/* 2007-11-11 Moonphases.js JavaScript functions. Moonphases are for Time zone 0 (UTC)! Dr. Rolf Schröder Möörkenweg 37 21029 Hamburg, Germany http://rschr.de The algorithm of the functions are mainly taken from the book: Astronomical Algorithms, Jean Meeus, 1991, First English Edition */ function dT(year) // dT [days] = TD - UT = Dynamical Time - Universal Time // ## (Atomic Clocks - Earth Rotation) // // This function is delicate: I used only a long time approximation given by Stephenson and Morrison (1995), // derived from 700 BCE to 1600 CE, which might give more or less large deviations for future dates. // Exchange or complete this function if better formulas are known. { var y = year - 1820; return (-20 + 0.0031*y*y)/86400; } function moonPhaseDates(year) // Returns array of arrays of all New Moons, First Quaters, Full Moons, Last Quaters; // ############## dArray[i] = [month,day,phase] (UTC) for entire year. // Phase: 0|.25|.5|.75 for years >= 2000, 0|-.75|-.5|-.25 for years < 2000. // // Note: dArray[2] contains the decimal day of Moon phase (UTC). Due to Meeus the mean error for the period // 1980 to 2020 should be 3.8 seconds plus the error introduced by the uncertainness of function dT() (look // at top of file). // This function 'moonPhaseDates()' returns only the integer part of the day, it is truncated by Math.floor() // (look at the end of this function). // { var MP = ["☻","☽","☺","☾"]; // Moon Phase Characters.: New Moon, 1st Quarter,... //var MP = ["●","◐","○","◑"]; // Moon Phase Characters.: alternative character set var flag, dy, i, j, k, n, m, y, JDE, T, Tq, E, M, M1, F, Om, sum, W; var Deg2Rad = Math.PI/180; var dArray = new Array(3); var moonDatesArray = new Array(); var A = new Array(); var B = [ 0.000325, // Additional corrections (Meeus) 0.000165, 0.000164, 0.000126, 0.000110, 0.000062, 0.000060, 0.000056, 0.000047, 0.000042, 0.000040, 0.000037, 0.000035, 0.000023]; y = Math.floor(year); k = Math.floor((y - 2000)*12.3685); // (47.2) (Meeus) for( flag=0; flag < 2; flag++) // Two steps to evaluate adequate start value for k in 'while'-loop. { j = 0; // Index for moonDatesArray[]; look at end of while-loop while(1) { T = k/1236.85; // (47.3) Tq = T*T; JDE = 2451550.09765 + 29.530588853*k + Tq*(0.0001337 + T*(-0.000000150 + T*0.00000000073)); // (47.1) E = 1 - T*(0.002516 + T*0.0000074); // (45.6) M = 2.5534 + 29.10535669*k - Tq*(0.0000218 + T*0.00000011); // (47.4) M %= 360; M *= Deg2Rad; Ms = 201.5643 + 385.81693528*k + Tq*(0.0107438 + T*(0.00001239 - T*0.000000058)); // (47.5) Ms %= 360; Ms *= Deg2Rad; F = 160.7108 + 390.67050274*k - Tq*(0.0016341 +T*(0.00000227 -T*0.000000011)); // (47.6) F %= 360; F *= Deg2Rad; Om = 124.7746 - 1.56375580*k + Tq*(0.0020691 + T*0.00000215); // (47.7) Om %= 360; Om *= Deg2Rad; A = [299.77 + 0.107408*k - Tq*0.009173, // Planetary arguments (Meeus) 251.88 + 0.016312*k, 251.83 + 26.651886*k, 349.42 + 36.412478*k, 84.66 + 18.206239*k, 141.74 + 53.303771*k, 207.14 + 2.435732*k, 154.84 + 7.306860*k, 34.52 + 27.261239*k, 207.19 + 0.121824*k, 291.34 + 1.844379*k, 161.72 + 24.198154*k, 239.56 + 25.513099*k, 331.55 + 3.592518*k]; for( i = 0; i < A.length; i++ ) { A[i] %= 360; A[i] *= Deg2Rad; } W = 0; n = k%1; // n: 0, +-0.25, +-0.5, +-0.75 (New Moon, 1st|3rd Quarter, Full Moon, 3rd|1st Quarter) switch(n) { case 0.5: // Full Moon case -0.5: sum = -0.40614 * Math.sin(Ms) // 