diff --git a/src/app/features/galaxy-system/galaxy-system-scene.component.ts b/src/app/features/galaxy-system/galaxy-system-scene.component.ts
index 1170b46..f472c75 100644
--- a/src/app/features/galaxy-system/galaxy-system-scene.component.ts
+++ b/src/app/features/galaxy-system/galaxy-system-scene.component.ts
@@ -2221,8 +2221,8 @@ export class GalaxySystemSceneComponent implements AfterViewInit, OnDestroy {
     this.systemGroup.add(this.systemRenderer.object);
     this.applyDisplay(this.display());
 
-    // Framed against the grid's outer ring rather than the outermost orbit — the ring is always
-    // the wider of the two — and against the camera this scene actually has, so the margin holds
+    // Framed against the outermost thing drawn — the grid's outer ring, or an eccentric orbit's
+    // aphelion where it runs past it — and against the camera this scene actually has, so the margin holds
     // whatever the window shape. Computed before the star, because how far away the star will be
     // seen from is what decides how big its halo has to be to stay visible.
     // Framed against the perspective camera whichever is active: the framing distance is what
@@ -2230,7 +2230,7 @@ export class GalaxySystemSceneComponent implements AfterViewInit, OnDestroy {
     const framingCamera = this.engine.getPerspectiveCamera();
     const viewport = { fovDegrees: framingCamera.fov, aspect: framingCamera.aspect };
     const framingDistance = systemFramingDistanceAu(
-      this.systemRenderer.gridOuterRadiusAu,
+      this.systemRenderer.outermostRadiusAu,
       viewport,
     );
 
diff --git a/src/app/features/galaxy-system/system-framing.spec.ts b/src/app/features/galaxy-system/system-framing.spec.ts
index bcda348..b920144 100644
--- a/src/app/features/galaxy-system/system-framing.spec.ts
+++ b/src/app/features/galaxy-system/system-framing.spec.ts
@@ -20,6 +20,8 @@ const GL_357 = { innermost: 0.035, outermost: 0.204 };
 const SOLAR = { innermost: 0.387, outermost: 30.07 };
 /** The solar system as the map draws it: out to Eris's semi-major axis, 67.93 AU. */
 const SOLAR_TO_ERIS = { innermost: 0.387, outermost: 67.93 };
+/** Eris's aphelion, a(1 + e) = 67.934 x 1.4382: past the 80 AU ring its semi-major axis gives. */
+const ERIS_APHELION_AU = 97.7;
 
 describe('starMarkerRadiusAu', () => {
   it('never reaches the innermost orbit', () => {
@@ -141,6 +143,14 @@ describe('the grid and the framing together', () => {
     }
   });
 
