/* JavaScript functions for positional astronomy by John Walker -- September, MIM http://www.fourmilab.ch/ This program is in the public domain. */ // Frequently-used constants var J2000 = 2451545.0, // Julian day of J2000 epoch JulianCentury = 36525.0, // Days in Julian century JulianMillennium = (JulianCentury * 10), // Days in Julian millennium AstronomicalUnit = 149597870.0, // Astronomical unit in kilometres TropicalYear = 365.24219878; // Mean solar tropical year /* ASTOR -- Arc-seconds to radians. */ function astor(a) { return a * (Math.PI / (180.0 * 3600.0)); } /* DTR -- Degrees to radians. */ function dtr(d) { return (d * Math.PI) / 180.0; } /* RTD -- Radians to degrees. */ function rtd(r) { return (r * 180.0) / Math.PI; } /* FIXANGLE -- Range reduce angle in degrees. */ function fixangle(a) { return a - 360.0 * (Math.floor(a / 360.0)); } /* FIXANGR -- Range reduce angle in radians. */ function fixangr(a) { return a - (2 * Math.PI) * (Math.floor(a / (2 * Math.PI))); } // DSIN -- Sine of an angle in degrees function dsin(d) { return Math.sin(dtr(d)); } // DCOS -- Cosine of an angle in degrees function dcos(d) { return Math.cos(dtr(d)); } /* MOD -- Modulus function which works for non-integers. */ function mod(a, b) { return a - (b * Math.floor(a / b)); } // AMOD -- Modulus function which returns numerator if modulus is zero function amod(a, b) { return mod(a - 1, b) + 1; } /* JHMS -- Convert Julian time to hour, minutes, and seconds, returned as a three-element array. */ function jhms(j) { var ij; j += 0.5; /* Astronomical to civil */ ij = ((j - Math.floor(j)) * 86400.0) + 0.5; return new Array( Math.floor(ij / 3600), Math.floor((ij / 60) % 60), Math.floor(ij % 60)); } // JWDAY -- Calculate day of week from Julian day var Weekdays = new Array( "Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday" ); function jwday(j) { return mod(Math.floor((j + 1.5)), 7); } /* OBLIQEQ -- Calculate the obliquity of the ecliptic for a given Julian date. This uses Laskar's tenth-degree polynomial fit (J. Laskar, Astronomy and Astrophysics, Vol. 157, page 68 [1986]) which is accurate to within 0.01 arc second between AD 1000 and AD 3000, and within a few seconds of arc for +/-10000 years around AD 2000. If we're outside the range in which this fit is valid (deep time) we simply return the J2000 value of the obliquity, which happens to be almost precisely the mean. */ var oterms = new Array ( -4680.93, -1.55, 1999.25, -51.38, -249.67, -39.05, 7.12, 27.87, 5.79, 2.45 ); function obliqeq(jd) { var eps, u, v, i; v = u = (jd - J2000) / (JulianCentury * 100); eps = 23 + (26 / 60.0) + (21.448 / 3600.0); if (Math.abs(u) < 1.0) { for (i = 0; i < 10; i++) { eps += (oterms[i] / 3600.0) * v; v *= u; } } return eps; } /* Periodic