Calculation of the log of the illuminance of the moon outside the atmosphere.

This is the base 10 log of equation 20, converted from foot-candles to lux,
from:

   Krisciunas K. and Schaefer B.E. (1991). A model of the brightness of
moonlight, Publ. Astron.  Soc. Pacif. 103(667), 1033-1039 (DOI:
http://dx.doi.org/10.1086/132921).

simgear/ephemeris/moonpos.cxx

@@ -26,6 +26,7 @@
 #include <string.h>
 
 #include <simgear/debug/logstream.hxx>
+#include <simgear/math/SGMath.hxx>
 
 #include <math.h>
 
@@ -82,8 +83,9 @@ void MoonPos::updatePosition(double mjd, double lst, double lat, Star *ourSun)
     Ls, Lm, D, F, mpar, gclat, rho, HA, g,
     geoRa, geoDec,
     cosN, sinN, cosvw, sinvw, sinvw_cosi, cosecl, sinecl, rcoslatEcl,
-    FlesstwoD, MlesstwoD, twoD, twoM, twolat;
+    FlesstwoD, MlesstwoD, twoD, twoM, twolat, alpha;
   
+  double conv = 1.0319696543787917;    // The log foot-candle to log lux conversion factor.
   updateOrbElements(mjd);
   actTime = sgCalcActTime(mjd);
 
@@ -215,4 +217,14 @@ void MoonPos::updatePosition(double mjd, double lst, double lat, Star *ourSun)
   // Moon age and phase calculation
   age = lonEcl - ourSun->getlonEcl();
   phase = (1 - cos(age)) / 2;
+
+  // The log of the illuminance of the moon outside the atmosphere.
+  // This is the base 10 log of equation 20 from Krisciunas K. and Schaefer B.E.
+  // (1991). A model of the brightness of moonlight, Publ. Astron. Soc. Pacif.
+  // 103(667), 1033-1039 (DOI: http://dx.doi.org/10.1086/132921).
+  alpha = SGD_RADIANS_TO_DEGREES * SGMiscd::normalizeAngle(age + SGMiscd::pi());
+  log_I = -0.4 * (3.84 + 0.026*fabs(alpha) + 4e-9*pow(alpha, 4.0));
+
+  // Convert from foot-candles to lux.
+  log_I += conv;
 }

simgear/ephemeris/moonpos.hxx

@@ -41,6 +41,7 @@ private:
     double distance;   // the moon's distance to the earth
     double age;        // the moon's age from 0 to 2pi
     double phase;      // the moon's phase
+    double log_I;      // the moon's illuminance outside the atmosphere (logged)
     // void TexInit();  // This should move to the constructor eventually.
 
     // GLUquadricObj *moonObject;
@@ -68,6 +69,7 @@ public:
     double getDistance() const;
     double getAge() const;
     double getPhase() const;
+    double getLogIlluminance() const;
 };
 
 inline double MoonPos::getM() const
@@ -115,4 +117,9 @@ inline double MoonPos::getPhase() const
   return phase;
 }
 
+inline double MoonPos::getLogIlluminance() const
+{
+  return log_I;
+}
+
 #endif // _MOONPOS_HXX_