+  it('leaves Eris’s aphelion its whole margin in every window shape, a phone held upright included', () => {
+    // The scene frames the aphelion where it runs past the ring. Under the old 500 AU ceiling the
+    // phone would hold it at 0.907 of the half-width instead of 1 / 1.12 = 0.893.
+    for (const viewport of VIEWPORTS) {
+      expect(ERIS_APHELION_AU / systemFrameRadiusAu(systemFramingDistanceAu(ERIS_APHELION_AU, viewport), viewport)).toBeLessThan(0.9);
+    }
+  });
+
   it('still encloses the outermost orbit, so no planet sits off the edge of the grid', () => {
     for (const { outermost } of [TRAPPIST_1, GL_357, SOLAR, { outermost: 1 }, { outermost: 12.4 }]) {
       expect(fit(outermost).ring).toBeGreaterThan(outermost);
diff --git a/src/app/features/galaxy-system/system-framing.ts b/src/app/features/galaxy-system/system-framing.ts
index 9395f26..4a4f3f2 100644
--- a/src/app/features/galaxy-system/system-framing.ts
+++ b/src/app/features/galaxy-system/system-framing.ts
@@ -61,15 +61,17 @@ const MIN_FRAMING_DISTANCE_AU = 0.06;
 /**
  * Ceiling on the framing distance, so a distant companion does not push the star to a dot.
  *
- * Generous enough to frame the solar system out to Eris in any window a reader holds: its grid's
- * outer ring, 80 AU, needs 192 AU on a landscape display and 416 on a 390 by 844 phone once the
- * camera's real field of view is accounted for, and 500 holds it down to an aspect of 0.385. At
- * 200, which framed Pluto's 40 AU ring, a portrait window arrived with Eris off screen, and a
- * phone with Makemake too. Only genuinely pathological systems reach it now — the handful with
- * directly-imaged companions hundreds of AU out — and those still arrive framed on their inner
- * region, with the orbit controls reaching far enough to pull back to the rest.
+ * Generous enough to frame the solar system out to Eris in any window a reader holds: Eris's
+ * aphelion, 97.7 AU, the furthest it draws, needs 235 AU on a landscape display and 508 on a 390
+ * by 844 phone once the camera's real field of view is accounted for, and 600 holds it down to an
+ * aspect of 0.39. At 500, framed on the 80 AU grid ring inside that aphelion, a phone arrived with
+ * Eris's orbit 3.5 px from the edge; at 200, which framed Pluto's 40 AU ring, a portrait window
+ * arrived with Eris off screen, and a phone with Makemake too. Only genuinely pathological systems
+ * reach it now — the handful with directly-imaged companions hundreds of AU out — and those still
+ * arrive framed on their inner region, with the orbit controls reaching far enough to pull back
+ * to the rest.
  */
-const MAX_FRAMING_DISTANCE_AU = 500;
+const MAX_FRAMING_DISTANCE_AU = 600;
 
 /** Framing for a star with no known planets, where there is nothing to fit. */
 const EMPTY_SYSTEM_FRAMING_DISTANCE_AU = 3;
@@ -137,8 +139,9 @@ export function systemFrameRadiusAu(distanceAu: number, viewport: SystemViewport
  * was tuned by eye against a 55-degree field, and the engine's camera is 50 — which left the
  * grid overflowing the frame in 368 of the 371 systems the datasets contain.
  *
- * Callers pass the outermost thing actually drawn, which is the reference grid's outer ring
- * rather than the outermost orbit — the ring is always the wider of the two, by construction.
+ * Callers pass the outermost thing actually drawn: the reference grid's outer ring, which runs past
+ * every semi-major axis by construction, or an eccentric orbit's aphelion where that runs past the
+ * ring, as Eris's does.
  */
 export function systemFramingDistanceAu(framedRadiusAu: number, viewport: SystemViewport = DEFAULT_SYSTEM_VIEWPORT): number {
   if (!Number.isFinite(framedRadiusAu) || framedRadiusAu <= 0) {
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 6d669ef..2247e36 100644
--- a/src/app/features/galaxy-system/system-orbits-renderer.spec.ts
+++ b/src/app/features/galaxy-system/system-orbits-renderer.spec.ts
@@ -449,6 +449,28 @@ describe('rotation without IAU elements', () => {
   });
 });
 
