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 8aa8c62..ae69d21 100644
--- a/src/app/features/galaxy-system/system-orbits-renderer.spec.ts
+++ b/src/app/features/galaxy-system/system-orbits-renderer.spec.ts
@@ -690,6 +690,33 @@ describe('solar-system bodies against Horizons', () => {
     }
   });
 
+  /** How far a top-level body is from its own drawn orbit line, in AU: from the nearest of its chords. */
+  function offLineAu(id: string): number {
+    const marker = renderer.members.find((member) => member.id === id)!.marker;
+    const line = renderer.object.children[renderer.object.children.indexOf(marker) - 1] as THREE.Line;
+    expect(line.name).toBe('orbit-line');
+    line.updateMatrixWorld();
+    const position = line.geometry.getAttribute('position');
+    const vertex = (index: number): THREE.Vector3 => new THREE.Vector3().fromBufferAttribute(position, index).applyMatrix4(line.matrixWorld);
+    const chord = new THREE.Line3();
+    const closest = new THREE.Vector3();
+    let nearest = Number.POSITIVE_INFINITY;
+    for (let index = 0; index + 1 < position.count; index++) {
+      nearest = Math.min(nearest, chord.set(vertex(index), vertex(index + 1)).closestPointToPoint(marker.position, true, closest).distanceTo(marker.position));
+    }
+    return nearest;
+  }
+
+  it('redraws a planet’s orbit as its axis and eccentricity drift, so Saturn and Mars stay on their lines at AD 1', () => {
+    // What is left is the 128 chords' own sag from the true ellipse: measured 0.0017 AU for Saturn and
+    // 0.0005 for Mars at AD 1, and 0.0011 for Saturn at J2000. Drawn at J2000's shape at AD 1, the
+    // lines were 0.054 AU from Saturn and 0.0022 from Mars.
+    for (const [id, days, maxAu] of [['saturn', -730000, 0.002], ['mars', -730000, 0.0006], ['saturn', 0, 0.0015]] as const) {
+      renderer.update(DEFAULT_EPOCH_JD + days);
+      expect(offLineAu(id)).toBeLessThan(maxAu);
+    }
+  });
+
   it('turns the Moon’s drawn orbit with its node, so the Moon stays on its own line', () => {
     // Half the node's 18.6-year turn on, the ellipse drawn at the epoch has the Moon 10 degrees off
     // its plane at the worst.
diff --git a/src/app/features/galaxy-system/system-orbits-renderer.ts b/src/app/features/galaxy-system/system-orbits-renderer.ts
index 54186ac..08b8041 100644
--- a/src/app/features/galaxy-system/system-orbits-renderer.ts
+++ b/src/app/features/galaxy-system/system-orbits-renderer.ts
@@ -129,20 +129,11 @@ const ORBIT_LINE_NAME = 'orbit-line';
  * ellipse fixed at one date has the Moon up to 2 sin 5.16° of its distance, 69 000 km, off its own
  * line nine years on.
  *
- * The shape is the epoch's. The planets' axes and eccentricities do drift, but Pluto's axis, the
- * fastest, moves 0.0045 AU a century against 39.5, which no drawn line shows.
+ * The shape is redrawn by {@link reshapeOrbitLine} as the planets' axes and eccentricities drift.
  */
 function buildOrbitLine(elements: OrbitalElements, kind: SystemMemberKind, frame: THREE.Quaternion): THREE.Line {
-  const points = orbitEllipsePoints({ ...elements, inclinationDeg: 0, longitudeOfAscendingNodeDeg: 0, argumentOfPeriapsisDeg: 0 });
-  const positions = new Float32Array(points.length * 3);
-  points.forEach((point, index) => {
-    positions[index * 3] = point.x;
-    positions[index * 3 + 1] = point.y;
-    positions[index * 3 + 2] = point.z;
-  });
-
   const geometry = new THREE.BufferGeometry();
-  geometry.setAttribute('position', new THREE.BufferAttribute(positions, 3));
+  geometry.setAttribute('position', new THREE.BufferAttribute(ellipseInItsPlane(elements, new Float32Array((ORBIT_LINE_SEGMENTS + 1) * 3)), 3));
 