1 (Meeus) +0.17302 * E * Math.sin(M) +0.01614 * Math.sin(2*Ms) +0.01043 * Math.sin(2*F) +0.00734 * E * Math.sin(Ms-M) // 5 -0.00515 * E * Math.sin(Ms+M) +0.00209 *E*E* Math.sin(2*M) -0.00111 * Math.sin(Ms-2*F) -0.00057 * Math.sin(Ms+2*F) +0.00056 * E * Math.sin(2*Ms+M) // 10 -0.00042 * Math.sin(3*Ms) +0.00042 * E * Math.sin(M+2*F) +0.00038 * E * Math.sin(M-2*F) -0.00024 * E * Math.sin(2*Ms-M) -0.00017 * Math.sin(Om) // 15 -0.00007 * Math.sin(Ms+2*M) +0.00004 * Math.sin(2*Ms-2*F) +0.00004 * Math.sin(3*M) +0.00003 * Math.sin(Ms+M-2*F) +0.00003 * Math.sin(2*Ms+2*F) // 20 -0.00003 * Math.sin(Ms+M+2*F) +0.00003 * Math.sin(Ms-M+2*F) -0.00002 * Math.sin(Ms-M-2*F) -0.00002 * Math.sin(3*Ms+M) +0.00002 * Math.sin(4*Ms); //25 break; case 0.25: // First Quarters case -0.25: // Last Quarters case 0.75: // Last Quarters case -0.75: // First Quarters sum = -0.62801 * Math.sin(Ms) // 1 (Meeus) +0.17172 * E * Math.sin(M) -0.01183 * E * Math.sin(Ms+M) +0.00862 * Math.sin(2*Ms) +0.00804 * Math.sin(2*F) // 5 +0.00454 * E * Math.sin(Ms-M) +0.00204 *E*E* Math.sin(2*M) -0.00180 * Math.sin(Ms-2*F) -0.00070 * Math.sin(Ms+2*F) -0.00040 * Math.sin(3*Ms) // 10 -0.00034 * E * Math.sin(2*Ms-M) +0.00032 * E * Math.sin(M+2*F) +0.00032 * E * Math.sin(M-2*F) -0.00028 *E*E* Math.sin(Ms+2*M) +0.00027 * E * Math.sin(2*Ms+M) // 15 -0.00017 * Math.sin(Om) -0.00005 * Math.sin(Ms-M-2*F) +0.00004 * Math.sin(2*Ms+2*F) -0.00004 * Math.sin(Ms+M+2*F) +0.00004 * Math.sin(Ms-2*M) // 20 +0.00003 * Math.sin(Ms+M-2*F) +0.00003 * Math.sin(3*M) +0.00002 * Math.sin(2*Ms-2*F) +0.00002 * Math.sin(Ms-M+2*F) -0.00002 * Math.sin(3*Ms+M); //25 W = 0.00306 - 0.00038*E*Math.cos(M) + 0.00026*Math.cos(Ms) - 0.00002*Math.cos(Ms-M) + 0.00002*Math.cos(Ms+M) + 0.00002*Math.cos(2*F); break; default: // New Moon (n == 0) sum = -0.40720 * Math.sin(Ms) // 1 (Meeus) +0.17241 * E * Math.sin(M) +0.01608 * Math.sin(2*Ms) +0.01039 * Math.sin(2*F) +0.00739 * E * Math.sin(Ms-M) // 5 -0.00514 * E * Math.sin(Ms+M) +0.00208 *E*E* Math.sin(2*M) -0.00111 * Math.sin(Ms-2*F) -0.00057 * Math.sin(Ms+2*F) +0.00056 * E * Math.sin(2*Ms+M) // 10 -0.00042 * Math.sin(3*Ms) +0.00042 * E * Math.sin(M+2*F) +0.00038 * E * Math.sin(M-2*F) -0.00024 * E * Math.sin(2*Ms-M) -0.00017 * Math.sin(Om) // 15 -0.00007 * Math.sin(Ms+2*M) +0.00004 * Math.sin(2*Ms-2*F) +0.00004 * Math.sin(3*M) +0.00003 * Math.sin(Ms+M-2*F) +0.00003 * Math.sin(2*Ms+2*F) // 20 -0.00003 * Math.sin(Ms+M+2*F) +0.00003 * Math.sin(Ms-M+2*F) -0.00002 * Math.sin(Ms-M-2*F) -0.00002 * Math.sin(3*Ms+M) +0.00002 * Math.sin(4*Ms); //25 break; } for( i = 0; i < A.length; i++ ) sum += B[i] * Math.sin(A[i]); // look definition for A and B JDE += sum - dT(y); // For New and Full Moon if( n == 0.25 || n == -0.75 ) JDE += W; // Add if Lirst Quarter if( n == -0.25 || n == 0.75 ) JDE -= W; // Sub if Last Quarter dArray = julday2dArray(JDE); if( flag == 0 ) // set k to adequate start value { dy = (dArray2julday([y,1,1.0]) - dArray2julday(dArray))/365; // Note: ACCIDENTLY dArray2julday(dArray) works also for the year -4712! k += Math.floor(dy*12.3685)-1; break; // break 'while'-loop in this step (flag==0). } if( dArray[0] > y ) break; n = ( n < 0 ) ? 4*(1 + n) : 4*n; // Index for Moon Symbol; Correction for negative k if( dArray[0] > y-1 && dArray[0] <= y) moonDatesArray[j++] = [dArray[1],Math.floor(dArray[2]),MP[n]]; k += 0.25; } } return moonDatesArray; }