+describe('outermostRadiusAu', () => {
+  function drawn(axis: number, eccentricity: number): BodyRecord {
+    return {
+      id: 'eris', systemStarId: 0, name: 'Eris', kind: 'dwarf', radiusKm: 1163, orbitSource: 'test',
+      orbit: { semiMajorAxisAu: axis, eccentricity, inclinationDeg: 44, longitudeOfAscendingNodeDeg: 36, argumentOfPeriapsisDeg: 151, meanAnomalyAtEpochDeg: 0, epochJd: DEFAULT_EPOCH_JD },
+      rates: keplerRates(axis, GM_SUN_AU3_PER_DAY2)
+    };
+  }
+
+  it('reaches as far as an eccentric orbit goes past the grid: Eris’s aphelion, 97.7 AU, not the 80 AU ring', () => {
+    const renderer = new SystemOrbitsRenderer([drawn(67.934, 0.4382)], []);
+    expect(renderer.outermostRadiusAu).toBeCloseTo(67.934 * 1.4382, 9);
+    renderer.dispose();
+  });
+
+  it('is the grid’s outer ring where every orbit stays inside it', () => {
+    const renderer = new SystemOrbitsRenderer([drawn(30, 0.01)], []);
+    expect(renderer.outermostRadiusAu).toBe(35);
+    renderer.dispose();
+  });
+});
+
 describe('photographs', () => {
   it('puts them on their bodies once loaded, one a frame, so the GPU is not handed every map at once, and in their own colours', () => {
     // Ids no other test here draws, since the loaded textures are shared through the cache.
diff --git a/src/app/features/galaxy-system/system-orbits-renderer.ts b/src/app/features/galaxy-system/system-orbits-renderer.ts
index 90ae8d4..b721fca 100644
--- a/src/app/features/galaxy-system/system-orbits-renderer.ts
+++ b/src/app/features/galaxy-system/system-orbits-renderer.ts
@@ -329,10 +329,12 @@ export class SystemOrbitsRenderer {
    */
   readonly referenceFrame: THREE.Quaternion;
   /**
-   * Outer radius (AU) of the reference grid, or 0 where there is none. This — not the outermost
-   * orbit — is the widest thing the system draws, so it is what the camera has to frame.
+   * How far (AU) from the star the system draws anything, or 0 where it draws nothing: what the
+   * camera has to frame. The reference grid's outer ring, which runs 15 per cent past the largest
+   * semi-major axis, unless an eccentric orbit reaches further at its aphelion — Eris's, 97.7 AU,
+   * does past the solar system's 80 AU ring, and some orbit does in 303 of the 1 190 exoplanet systems.
    */
-  readonly gridOuterRadiusAu: number;
+  readonly outermostRadiusAu: number;
 
   private readonly topLevelBodies: TrackedTopLevelBody[] = [];
   private readonly moons: TrackedMoon[] = [];
@@ -376,10 +378,11 @@ export class SystemOrbitsRenderer {
     const members: SystemMember[] = [];
     const topLevelBodiesById = new Map<string, BodyRecord>();
 
-    const topLevelAxes = [
-      ...bodies.filter((body) => !body.parentBodyId).map((body) => body.orbit.semiMajorAxisAu),
-      ...exoplanets.filter((exoplanet) => isPropagatableOrbit(exoplanet.orbit)).map((exoplanet) => exoplanet.orbit.semiMajorAxisAu!)
-    ].filter((axis) => Number.isFinite(axis) && axis > 0);
+    const topLevelOrbits = [
+      ...bodies.filter((body) => !body.parentBodyId).map(({ orbit }) => ({ axis: orbit.semiMajorAxisAu, eccentricity: orbit.eccentricity })),
+      ...exoplanets.filter((exoplanet) => isPropagatableOrbit(exoplanet.orbit)).map(({ orbit }) => ({ axis: orbit.semiMajorAxisAu!, eccentricity: orbit.eccentricity ?? 0 }))
+    ].filter(({ axis }) => Number.isFinite(axis) && axis > 0);
+    const topLevelAxes = topLevelOrbits.map(({ axis }) => axis);
     this.maxTopLevelSemiMajorAxisAu = topLevelAxes.length > 0 ? Math.max(...topLevelAxes) : 0;
     this.minTopLevelSemiMajorAxisAu = topLevelAxes.length > 0 ? Math.min(...topLevelAxes) : 0;
 
@@ -453,7 +456,7 @@ export class SystemOrbitsRenderer {
     this.referenceFrame = bodies.some((body) => !body.parentBodyId) ? ECLIPTIC_FRAME.clone() : exoplanetFrame;
 
     const rings = systemGridRingsAu(this.maxTopLevelSemiMajorAxisAu);
-    this.gridOuterRadiusAu = rings.length > 0 ? rings[rings.length - 1] : 0;
+    this.outermostRadiusAu = Math.max(rings.length > 0 ? rings[rings.length - 1] : 0, ...topLevelOrbits.map(({ axis, eccentricity }) => axis * (1 + eccentricity)));
     if (rings.length > 0) {
       this.grid = new PolarGridPlane({
         ringRadii: rings,