static void ConvertEclipticToEquatorial(double jday, double lon, double lat, out double rasc, out double decl)
{
double d = jday - 2451543.5;
double oblecl = 23.4393 - 3.563E-7 * d;
double x = Degrees.Cos(lon) * Degrees.Cos(lat);
double y = Degrees.Sin(lon) * Degrees.Cos(lat);
double z = Degrees.Sin(lat);
double xe = x;
double ye = y * Degrees.Cos(oblecl) - z * Degrees.Sin(oblecl);
double ze = y * Degrees.Sin(oblecl) + z * Degrees.Cos(oblecl);
double r = Math.Sqrt(xe * xe + ye * ye);
rasc = Degrees.Atan2(ye, xe);
decl = Degrees.Atan2(ze, r);
}
static void ConvertEquatorialToHorizontal(double jday, double longitude, double latitude, double rasc, double decl, out double azimuth, out double altitude)
{
double d = jday - 2451543.5;
double w = 282.9404 + 4.70935E-5 * d;
double M = 356.0470 + 0.9856002585 * d;
double L = w + M;
double UT = Degrees.Normalize(Math.IEEERemainder(d, 1.0) * 360.0);
double hourAngle = Degrees.Normalize(longitude + L + 180.0 + UT - rasc);
double x = Degrees.Cos(hourAngle) * Degrees.Cos(decl);
double y = Degrees.Sin(hourAngle) * Degrees.Cos(decl);
double z = Degrees.Sin(decl);
double xhor = x * Degrees.Sin(latitude) - z * Degrees.Cos(latitude);
double yhor = y;
double zhor = x * Degrees.Cos(latitude) + z * Degrees.Sin(latitude);
azimuth = Degrees.Atan2(yhor, xhor) + 180.0;
altitude = Degrees.Atan2(zhor, Math.Sqrt(xhor * xhor + yhor * yhor));
}
public static Quaternion GetSunPosition(double jday, double longitude, double latitude)
{
double d = jday - 2451543.5;
double w = 282.9404 + 4.70935E-5 * d;
double e = 0.016709 - 1.151E-9 * d;
double M = Degrees.Normalize(356.0470 + 0.9856002585 * d);
double E = Degrees.Normalize(M + Radians.ToDegrees(e) * Degrees.Sin(M) * (1 + e * Degrees.Cos(M)));
double xv = Degrees.Cos(E) - e;
double yv = Degrees.Sin(E) * Math.Sqrt(1 - e * e);
double r = Math.Sqrt(xv * xv + yv * yv);
double lon = Degrees.Atan2(yv, xv) + w;
double lat = 0;
double rasc, decl;
ConvertEclipticToEquatorial(jday, lon, lat, out rasc, out decl);
ConvertEquatorialToHorizontal(jday, longitude, latitude, rasc, decl, out double azimuth, out double altitude);
// convert to unity rotation azim, altitude y then x
return(Quaternion.Euler(0f, (float)azimuth + 180.0f, 0f) * Quaternion.Euler((float)altitude, 0f, 0f));
}
// Sun Calculations
static void ConvertRectangularToSpherical(double x, double y, double z, out double rasc, out double decl, out double dist)
{
dist = Math.Sqrt(x * x + y * y + z * z);
rasc = Degrees.Atan2(y, x);
decl = Degrees.Atan2(z, Math.Sqrt(x * x + y * y));
}
static void GetEclipticMoonPosition(double jday, out double lon, out double lat, out double dist)
{
double d = jday - 2451543.5;
double N = 125.1228 - 0.0529538083 * d; // long asc node
double i = 5.1454; // inclination
double wm = 318.0634 + 0.1643573223 * d; // arg of perigee
double a = 60.2666; // mean distance
double e = 0.054900; // eccentricity
double ws = 282.9404 + 4.70935E-5 * d;
double Ms = Degrees.Normalize(356.0470 + 0.9856002585 * d); // Sun's mean anomaly
double Mm = Degrees.Normalize(115.3654 + 13.0649929505 * d); // Moon's mean anomaly
double Ls = Degrees.Normalize(ws + Ms); // Sun's mean longitude
double Lm = Degrees.Normalize(N + wm + Mm); // Moon's mean longitude
double D = Degrees.Normalize(Lm - Ls); // Moon's mean elongation
double F = Degrees.Normalize(Lm - N); // Moon's argument of latitude
double E0 = Mm + e * Degrees.Sin(Mm) * (1.0 + e * Degrees.Cos(Mm));
double diff = 1.0;
while (diff > 0.005)
{
double E1 = E0 - (E0 - e * Degrees.Sin(E0) - Mm) / (1.0 + e * Degrees.Cos(E0));
diff = Math.Abs(E0 - E1);
E0 = E1;
}
// rectangular coordinates in the plane of lunar orbit
