Calculation and exposure of the moon's age and phase.

To obtain the sun's true longitude, the Star::getlonEcl() function has been
created.  The moon's age is then calculated as the difference between the moon's
and sun's true longitudes.  The phase is then simply half of one minus the
cosine of the age.  Hence these calculations are very cheap compared to the rest
of the moon position calculations.  The algorithm is from:

    Duffett-Smith, Peter. Practical Astronomy With Your Calculator. 3rd ed.
Cambridge: Cambridge University Press, 1981. ISBN 0-521-28411-2.

The code can replicate the example in the book of Feb 26, 1979 at 16h UT, with
an age of -0.4767 degrees a phase of 0.0:

$ fgfs --aircraft=UFO --start-date-gmt=1979:02:26:16:00:00 --airport=EGLL \
--altitude=50000 --enable-hud

The calculated phase is 1.459e-5 and the age is -6.2908 (which is -0.43628
degrees).  For a recent full moon:

$ fgfs --aircraft=UFO --start-date-gmt=2015:11:25:22:44:00 --airport=EGLL \
--altitude=50000 --enable-hud

The calculated age is -3.1413 and the phase is 0.9999999778.

simgear/ephemeris/moonpos.cxx

@@ -211,4 +211,8 @@ void MoonPos::updatePosition(double mjd, double lst, double lat, Star *ourSun)
   /* SG_LOG( SG_GENERAL, SG_INFO, 
 	  "Ra = (" << (SGD_RADIANS_TO_DEGREES *rightAscension) 
 	  << "), Dec= (" << (SGD_RADIANS_TO_DEGREES *declination) << ")" ); */
+
+  // Moon age and phase calculation
+  age = lonEcl - ourSun->getlonEcl();
+  phase = (1 - cos(age)) / 2;
 }

simgear/ephemeris/moonpos.hxx

@@ -39,6 +39,8 @@ private:
     double xg, yg;     // the moon's rectangular geocentric coordinates
     double ye, ze;     // the moon's rectangular equatorial coordinates
     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
     // void TexInit();  // This should move to the constructor eventually.
 
     // GLUquadricObj *moonObject;
@@ -64,6 +66,8 @@ public:
     double getye() const;
     double getze() const;
     double getDistance() const;
+    double getAge() const;
+    double getPhase() const;
 };
 
 inline double MoonPos::getM() const
@@ -101,4 +105,14 @@ inline double MoonPos::getDistance() const
   return distance;
 }
 
+inline double MoonPos::getAge() const
+{
+  return age;
+}
+
+inline double MoonPos::getPhase() const
+{
+  return phase;
+}
+
 #endif // _MOONPOS_HXX_

simgear/ephemeris/star.hxx

@@ -33,6 +33,7 @@ class Star : public CelestialBody
 
 private:
 
+    double lonEcl;     // the sun's true longitude
     double xs, ys;     // the sun's rectangular geocentric coordinates
     double ye, ze;     // the sun's rectangularequatorial rectangular geocentric coordinates
     double distance;   // the sun's distance to the earth
@@ -50,6 +51,7 @@ public:
     double getye() const;
     double getze() const;
     double getDistance() const;
+    double getlonEcl() const;
 };
 
 
@@ -88,6 +90,10 @@ inline double Star::getDistance() const
   return distance;
 }
 
+inline double Star::getlonEcl() const
+{
+  return lonEcl;
+}
 
 #endif // _STAR_HXX_