terms for nutation in longiude (delta \Psi) and obliquity (delta \Epsilon) as given in table 21.A of Meeus, "Astronomical Algorithms", first edition. */ var nutArgMult = new Array( 0, 0, 0, 0, 1, -2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -2, 1, 0, 2, 2, 0, 0, 0, 2, 1, 0, 0, 1, 2, 2, -2, -1, 0, 2, 2, -2, 0, 1, 0, 0, -2, 0, 0, 2, 1, 0, 0, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, -1, 2, 2, 0, 0, -1, 0, 1, 0, 0, 1, 2, 1, -2, 0, 2, 0, 0, 0, 0, -2, 2, 1, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, -2, 0, 1, 2, 2, 0, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, -1, 2, 1, 0, 2, 0, 0, 0, 2, 0, -1, 0, 1, -2, 2, 0, 2, 2, 0, 1, 0, 0, 1, -2, 0, 1, 0, 1, 0, -1, 0, 0, 1, 0, 0, 2, -2, 0, 2, 0, -1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 0, 2, 2, -2, 1, 1, 0, 0, 0, -1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 1, 0, 0, -2, 0, 2, 2, 2, -2, 0, 1, 2, 1, 2, 0, -2, 0, 1, 2, 0, 0, 0, 1, 0, -1, 1, 0, 0, -2, -1, 0, 2, 1, -2, 0, 0, 0, 1, 0, 0, 2, 2, 1, -2, 0, 2, 0, 1, -2, 1, 0, 2, 1, 0, 0, 1, -2, 0, -1, 0, 1, 0, 0, -2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, -1, -1, 1, 0, 0, 0, 1, 1, 0, 0, 0, -1, 1, 2, 2, 2, -1, -1, 2, 2, 0, 0, -2, 2, 2, 0, 0, 3, 2, 2, 2, -1, 0, 2, 2 ); var nutArgCoeff = new Array( -171996, -1742, 92095, 89, /* 0, 0, 0, 0, 1 */ -13187, -16, 5736, -31, /* -2, 0, 0, 2, 2 */ -2274, -2, 977, -5, /* 0, 0, 0, 2, 2 */ 2062, 2, -895, 5, /* 0, 0, 0, 0, 2 */ 1426, -34, 54, -1, /* 0, 1, 0, 0, 0 */ 712, 1, -7, 0, /* 0, 0, 1, 0, 0 */ -517, 12, 224, -6, /* -2, 1, 0, 2, 2 */ -386, -4, 200, 0, /* 0, 0, 0, 2, 1 */ -301, 0, 129, -1, /* 0, 0, 1, 2, 2 */ 217, -5, -95, 3, /* -2, -1, 0, 2, 2 */ -158, 0, 0, 0, /* -2, 0, 1, 0, 0 */ 129, 1, -70, 0, /* -2, 0, 0, 2, 1 */ 123, 0, -53, 0, /* 0, 0, -1, 2, 2 */ 63, 0, 0, 0, /* 2, 0, 0, 0, 0 */ 63, 1, -33, 0, /* 0, 0, 1, 0, 1 */ -59, 0, 26, 0, /* 2, 0, -1, 2, 2 */ -58, -1, 32, 0, /* 0, 0, -1, 0, 1 */ -51, 0, 27, 0, /* 0, 0, 1, 2, 1 */ 48, 0, 0, 0, /* -2, 0, 2, 0, 0 */ 46, 0, -24, 0, /* 0, 0, -2, 2, 1 */ -38, 0, 16, 0, /* 2, 0, 0, 2, 2 */ -31, 0, 13, 0, /* 0, 0, 2, 2, 2 */ 29, 0, 0, 0, /* 0, 0, 2, 0, 0 */ 29, 0, -12, 0, /* -2, 0, 1, 2, 2 */ 26, 0, 0, 0, /* 0, 0, 0, 2, 0 */ -22, 0, 0, 0, /* -2, 0, 0, 2, 0 */ 21, 0, -10, 0, /* 0, 0, -1, 2, 1 */ 17, -1, 0, 0, /* 0, 2, 0, 0, 0 */ 16, 0, -8, 0, /* 2, 0, -1, 0, 1 */ -16, 1, 7, 0, /* -2, 2, 0, 2, 2 */ -15, 0, 9, 0, /* 0, 1, 0, 0, 1 */ -13, 0, 7, 0, /* -2, 0, 1, 0, 1 */ -12, 0, 6, 0, /* 0, -1, 0, 0, 1 */ 11, 0, 0, 0, /* 0, 0, 2, -2, 0 */ -10, 0, 5, 0, /* 2, 0, -1, 2, 1 */ -8, 0, 3, 0, /* 2, 0, 1, 2, 2 */ 7, 0, -3, 0, /* 0, 1, 0, 2, 2 */ -7, 0, 0, 0, /* -2, 1, 1, 0, 0 */ -7, 0, 3, 0, /* 0, -1, 0, 2, 2 */ -7, 0, 3, 0, /* 2, 0, 0, 2, 1 */ 6, 0, 0, 0, /* 2, 0, 1, 0, 0 */ 6, 