Sidereal (LST) and apparent-solar time-row modes

mk4-time/Core/Inc/astro.h

@@ -38,6 +38,9 @@ int    moon_phase_index(double phase);            /* 0..7, see ASTRO_MOON_NAMES
 /* (d) Equation of time in minutes (+ = apparent sun ahead of mean/clock sun). */
 double equation_of_time(double unix_s);
 
+double local_sidereal_time(double unix_s, double lon); /* LMST, hours [0,24), lon E+ */
+double local_solar_time(double unix_s, double lon);    /* apparent solar, hours [0,24) */
+
 /* (e) 6-character Maidenhead locator for (lat, lon). out must hold >= 7 bytes.
  *     Writes "----\0" if either coordinate is non-finite. */
 void   maidenhead(double lat, double lon, char out[7]);

mk4-time/Core/Inc/main.h

@@ -171,13 +171,20 @@ enum {
   MODE_GRID,       // Maidenhead grid locator
   MODE_LATLON,     // latitude / longitude, auto-paged
 
+  // Alternate-timebase TIME-ROW modes: the big digits tick Local Sidereal Time or
+  // apparent solar ("sundial") time, reseeded from the GPS-disciplined second; the
+  // date row keeps the civil date and a dedicated colon animation marks the mode.
+  MODE_LST,
+  MODE_SUNDIAL,
+
   NUM_DISPLAY_MODES
 };
 
 enum {
   COUNT_NORMAL =0,
   COUNT_HIDDEN,
-  COUNT_DOWN
+  COUNT_DOWN,
+  COUNT_ALT      // time row driven by the alternate timebase (MODE_LST / MODE_SUNDIAL)
 };
 
 enum {

mk4-time/Core/Src/astro.c

@@ -22,6 +22,19 @@ const char *const ASTRO_MOON_NAMES[8] = {
 
 static double days_since_j2000(double unix_s) { return (unix_s - J2000_UNIX) / 86400.0; }
 
+/* Greenwich Mean Sidereal Time in hours [0,24). Factored out so sun_az_el and
+ * local_sidereal_time share one series and can never drift apart. The quadratic
+ * term keeps truncation below ~1 ms for decades (the linear series alone drifts to
+ * ~10 ms by 2033). Note the input is GPS-derived UTC, not UT1: true-sky sidereal
+ * accuracy is floored by DUT1 (up to +/-0.9 s) by design. */
+static double gmst_hours(double n) {
+    double T = n / 36525.0;
+    double g = fmod(18.697374558 + 24.06570982441908 * n + 0.000026 * T * T, 24.0);
+    if (g < 0.0) g += 24.0;
+    if (g >= 24.0) g -= 24.0;
+    return g;
+}
+
 /* The shared low-precision solar block: from days-since-J2000 produce mean
  * longitude L, anomaly g, ecliptic longitude lambda, obliquity eps, and the
  * apparent right ascension alpha (deg) and declination delta (rad). */
@@ -46,7 +59,7 @@ void sun_az_el(double lat, double lon, double unix_s, double *az, double *el) {
     double alpha, delta;
     sun_ecliptic(n, NULL, NULL, NULL, NULL, &alpha, &delta);
 
-    double gmst = fmod(18.697374558 + 24.06570982441908 * n, 24.0); /* GMST in hours, used as-is */
+    double gmst = gmst_hours(n);                                    /* hours */
     double lst = gmst * 15.0 + lon;                                 /* degrees */
     double ha = (lst - alpha) * DEG;                                /* radians */
 
@@ -67,6 +80,27 @@ double equation_of_time(double unix_s) {
     return 4.0 * diff; /* minutes */
 }
 
+/* Local Mean Sidereal Time, decimal hours [0,24). LMST = GMST + longitude/15
+ * (east-positive). Anchors: GMST(J2000.0) = 18.697374558 h (IAU); Meeus ex. 12.b. */
+double local_sidereal_time(double unix_s, double lon) {
+    double lst = fmod(gmst_hours(days_since_j2000(unix_s)) + lon / 15.0, 24.0);
+    if (lst < 0.0) lst += 24.0;
+    if (lst >= 24.0) lst -= 24.0;   /* fmod residue can round the wrap to exactly 24.0 */
+    return lst; /* hours [0,24) */
+}
+
+/* Local apparent solar ("sundial") time, decimal hours [0,24).
+ * Apparent solar = mean solar (UTC shifted by longitude) + equation of time.
+ * At the sun's meridian transit this equals 12.0 exactly, consistent with
+ * sun_times()'s solar_noon = 12 - eot/60 - lon/15. */
+double local_solar_time(double unix_s, double lon) {
+    double utc_h = fmod(unix_s / 3600.0, 24.0);
+    double t = fmod(utc_h + lon / 15.0 + equation_of_time(unix_s) / 60.0, 24.0);
+    if (t < 0.0) t += 24.0;
+    if (t >= 24.0) t -= 24.0;
+    return t; /* hours [0,24) */
+}
+
 int sun_times(double lat, double lon, double unix_s,
               double *sunrise, double *sunset, double *solar_noon,
               double *civil_dusk, double *nautical_dusk, double *golden_dusk) {