   const material = new THREE.LineBasicMaterial({
     color: colorForKind(kind),
@@ -152,10 +143,49 @@ function buildOrbitLine(elements: OrbitalElements, kind: SystemMemberKind, frame
 
   const line = new THREE.Line(geometry, material);
   line.name = ORBIT_LINE_NAME;
+  line.userData = { semiMajorAxisAu: elements.semiMajorAxisAu, eccentricity: elements.eccentricity };
   orientOrbit(line.quaternion, elements, frame);
   return line;
 }
 
+const ORBIT_LINE_SEGMENTS = 128;
+
+/** The orbit's ellipse in its own plane, periapsis along +X, written into `positions`. */
+function ellipseInItsPlane(elements: OrbitalElements, positions: Float32Array): Float32Array {
+  orbitEllipsePoints({ ...elements, inclinationDeg: 0, longitudeOfAscendingNodeDeg: 0, argumentOfPeriapsisDeg: 0 }, ORBIT_LINE_SEGMENTS).forEach((point, index) => {
+    positions[index * 3] = point.x;
+    positions[index * 3 + 1] = point.y;
+    positions[index * 3 + 2] = point.z;
+  });
+  return positions;
+}
+
+/**
+ * How far, in AU, an orbit's drawn ellipse may be from its current one before it is drawn again:
+ * well under the 128 chords' own sag from the true curve, 0.0005 AU for Mars and 0.003 for Saturn.
+ */
+const ORBIT_RESHAPE_AU = 1e-4;
+
+/**
+ * Draws an orbit line's ellipse again once the axis and eccentricity it was drawn with have drifted
+ * from `elements`' by more than {@link ORBIT_RESHAPE_AU}. Standish's rates move Saturn's
+ * eccentricity 0.0064 in twenty centuries, and left at J2000's, the line passed 0.056 AU, 8.4
+ * million km, from Saturn at AD 1; Jupiter 0.016 AU there, Pluto 0.021 at AD 3000. The moons' and
+ * the exoplanets' elements carry no such rates, so their lines are drawn once.
+ */
+function reshapeOrbitLine(line: THREE.Line, elements: OrbitalElements): void {
+  const drawn = line.userData as { semiMajorAxisAu: number; eccentricity: number };
+  const driftAu = Math.abs(elements.semiMajorAxisAu - drawn.semiMajorAxisAu) + elements.semiMajorAxisAu * Math.abs(elements.eccentricity - drawn.eccentricity);
+  if (driftAu <= ORBIT_RESHAPE_AU) {
+    return;
+  }
+  const position = line.geometry.getAttribute('position') as THREE.BufferAttribute;
+  ellipseInItsPlane(elements, position.array as Float32Array);
+  position.needsUpdate = true;
+  line.geometry.computeBoundingSphere();
+  line.userData = { semiMajorAxisAu: elements.semiMajorAxisAu, eccentricity: elements.eccentricity };
+}
+
 /**
  * A marker sphere, surfaced with the body's own photograph where one has ever been taken, and
  * with a texture derived from its measurements where none has — and lit by its star either way,
@@ -498,6 +528,7 @@ export class SystemOrbitsRenderer {
       body.position.set(orbital.x, orbital.y, orbital.z).applyQuaternion(body.frame);
       body.marker.position.copy(body.position);
       orientOrbit(body.orbitLine.quaternion, current, body.frame);
+      reshapeOrbitLine(body.orbitLine, current);
       if (body.rotationalElements) {
         bodyOrientation(body.rotationalElements, epochJd, body.marker.quaternion, body.id === 'earth');
       } else if (body.rotationPeriodHours) {