0, -3, 0, /* -2, 0, 2, 2, 2 */ 6, 0, -3, 0, /* -2, 0, 1, 2, 1 */ -6, 0, 3, 0, /* 2, 0, -2, 0, 1 */ -6, 0, 3, 0, /* 2, 0, 0, 0, 1 */ 5, 0, 0, 0, /* 0, -1, 1, 0, 0 */ -5, 0, 3, 0, /* -2, -1, 0, 2, 1 */ -5, 0, 3, 0, /* -2, 0, 0, 0, 1 */ -5, 0, 3, 0, /* 0, 0, 2, 2, 1 */ 4, 0, 0, 0, /* -2, 0, 2, 0, 1 */ 4, 0, 0, 0, /* -2, 1, 0, 2, 1 */ 4, 0, 0, 0, /* 0, 0, 1, -2, 0 */ -4, 0, 0, 0, /* -1, 0, 1, 0, 0 */ -4, 0, 0, 0, /* -2, 1, 0, 0, 0 */ -4, 0, 0, 0, /* 1, 0, 0, 0, 0 */ 3, 0, 0, 0, /* 0, 0, 1, 2, 0 */ -3, 0, 0, 0, /* -1, -1, 1, 0, 0 */ -3, 0, 0, 0, /* 0, 1, 1, 0, 0 */ -3, 0, 0, 0, /* 0, -1, 1, 2, 2 */ -3, 0, 0, 0, /* 2, -1, -1, 2, 2 */ -3, 0, 0, 0, /* 0, 0, -2, 2, 2 */ -3, 0, 0, 0, /* 0, 0, 3, 2, 2 */ -3, 0, 0, 0 /* 2, -1, 0, 2, 2 */ ); /* NUTATION -- Calculate the nutation in longitude, deltaPsi, and obliquity, deltaEpsilon for a given Julian date jd. Results are returned as a two element Array giving (deltaPsi, deltaEpsilon) in degrees. */ function nutation(jd) { var deltaPsi, deltaEpsilon, i, j, t = (jd - 2451545.0) / 36525.0, t2, t3, to10, ta = new Array, dp = 0, de = 0, ang; t3 = t * (t2 = t * t); /* Calculate angles. The correspondence between the elements of our array and the terms cited in Meeus are: ta[0] = D ta[0] = M ta[2] = M' ta[3] = F ta[4] = \Omega */ ta[0] = dtr(297.850363 + 445267.11148 * t - 0.0019142 * t2 + t3 / 189474.0); ta[1] = dtr(357.52772 + 35999.05034 * t - 0.0001603 * t2 - t3 / 300000.0); ta[2] = dtr(134.96298 + 477198.867398 * t + 0.0086972 * t2 + t3 / 56250.0); ta[3] = dtr(93.27191 + 483202.017538 * t - 0.0036825 * t2 + t3 / 327270); ta[4] = dtr(125.04452 - 1934.136261 * t + 0.0020708 * t2 + t3 / 450000.0); /* Range reduce the angles in case the sine and cosine functions don't do it as accurately or quickly. */ for (i = 0; i < 5; i++) { ta[i] = fixangr(ta[i]); } to10 = t / 10.0; for (i = 0; i < 63; i++) { ang = 0; for (j = 0; j < 5; j++) { if (nutArgMult[(i * 5) + j] != 0) { ang += nutArgMult[(i * 5) + j] * ta[j]; } } dp += (nutArgCoeff[(i * 4) + 0] + nutArgCoeff[(i * 4) + 1] * to10) * Math.sin(ang); de += (nutArgCoeff[(i * 4) + 2] + nutArgCoeff[(i * 4) + 3] * to10) * Math.cos(ang); } /* Return the result, converting from ten thousandths of arc seconds to radians in the process. */ deltaPsi = dp / (3600.0 * 10000.0); deltaEpsilon = de / (3600.0 * 10000.0); return new Array(deltaPsi, deltaEpsilon); } /* ECLIPTOEQ -- Convert celestial (ecliptical) longitude and latitude into right ascension (in degrees) and declination. We must supply the time of the conversion in order to compensate correctly for the varying obliquity of the ecliptic over time. The right ascension and declination are returned as a two-element Array in that order. */ function ecliptoeq(jd, Lambda, Beta) { var