//***********************************************************************/
//* Name:    calGeomMeanLongSun							*/
//* Type:    Function									*/
//* Purpose: calculate the Geometric Mean Longitude of the Sun		*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   the Geometric Mean Longitude of the Sun in degrees			*/
//***********************************************************************/

	function calcGeomMeanLongSun(t)
	{
		GeomMeanLongSun = 280.46646 + t * (36000.76983 + 0.0003032 * t);
		while(GeomMeanLongSun > 360.0)
		{
			GeomMeanLongSun -= 360.0;
		}
		while(L0 < 0.0)
		{
			GeomMeanLongSun += 360.0;
		}
		return GeomMeanLongSun;		// in degrees
	}


//***********************************************************************/
//* Name:    calGeomAnomalySun							*/
//* Type:    Function									*/
//* Purpose: calculate the Geometric Mean Anomaly of the Sun		*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   the Geometric Mean Anomaly of the Sun in degrees			*/
//***********************************************************************/

	function calcGeomMeanAnomalySun(t)
	{
		GeomMeanAnomalySun = 357.52911 + t * (35999.05029 - 0.0001537 * t);
		return GeomMeanAnomalySun;		// in degrees
	}

//***********************************************************************/
//* Name:    calcEccentricityEarthOrbit						*/
//* Type:    Function									*/
//* Purpose: calculate the eccentricity of earth's orbit			*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   the unitless eccentricity							*/
//***********************************************************************/


	function calcEccentricityEarthOrbit(t)
	{
		EccentricityEarthOrbit = 0.016708634 - t * (0.000042037 + 0.0000001267 * t);
		return EccentricityEarthOrbit;		// unitless
	}

//***********************************************************************/
//* Name:    calcSunEqOfCentre							*/
//* Type:    Function									*/
//* Purpose: calculate the equation of centre for the sun			*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   in degrees										*/
//***********************************************************************/

function calcSunEqOfCentre(t)
	{
		var m = calcGeomMeanAnomalySun(t);
 		var mrad = degToRad(m);
		var sinm = Math.sin(mrad);
		var sin2m = Math.sin(mrad+mrad);
		var sin3m = Math.sin(mrad+mrad+mrad);
		var sin4m = Math.sin(mrad+mrad+mrad+mrad);
		var sin5m = Math.sin(mrad+mrad+mrad+mrad+mrad);
		var sin6m = Math.sin(mrad+mrad+mrad+mrad+mrad+mrad);
    var ecc = EccentricityEarthOrbit
		SunEqOfCentre = 
      (2 * ecc - (1 / 4) * Math.pow(ecc,3) + (5 / 96)* Math.pow(ecc,5))* sinm + ((5 / 4) * Math.pow(ecc,2) - (11 / 24) * Math.pow(ecc,4) + 
      (17 / 192)* Math.pow(ecc,6)) * sin2m + ((13 / 12) * Math.pow(ecc,3) - (43 / 64) * Math.pow(ecc,5))* sin3m + ((103 / 96) * Math.pow(ecc,4) - (451 / 480) * Math.pow(ecc,6)) * 
       sin4m + (1097 / 960) * Math.pow(ecc,5) * sin5m + (1223 / 960) * Math.pow(ecc,6) * sin6m
       
		return SunEqOfCentre;		// in degrees
	}

//***********************************************************************/
//* Name:    calcSunTrueLong								*/
//* Type:    Function									*/
//* Purpose: calculate the true longitude of the sun				*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   sun's true longitude in degrees						*/
//***********************************************************************/


	function calcSunTrueLong(t)
	{
		var l0 = calcGeomMeanLongSun(t);
		var c = calcSunEqOfCentre(t);

		SunTrueLong = l0 + c;
		return SunTrueLong;		// in degrees
	}

//***********************************************************************/
//* Name:    calcSunTrueAnomaly							*/
//* Type:    Function									*/
//* Purpose: calculate the true anamoly of the sun				*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   sun's true anamoly in degrees							*/
//***********************************************************************/

	function calcSunTrueAnomaly(t)
	{
		var m = calcGeomMeanAnomalySun(t);
		var c = calcSunEqOfCentre(t);

		SunTrueAnomaly = m + c;
		return SunTrueAnomaly;		// in degrees
	}

//***********************************************************************/
//* Name:    calcSunRadVector								*/
//* Type:    Function									*/
//* Purpose: calculate the distance to the sun in AU				*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   sun radius vector in AUs							*/
//***********************************************************************/

	function calcSunRadVector(t)
	{
		var v = calcSunTrueAnomaly(t);
		var e = calcEccentricityEarthOrbit(t);
 
