diff --git a/src/app/shared/astro/constants.spec.ts b/src/app/shared/astro/constants.spec.ts
index 40a597b..b3c7f09 100644
--- a/src/app/shared/astro/constants.spec.ts
+++ b/src/app/shared/astro/constants.spec.ts
@@ -20,12 +20,21 @@ describe('ttMinusUtSeconds', () => {
     expect(ttMinusUtSeconds(jd(2999, 1, 1))).toBe(69.184);
   });
 
-  it('joins its pieces without a jump of more than a second', () => {
-    for (const year of [500, 1600, 1700, 1800, 1860, 1900, 1920, 1941, 1961, 1972]) {
+  it('joins its polynomials without a jump of more than 0.3 s, the 0.25 s at 1600 the worst', () => {
+    for (const year of [500, 1600, 1700, 1800, 1860, 1900, 1920, 1941, 1961]) {
       const at = 2451544.5 + (year - 2000) * 365.2425;
-      expect(Math.abs(ttMinusUtSeconds(at + 0.01) - ttMinusUtSeconds(at - 0.01))).toBeLessThan(1);
+      expect(Math.abs(ttMinusUtSeconds(at + 0.01) - ttMinusUtSeconds(at - 0.01))).toBeLessThan(0.3);
     }
   });
+
+  it('hands over from the polynomial to the leap seconds at the start of 1972, 0.07 s apart', () => {
+    // The switch is placed by the calendar, not by a 365.2425-day year, so it is sampled on either
+    // side of midnight; and the last day of 1971 must still be the polynomial's 42.25 s, not the
+    // table's 42.184, or the switch has moved.
+    const start = jd(1972);
+    expect(Math.abs(ttMinusUtSeconds(start) - ttMinusUtSeconds(start - 1e-6))).toBeLessThan(0.1);
+    expect(Math.abs(ttMinusUtSeconds(jd(1971, 12, 31)) - 42.2485)).toBeLessThan(0.01);
+  });
 });
 
 describe('tdbFromUtc', () => {
diff --git a/src/app/shared/astro/constants.ts b/src/app/shared/astro/constants.ts
index 5c4cc9d..a84775d 100644
--- a/src/app/shared/astro/constants.ts
+++ b/src/app/shared/astro/constants.ts
@@ -32,12 +32,16 @@ const JD_1972 = Date.UTC(1972, 0, 1) / 86400000 + 2440587.5;
  * has fallen behind the uniform time the ephemerides run on.
  *
  * From 1972 the clock is UTC, held to within 0.9 s of UT by leap seconds, and TT - UTC is exact:
- * 32.184 s plus the 10 to 37 of them. After the last, at the start of 2017, it is held at 69.184 s,
- * as Horizons holds it: no one knows the leap seconds to come. Before 1972 it is ΔT from the
- * Espenak-Meeus polynomials (NASA's Five Millennium Canon, 2006), which fit the historical record
- * of eclipses and occultations: 10 570 s at AD 1, 1 574 at AD 1000, 29 in 1950. Held at 69 s there,
- * as it was, every spin but Earth's was a turn of (ΔT - 69 s) times its rate out, 15 degrees for
- * Jupiter at AD 1000 and 106 at AD 1, and the Moon 0.22 and 1.43 degrees along its orbit.
+ * 32.184 s plus TAI - UTC, which is the 10 s UTC started from in 1972 and the 27 leap seconds taken
+ * since, 37 s from 2017. After the last, at the start of 2017, it is held at 69.184 s, as Horizons
+ * holds it: no one knows the leap seconds to come. Before 1972 it is ΔT from the Espenak-Meeus
+ * polynomials (NASA's Five Millennium Canon, 2006), which fit the historical record of eclipses and
+ * occultations: 10 570 s at AD 1, 1 574 at AD 1000, 29 in 1950. As published they join within
+ * 0.26 s (at 1600; 0.16 s at 1700, under 0.09 s elsewhere), and the last meets the leap-second
+ * table 0.07 s apart. Held at 69 s there, as it was, every spin but Earth's was a turn of
+ * (ΔT - 69 s) times its rate out, 15 degrees for Jupiter at AD 1000 and 106 at AD 1, and the Moon
+ * 0.21 to 0.26 and 1.44 to 1.79 degrees along its orbit, as its eccentric orbit carries it faster
+ * or slower through those hours.
  */
 export function ttMinusUtSeconds(jdUt: number): number {
   if (jdUt >= JD_1972) {