eps, Ra, Dec; /* Obliquity of the ecliptic. */ eps = dtr(obliqeq(jd)); log += "Obliquity: " + rtd(eps) + "\n"; Ra = rtd(Math.atan2((Math.cos(eps) * Math.sin(dtr(Lambda)) - (Math.tan(dtr(Beta)) * Math.sin(eps))), Math.cos(dtr(Lambda)))); log += "RA = " + Ra + "\n"; Ra = fixangle(rtd(Math.atan2((Math.cos(eps) * Math.sin(dtr(Lambda)) - (Math.tan(dtr(Beta)) * Math.sin(eps))), Math.cos(dtr(Lambda))))); Dec = rtd(Math.asin((Math.sin(eps) * Math.sin(dtr(Lambda)) * Math.cos(dtr(Beta))) + (Math.sin(dtr(Beta)) * Math.cos(eps)))); return new Array(Ra, Dec); } /* DELTAT -- Determine the difference, in seconds, between Dynamical time and Universal time. */ /* Table of observed Delta T values at the beginning of even numbered years from 1620 through 2002. */ var deltaTtab = new Array( 121, 112, 103, 95, 88, 82, 77, 72, 68, 63, 60, 56, 53, 51, 48, 46, 44, 42, 40, 38, 35, 33, 31, 29, 26, 24, 22, 20, 18, 16, 14, 12, 11, 10, 9, 8, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 15, 15, 14, 13, 13.1, 12.5, 12.2, 12, 12, 12, 12, 12, 12, 11.9, 11.6, 11, 10.2, 9.2, 8.2, 7.1, 6.2, 5.6, 5.4, 5.3, 5.4, 5.6, 5.9, 6.2, 6.5, 6.8, 7.1, 7.3, 7.5, 7.6, 7.7, 7.3, 6.2, 5.2, 2.7, 1.4, -1.2, -2.8, -3.8, -4.8, -5.5, -5.3, -5.6, -5.7, -5.9, -6, -6.3, -6.5, -6.2, -4.7, -2.8, -0.1, 2.6, 5.3, 7.7, 10.4, 13.3, 16, 18.2, 20.2, 21.1, 22.4, 23.5, 23.8, 24.3, 24, 23.9, 23.9, 23.7, 24, 24.3, 25.3, 26.2, 27.3, 28.2, 29.1, 30, 30.7, 31.4, 32.2, 33.1, 34, 35, 36.5, 38.3, 40.2, 42.2, 44.5, 46.5, 48.5, 50.5, 52.2, 53.8, 54.9, 55.8, 56.9, 58.3, 60, 61.6, 63, 65, 66.6 ); function deltat(year) { var dt, f, i, t; if ((year >= 1620) && (year <= 2000)) { i = Math.floor((year - 1620) / 2); f = ((year - 1620) / 2) - i; /* Fractional part of year */ dt = deltaTtab[i] + ((deltaTtab[i + 1] - deltaTtab[i]) * f); } else { t = (year - 2000) / 100; if (year < 948) { dt = 2177 + (497 * t) + (44.1 * t * t); } else { dt = 102 + (102 * t) + (25.3 * t * t); if ((year > 2000) && (year < 2100)) { dt += 0.37 * (year - 2100); } } } return dt; } /* EQUINOX -- Determine the Julian Ephemeris Day of an equinox or solstice. The "which" argument selects the item to be computed: 0 March equinox 1 June solstice 2 September equinox 3 December solstice */ // Periodic terms to obtain true time var EquinoxpTerms = new Array( 485, 324.96, 1934.136, 203, 337.23, 32964.467, 199, 342.08, 20.186, 182, 27.85, 445267.112, 156, 73.14, 45036.886, 136, 171.52, 22518.443, 77, 222.54, 65928.934, 74, 296.72, 3034.906, 70, 243.58, 9037.513, 58, 119.81, 33718.147, 52, 297.17, 150.678, 50, 21.02, 2281.226, 45, 247.54, 29929.562, 44, 325.15, 31555.956, 29, 60.93, 4443.417, 18, 155.12, 67555.328, 17, 288.79, 4562.452, 16, 198.04, 62894.029, 14, 199.76, 31436.921, 12, 95.39, 14577.848, 12, 287.11, 31931.756, 12, 320.81, 