		SunRadVector = (1.000001018 * (1 - e * e)) / (1 + e * Math.cos(degToRad(v)));
		return SunRadVector;		// in AUs
	}

//***********************************************************************/
//* Name:    calcSunApparentLong							*/
//* Type:    Function									*/
//* Purpose: calculate the apparent longitude of the sun			*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   sun's apparent longitude in degrees						*/
//***********************************************************************/

	function calcSunApparentLong(t)
	{
		var o = calcSunTrueLong(t);

		var omega = 125.04 - 1934.136 * t;
		SunApparentLong = o - 0.00569 - 0.00478 * Math.sin(degToRad(omega));
		return SunApparentLong;		// in degrees
	}

//***********************************************************************/
//* Name:    calcMeanObliquityOfEcliptic						*/
//* Type:    Function									*/
//* Purpose: calculate the mean obliquity of the ecliptic			*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   mean obliquity in degrees							*/
//***********************************************************************/

	function calcMeanObliquityOfEcliptic(t)
	{
		var seconds = 21.448 - t*(46.8150 + t*(0.00059 - t*(0.001813)));
		MeanObliquityOfEcliptic = 23.0 + (26.0 + (seconds/60.0))/60.0;
		return MeanObliquityOfEcliptic;		// in degrees
	}

//***********************************************************************/
//* Name:    calcObliquityCorrection						*/
//* Type:    Function									*/
//* Purpose: calculate the corrected obliquity of the ecliptic		*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   corrected obliquity in degrees						*/
//***********************************************************************/

	function calcObliquityCorrection(t)
	{
		var e0 = calcMeanObliquityOfEcliptic(t);

		var omega = 125.04 - 1934.136 * t;
		ObliquityCorrection = e0 + 0.00256 * Math.cos(degToRad(omega));
		return ObliquityCorrection;		// in degrees
	}

//***********************************************************************/
//* Name:    calcSunRtAscension							*/
//* Type:    Function									*/
//* Purpose: calculate the right ascension of the sun				*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   sun's right ascension in degrees						*/
//***********************************************************************/

	function calcSunRtAscension(t)
	{
		var e = calcObliquityCorrection(t);
		var lambda = calcSunApparentLong(t);
 
		var tananum = (Math.cos(degToRad(e)) * Math.sin(degToRad(lambda)));
		var tanadenom = (Math.cos(degToRad(lambda)));
		SunRtAscension = radToDeg(Math.atan2(tananum, tanadenom));
		return SunRtAscension;		// in degrees
	}

//***********************************************************************/
//* Name:    calcSunDeclination							*/
//* Type:    Function									*/
//* Purpose: calculate the declination of the sun				*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   sun's declination in degrees							*/
//***********************************************************************/

	function calcSunDeclination(t)
	{
		var e = calcObliquityCorrection(t);
		var lambda = calcSunApparentLong(t);

		var sint = Math.sin(degToRad(e)) * Math.sin(degToRad(lambda));
		SunDeclination = radToDeg(Math.asin(sint));
		return SunDeclination;		// in degrees
	}

//***********************************************************************/
//* Name:    calcEquationOfTime							*/
//* Type:    Function									*/
//* Purpose: calculate the difference between true solar time and mean	*/
//*		solar time									*/
//* Arguments:										*/
//*   t : number of Julian centuries since J2000.0				*/
//* Return value:										*/
//*   equation of time in minutes of time						*/
//***********************************************************************/

	function calcEquationOfTime(t)
	{
		var epsilon = calcObliquityCorrection(t);
		var l0 = calcGeomMeanLongSun(t);
		var e = calcEccentricityEarthOrbit(t);
		var m = calcGeomMeanAnomalySun(t);

		var y = Math.tan(degToRad(epsilon)/2.0);
		y *= y;

		var sin2l0 = Math.sin(2.0 * degToRad(l0));
		var sinm   = Math.sin(degToRad(m));
		var cos2l0 = Math.cos(2.0 * degToRad(l0));
		var sin4l0 = Math.sin(4.0 * degToRad(l0));
		var sin2m  = Math.sin(2.0 * degToRad(m));

		Etime = y * sin2l0 - 2.0 * e * sinm + 4.0 * e * y * sinm * cos2l0
				- 0.5 * y * y * sin4l0 - 1.25 * e * e * sin2m;
		Etime = radToDeg(Etime)*4.0

		return Etime	// in minutes of time
	}