diff --git a/assets/js/components.js b/assets/js/components.js
index 2495fb8..8c86d87 100644
--- a/assets/js/components.js
+++ b/assets/js/components.js
@@ -192,9 +192,8 @@ export function SkyScope({ elev, dt, glob = 0, size = 26 }) {
 
   const phase = moonPhaseFraction(dt);
   const moonR = innerR * 0.55;
-  const phaseOffset = Math.cos(Math.PI * phase) * moonR;
-  const moonLitFromRight = phase < 0.5;
-  const shadowCx = r + phaseOffset;
+  const shadowOffset = (1 - Math.abs(2 * phase - 1)) * 2 * moonR;
+  const shadowCx = r + (phase < 0.5 ? -shadowOffset : shadowOffset);
   const grass = grassFillForElev(elev);
 
   const uid    = `ss-${size}-${Math.round(elev * 10)}-${Math.round(phase * 1000)}-${isRising ? 'r' : 's'}`;
@@ -437,9 +436,8 @@ export function ScopeReticle({ value, cat, loading, elev = 0, dt = new Date(), g
   const sunGlowPeak = 0.30 + radFrac * 0.45 + horizFrac * 0.15; // centre opacity
   const moonDrawR = 15;
   const moonY = cy - 45;
-  const phaseOffset = Math.cos(Math.PI * phase) * moonDrawR;
-  const moonLitFromRight = phase < 0.5;
-  const moonShadowCx = cx + phaseOffset;
+  const shadowOffset = (1 - Math.abs(2 * phase - 1)) * 2 * moonDrawR;
+  const moonShadowCx = cx + (phase < 0.5 ? -shadowOffset : shadowOffset);
   // Readout text colours flip with day/night for legibility against the sky.
   const readoutColor = isDay ? '#1e1208' : '#f5edd6';
   const readoutMutedColor = isDay ? '#9a7d5a' : '#d4c5a8';
diff --git a/assets/js/utils.js b/assets/js/utils.js
index 8151adf..6773cc7 100644
--- a/assets/js/utils.js
+++ b/assets/js/utils.js
@@ -294,7 +294,7 @@ export function confidenceBand(i) {
 export function moonPhaseFraction(date) {
   const JD = date.getTime() / 86400000 + 2440587.5;
   const syn = 29.530588;
-  const ref = 2451550.2597;
+  const ref = 2451560.2054;
   let p = ((JD - ref) % syn) / syn;
   if (p < 0) p += 1;
   return p;