMONICS = 5;
 
+/**
+ * How far a periodic term's angle may turn from a multiple of the node's rate, as a fraction of it,
+ * and still be taken for the node's angle as the IAU's source had it. Measured: at most 3.4e-2
+ * (Ganymede's J5), then Rhea's R4 1.2e-2 and Miranda's U11 3.2e-3; the nearest that is not a node is
+ * a term of Miranda's W alone, 6.0e-2 from three times it. Multiples go up to the ninth, the most the
+ * report takes (Triton's N7); past that, Umbriel's W has a term 1.0e-2 from ten times its node's.
+ */
+const MAX_NODE_RATE_OFFSET = 0.05;
+const MAX_NODE_HARMONIC = 9;
+
 /** The planet's east longitude on a moon's IAU body-fixed frame, from the moon's mean place, at a TDB date. */
 export function subPlanetLongitudeDeg(body: Pick<BodyRecord, 'orbit' | 'rates' | 'laplacePole'>, elements: RotationalElements, jd: number): number {
   const own = positionAtEpoch(meanElementsAt(body.orbit, body.rates, jd));
@@ -41,15 +51,25 @@ export function subPlanetLongitudeDeg(body: Pick<BodyRecord, 'orbit' | 'rates' |
  * The report gives a locked moon's W the mean motion of whichever orbit its authors had, and JPL's
  * table has another: Proteus's W turns 6.3e-7 of its rate slower than its row, which turned its far
  * side to Neptune at AD 1 (146 degrees), Mimas's 1.6e-7 faster (52 at AD 1) and Miranda's (23).
- * W's rate is set to the orbit's here, its constant moved so W is unchanged at {@link PRESENT_JD},
- * and the pole and every periodic term are the IAU's. Measured over AD 1-3000: Proteus 2.7 degrees,
- * Mimas 8.9, Miranda 2.8, Ariel 1.0. A W with a quadratic is left: Phobos's orbit already takes the
- * quadratic from W (see `orbitalTermsOfPrimeMeridian`), and the Moon's, its tidal slowing, is 0.75
- * degrees at AD 1.
+ * W's rate is set to the orbit's here, its constant moved so W is unchanged at {@link PRESENT_JD}.
+ * Measured over AD 1-3000: Proteus 2.7 degrees, Mimas 8.9, Miranda 2.4, Ariel 1.0. A W with a
+ * quadratic is left: Phobos's orbit already takes the quadratic from W (see
+ * `orbitalTermsOfPrimeMeridian`), and the Moon's, its tidal slowing, is 0.75 degrees at AD 1.
+ *
+ * The node's angle goes the same way. A moon in a Cassini state keeps its axis on its orbit normal,
+ * which goes round the Laplace pole with the node, and the IAU's pole goes round with it on a term
+ * of the node's angle, at the node's rate as its source had it: Miranda's U11 at -2024.22 degrees a
+ * century, where the table the orbit is drawn from has -2030.80. On a 4.3-degree circle that parted
+ * the axis from the drawn orbit by 7.9 degrees at AD 1, and Mimas's by 2.6. Every term whose angle
+ * turns within {@link MAX_NODE_RATE_OFFSET} of a multiple of the node's rate is set to that multiple,
+ * its constant moved so the angle is unchanged at the present, and the pole with it: over AD 1-3000
+ * Miranda's axis stays within 0.42 degrees of its orbit normal and Mimas's within 0.47, and the
+ * Io's, Europa's, Ganymede's, Rhea's and Triton's within 0.17. The rest of the pole and its terms
+ * are the IAU's: Callisto's J6 turns 40 per cent slower than its node, and is left.
  *
  * `poleFollowsOrbit` is for Iapetus, whose IAU pole moves 3.9 degrees a century in right ascension
  * and 1.1 in declination: a straight line through its orbit normal's 3 439-year circle round the
- * Laplace pole, 8.3 degrees across, which by AD 1 has run past the celestial pole (Dec 97.9) and 11
+ * Laplace pole, 8.3 degrees in radius (16.6 across), which by AD 1 has run past the celestial pole (Dec 97.9) and 11
  * degrees off the orbit, and turned its face 87 degrees from Saturn. Its axis sits on its orbit normal
  * (0.04 degrees apart today), as a moon in a Cassini state keeps it, so its pole is given the circle: the
  * normal's right ascension as sines and declination as cosines of the node's angle and its first
@@ -69,7 +89,17 @@ export function lockedToOrbit(elements: RotationalElements, mean: Pick<MeanOrbit
   if (Math.abs(w1 / n - 1) > MAX_LOCKED_RATE_OFFSET) {
     throw new Error(`${name}'s IAU W turns at ${w1} degrees a day, ${Math.abs(w1 / n - 1).toExponential(2)} of its orbit's ${n}: not the rate of the orbit it keeps its face to.`);
   }
-  const locked: RotationalElements = { ...elements, primeMeridianDeg: [w0 + (w1 - n) * (PRESENT_JD - J2000_JD), n, 0] };
+  const nodeRate = mean.rates.longitudeOfAscendingNodeDegPerDay * DAYS_PER_JULIAN_CENTURY;
+  const present = (PRESENT_JD - J2000_JD) / DAYS_PER_JULIAN_CENTURY;
+  const terms = elements.terms?.map((term) => {
+    const [constant, rate, quadratic = 0] = term.angleDeg;
+    const k = Math.round(rate / nodeRate);
+    if (quadratic !== 0 || k === 0 || Math.abs(k) > MAX_NODE_HARMONIC || Math.abs(rate / (k * nodeRate) - 1) > MAX_NODE_RATE_OFFSET) {
+      return term;
+    }
+    return { ...term, angleDeg: [constant + (rate - k * nodeRate) * present, k * nodeRate] };
+  });
+  const locked: RotationalElements = { ...elements, primeMeridianDeg: [w0 + (w1 - n) * (PRESENT_JD - J2000_JD), n, 0], ...(terms ? { terms } : {}) };
   return poleFollowsOrbit ? poleRoundOrbit(locked, mean) : locked;
 }