double x = a * (Degrees.Cos(E0) - e);
double y = a * Math.Sqrt(1.0 - e * e) * Degrees.Sin(E0);
// distance and true anomaly
double r = Math.Sqrt(x * x + y * y);
double v = Degrees.Atan2(y, x);
// position in ecliptic coordinates
double xe = Degrees.Cos(N) * Degrees.Cos(v + wm) - Degrees.Sin(N) * Degrees.Sin(v + wm) * Degrees.Cos(i);
double ye = Degrees.Sin(N) * Degrees.Cos(v + wm) + Degrees.Cos(N) * Degrees.Sin(v + wm) * Degrees.Cos(i);
double ze = Degrees.Sin(v + wm) * Degrees.Sin(i);
double longitude = Degrees.Atan2(ye, xe);
double latitude = Degrees.Atan2(ze, Math.Sqrt(xe * xe + ye * ye));
lon = longitude
- 1.274 * Degrees.Sin(Mm - 2 * D) // Evection
+ 0.658 * Degrees.Sin(2 * D) // Variation
- 0.186 * Degrees.Sin(Ms) // Yearly equation
- 0.059 * Degrees.Sin(2 * Mm - 2 * D)
- 0.057 * Degrees.Sin(Mm - 2 * D + Ms)
+ 0.053 * Degrees.Sin(Mm + 2 * D)
+ 0.046 * Degrees.Sin(2 * D - Ms)
+ 0.041 * Degrees.Sin(Mm - Ms)
- 0.035 * Degrees.Sin(D) // Parallactic equation
- 0.031 * Degrees.Sin(Mm + Ms)
- 0.015 * Degrees.Sin(2 * F - 2 * D)
+ 0.011 * Degrees.Sin(Mm - 4 * D);
lat = latitude
- 0.173 * Degrees.Sin(F - 2 * D)
- 0.055 * Degrees.Sin(Mm - F - 2 * D)
- 0.046 * Degrees.Sin(Mm + F - 2 * D)
+ 0.033 * Degrees.Sin(F + 2 * D)
+ 0.017 * Degrees.Sin(2 * Mm + F);
dist = r
- 0.58 * Degrees.Cos(Mm - 2 * D)
- 0.46 * Degrees.Cos(2 * D);
lon = Degrees.Normalize(lon);
lat = Degrees.Normalize(lat);
}
public static void GetSunRiseSet(TimeZoneInfo tz, DateTime dt, double longitude, double latitude, out float sunRiseStart, out float sunRiseEnd, out float sunSetStart, out float sunSetEnd)
{
// get julian day at noon
var utcNoon = TimeZoneInfo.ConvertTimeToUtc(new DateTime(dt.Year, dt.Month, dt.Day, 12, 0, 0, DateTimeKind.Unspecified), tz);
double jdayNoon = GetJulianDayFromGregorianDateTime(utcNoon);
float sunUpperLimb = -0.833f;
float sunLowerLimb = 3f; // more than lower limb at horizon to look better
// magic
double d = jdayNoon - 2451543.5;
double w = 282.9404 + 4.70935E-5 * d;
double e = 0.016709 - 1.151E-9 * d;
double M = Degrees.Normalize(356.0470 + 0.9856002585 * d);
double E = Degrees.Normalize(M + Radians.ToDegrees(e) * Degrees.Sin(M) * (1 + e * Degrees.Cos(M)));
double xv = Degrees.Cos(E) - e;
double yv = Degrees.Sin(E) * Math.Sqrt(1 - e * e);
double lon = Degrees.Atan2(yv, xv) + w;
double lat = 0;
double rasc, decl;
ConvertEclipticToEquatorial(jdayNoon, lon, lat, out rasc, out decl);
double Ls = Degrees.Normalize(w + M);
double GMST = Degrees.Normalize(Ls + 180);
double UTSunInSouth = Degrees.Normalize(rasc - GMST - longitude) / 15.0f;
var noonUtc = new DateTime(dt.Year, dt.Month, dt.Day, 12, 0, 0, DateTimeKind.Utc);
var offset = tz.GetUtcOffset(noonUtc);
double cosLHA = (Degrees.Sin(sunUpperLimb) - Degrees.Sin(latitude) * Degrees.Sin(decl)) / (Degrees.Cos(latitude) * Degrees.Cos(decl));
if (cosLHA < -1)
{
// never set
sunRiseStart = 0;
sunSetEnd = 24;
}
else if (cosLHA > 1)
{
// never rise
sunRiseStart = 24;
sunSetEnd = 0;
}
else
{
double LHA = Degrees.Acos(cosLHA);
double convert = LHA / 15f;
sunRiseStart = (float)(UTSunInSouth - convert + offset.TotalHours);
sunSetEnd = (float)(UTSunInSouth + convert + offset.TotalHours);
}
cosLHA = (Degrees.Sin(sunLowerLimb) - Degrees.Sin(latitude) * Degrees.Sin(decl)) / (Degrees.Cos(latitude) * Degrees.Cos(decl));
if (cosLHA < -1)
{
// never set
sunRiseEnd = 0;
sunSetStart = 24;
}
else if (cosLHA > 1)
{
// never rise
sunRiseEnd = 24;
sunSetStart = 0;
}
else
{
double LHA = Degrees.Acos(cosLHA);
double convert = LHA / 15f;
sunRiseEnd = (float)(UTSunInSouth - convert + offset.TotalHours);
sunSetStart = (float)(UTSunInSouth + convert + offset.TotalHours);
}
}
