diff --git a/src/app/shared/state/time.store.spec.ts b/src/app/shared/state/time.store.spec.ts
index 762a47f..9895c92 100644
--- a/src/app/shared/state/time.store.spec.ts
+++ b/src/app/shared/state/time.store.spec.ts
@@ -85,6 +85,22 @@ describe('TimeStore', () => {
     expect(time.date().toISOString()).toBe('2020-12-21T19:00:01.000Z');
   });
 
+  it('stops a running clock at either end of the window, at real time turned back into it', () => {
+    time.setDate(new Date('0001-01-10T00:00Z'));
+    time.setRate(-2_629_800); // a month a second, backwards
+    vi.advanceTimersByTime(60_000);
+    expect(time.date().toISOString()).toBe('0001-01-01T00:00:00.000Z');
+    expect(time.rate()).toBe(1);
+    vi.advanceTimersByTime(1000);
+    expect(time.date().toISOString()).toBe('0001-01-01T00:00:01.000Z');
+
+    time.setDate(new Date('2999-12-01T00:00Z'));
+    time.setRate(2_629_800);
+    vi.advanceTimersByTime(60_000);
+    expect(time.date().toISOString()).toBe('3000-01-01T00:00:00.000Z');
+    expect(time.rate()).toBe(-1);
+  });
+
   it('refuses a date the planets’ elements were never fitted for, and stays where it was', () => {
     const before = time.date().toISOString();
 
diff --git a/src/app/shared/state/time.store.ts b/src/app/shared/state/time.store.ts
index ca66ffc..1101974 100644
--- a/src/app/shared/state/time.store.ts
+++ b/src/app/shared/state/time.store.ts
@@ -40,6 +40,10 @@ const WINDOW_MS = {
   min: Date.parse(`${CLOCK_WINDOW.min}Z`),
   max: Date.parse(`${CLOCK_WINDOW.max}Z`),
 };
+const WINDOW_JD = {
+  min: WINDOW_MS.min / MS_PER_DAY + JULIAN_DATE_AT_EPOCH,
+  max: WINDOW_MS.max / MS_PER_DAY + JULIAN_DATE_AT_EPOCH,
+};
 
 /**
  * The date the map is drawn for.
@@ -65,9 +69,22 @@ export class TimeStore {
   private anchorJd = dateToJulianDate();
   private anchorWallMs = Date.now();
 
-  /** Julian date for this instant, at the rate the reader chose. */
+  /**
+   * Julian date for this instant, at the rate the reader chose, held to {@link CLOCK_WINDOW}: a
+   * clock run past either end stops there, at real time turned back into the window, as if the
+   * reader had set that date. Unheld, a month a second carried it past AD 3000, where the planets'
+   * elements were never fitted, and before AD 1, where `toISOString` writes a six-digit year the
+   * date strip, the note and the date field cut in the wrong places ("-000001-12-01 00 UTC").
+   */
   julianDate(): number {
-    return this.anchorJd + ((Date.now() - this.anchorWallMs) * this.rate()) / MS_PER_DAY;
+    const jd = this.anchorJd + ((Date.now() - this.anchorWallMs) * this.rate()) / MS_PER_DAY;
+    if (jd >= WINDOW_JD.min && jd <= WINDOW_JD.max) {
+      return jd;
+    }
+    this.anchorJd = jd < WINDOW_JD.min ? WINDOW_JD.min : WINDOW_JD.max;
+    this.anchorWallMs = Date.now();
+    this.rate.set(jd < WINDOW_JD.min ? 1 : -1);
+    return this.anchorJd;
   }
 
   /**