diff --git a/src/main/java/com/kosherjava/zmanim/util/SPACalculator.java b/src/main/java/com/kosherjava/zmanim/util/SPACalculator.java
index 93651f86..77964252 100644
--- a/src/main/java/com/kosherjava/zmanim/util/SPACalculator.java
+++ b/src/main/java/com/kosherjava/zmanim/util/SPACalculator.java
@@ -79,6 +79,15 @@ public class SPACalculator extends AstronomicalCalculator {
 	/** Julian days per century. */
 	private static final double JULIAN_DAYS_PER_CENTURY = 36525.0;
 
+	/**
+	 * The largest difference, in degrees, between the Sun's zenith at the solved time and the requested zenith that is still
+	 * accepted as a sunrise or sunset. When the secant iteration in {@link #solveRiseSet} ends further off than this, it did
+	 * not converge, and there is no event on that date. Converged solutions end below 1e-6° (floating-point noise in the
+	 * Julian day), and failed ones almost always above 1e-3°. 1e-4° leaves a wide margin above the noise and is still
+	 * below the SPA's stated accuracy of ±0.0003°.
+	 */
+	private static final double MAX_ZENITH_RESIDUAL = 1e-4;
+
 	/** Whether to apply the ΔT (TT−UT) correction. Defaults to {@code true}. */
 	private boolean applyDeltaT = true;
 
@@ -331,6 +340,11 @@ private double solveRiseSet(LocalDate localDate, GeoLocation geoLocation, double
 			t1 = t2;
 			f1 = topocentricTrueZenith(jdDay + t1 / 1440.0, lat, geoLocation.getLongitude(), elevation) - adjustedZenith;
 		}
+		// Near the poles the closed-form guess can report an event the topocentric Sun never reaches. The iteration then
+		// wanders off without converging, and the last guess is an arbitrary time, not a solution.
+		if (!(Math.abs(f1) <= MAX_ZENITH_RESIDUAL)) {
+			return Double.NaN;
+		}
 		return t1;
 	}
 
diff --git a/src/test/java/com/kosherjava/zmanim/util/SPACalculatorTest.java b/src/test/java/com/kosherjava/zmanim/util/SPACalculatorTest.java
index 18cc1357..b9f8c58b 100644
--- a/src/test/java/com/kosherjava/zmanim/util/SPACalculatorTest.java
+++ b/src/test/java/com/kosherjava/zmanim/util/SPACalculatorTest.java
@@ -116,6 +116,19 @@ public void getUTCSunset() {
 		}
 	}
 
+	/**
+	 * Near the South Pole in March the closed-form first guess says the Sun reaches 10.2&deg; below the horizon, but the
+	 * topocentric Sun only gets to about 10.04&deg;. The secant iteration never converges and used to return an arbitrary
+	 * time. There is no event, so the result must be NaN.
+	 */
+	@Test
+	public void unconvergedRiseSetIsNoEvent() {
+		GeoLocation location = new GeoLocation("Antarctica", -77.26876171057897, -92.86928302120835, 3965.3333110036533,
+				java.time.ZoneId.of("Etc/GMT+6"));
+		double actual = calculator().getUTCSunrise(date("2127-03-14"), location, 100.2, false);
+		assertTrue("Sun never reaches 100.2° zenith; expected NaN but got " + actual, Double.isNaN(actual));
+	}
+
 	@Test
 	public void getUTCNoon() {
 		Object[][] cases = {