34777.259, 9, 227.73, 1222.114, 8, 15.45, 16859.074 ); JDE0tab1000 = new Array( new Array(1721139.29189, 365242.13740, 0.06134, 0.00111, -0.00071), new Array(1721233.25401, 365241.72562, -0.05323, 0.00907, 0.00025), new Array(1721325.70455, 365242.49558, -0.11677, -0.00297, 0.00074), new Array(1721414.39987, 365242.88257, -0.00769, -0.00933, -0.00006) ); JDE0tab2000 = new Array( new Array(2451623.80984, 365242.37404, 0.05169, -0.00411, -0.00057), new Array(2451716.56767, 365241.62603, 0.00325, 0.00888, -0.00030), new Array(2451810.21715, 365242.01767, -0.11575, 0.00337, 0.00078), new Array(2451900.05952, 365242.74049, -0.06223, -0.00823, 0.00032) ); function equinox(year, which) { var deltaL, i, j, JDE0, JDE, JDE0tab, S, T, W, Y; /* Initialise terms for mean equinox and solstices. We have two sets: one for years prior to 1000 and a second for subsequent years. */ if (year < 1000) { JDE0tab = JDE0tab1000; Y = year / 1000; } else { JDE0tab = JDE0tab2000; Y = (year - 2000) / 1000; } JDE0 = JDE0tab[which][0] + (JDE0tab[which][1] * Y) + (JDE0tab[which][2] * Y * Y) + (JDE0tab[which][3] * Y * Y * Y) + (JDE0tab[which][4] * Y * Y * Y * Y); //document.debug.log.value += "JDE0 = " + JDE0 + "\n"; T = (JDE0 - 2451545.0) / 36525; //document.debug.log.value += "T = " + T + "\n"; W = (35999.373 * T) - 2.47; //document.debug.log.value += "W = " + W + "\n"; deltaL = 1 + (0.0334 * dcos(W)) + (0.0007 * dcos(2 * W)); //document.debug.log.value += "deltaL = " + deltaL + "\n"; // Sum the periodic terms for time T S = 0; for (i = j = 0; i < 24; i++) { S += EquinoxpTerms[j] * dcos(EquinoxpTerms[j + 1] + (EquinoxpTerms[j + 2] * T)); j += 3; } //document.debug.log.value += "S = " + S + "\n"; //document.debug.log.value += "Corr = " + ((S * 0.00001) / deltaL) + "\n"; JDE = JDE0 + ((S * 0.00001) / deltaL); return JDE; } /* SUNPOS -- Position of the Sun. Please see the comments on the return statement at the end of this function which describe the array it returns. We return intermediate values because they are useful in a variety of other contexts. */ function sunpos(jd) { var T, T2, L0, M, e, C, sunLong, sunAnomaly, sunR, Omega, Lambda, epsilon, epsilon0, Alpha, Delta, AlphaApp, DeltaApp; T = (jd - J2000) / JulianCentury; //document.debug.log.value += "Sunpos. T = " + T + "\n"; T2 = T * T; L0 = 280.46646 + (36000.76983 * T) + (0.0003032 * T2); //document.debug.log.value += "L0 = " + L0 + "\n"; L0 = fixangle(L0); //document.debug.log.value += "L0 = " + L0 + "\n"; M = 357.52911 + (35999.05029 * T) + (-0.0001537 * T2); //document.debug.log.value += "M = " + M + "\n"; M = fixangle(M); //document.debug.log.value += "M = " + M + "\n"; e = 0.016708634 + (-0.000042037 * T) + (-0.0000001267 * T2); //document.debug.log.value += "e = " + e + "\n"; C = ((1.914602 + (-0.004817 * T) + (-0.000014 * T2)) * dsin(M)) + ((0.019993 - (0.000101 * T)) * dsin(2 * M)) + (0.000289 * dsin(3 * M)); //document.debug.log.value += "C = " + C + "\n"; sunLong = L0 + C; //document.debug.log.value += "sunLong = " + sunLong + "\n"; sunAnomaly = M + C; //document.debug.log.value += "sunAnomaly = " + sunAnomaly + "\n"; sunR = (1.000001018 * (1 - (e * e))) / (1 + (e * dcos(sunAnomaly))); //document.debug.log.value += "sunR = " + sunR + "\n"; Omega = 125.04 - (1934.136 * T); //document.debug.log.value += "Omega = " + Omega + "\n"; Lambda = sunLong + (-0.00569) + (-0.00478 * dsin(Omega)); //document.debug.log.value += "Lambda = " + Lambda + "\n"; epsilon0 = obliqeq(jd); //document.debug.log.value += "epsilon0 = " + epsilon0 + "\n"; epsilon = epsilon0 + (0.00256 * dcos(Omega)); //document.debug.log.value += "epsilon = " + epsilon + "\n"; Alpha = rtd(Math.atan2(dcos(epsilon0) * dsin(sunLong), dcos(sunLong))); //document.debug.log.value += "Alpha = " + Alpha + "\n"; Alpha = fixangle(Alpha); ////document.debug.log.value += "Alpha = " + Alpha + "\n"; Delta = rtd(Math.asin(dsin(epsilon0) * dsin(sunLong))); ////document.debug.log.value += "Delta = " + Delta + "\n"; AlphaApp = rtd(Math.atan2(dcos(epsilon) * dsin(Lambda), dcos(Lambda))); //document.debug.log.value += "AlphaApp = " + AlphaApp + "\n"; AlphaApp = fixangle(AlphaApp); //document.debug.log.value += "AlphaApp = " + AlphaApp + "\n"; DeltaApp = rtd(Math.asin(dsin(epsilon) * dsin(Lambda))); //document.debug.log.value += "DeltaApp = " + DeltaApp + "\n"; return new Array( // Angular quantities are expressed in decimal degrees L0, // [0] Geometric mean longitude of the Sun M, // [1] Mean anomaly of the Sun e, // [2] Eccentricity of the Earth's orbit C, // [3] Sun's equation of the Centre sunLong, // [4] Sun's true longitude sunAnomaly, // [5] Sun's true anomaly sunR, // [6] Sun's radius vector in AU Lambda, // [7] Sun's apparent longitude at true equinox of the date Alpha, // [8] Sun's true right ascension Delta, // [9] Sun's true declination AlphaApp, // [10] Sun's apparent right ascension DeltaApp // [11] Sun's apparent declination ); } /* EQUATIONOFTIME -- Compute equation of time for a given moment. Returns the equation of time as a fraction of a day. */ function equationOfTime(jd) { var alpha, deltaPsi, E, epsilon, L0, tau tau = (jd - J2000) / JulianMillennium; //document.debug.log.value += "equationOfTime. tau = " + tau + "\n"; L0 = 280.4664567 + (360007.6982779 * tau) + (0.03032028 * tau * tau) + ((tau * tau * tau) / 49931) + (-((tau * tau * tau * tau) / 15300)) + (-((tau * tau * tau * tau * tau) / 2000000)); //document.debug.log.value += "L0 = " + L0 + "\n"; L0 = fixangle(L0); //document.debug.log.value += "L0 = " + L0 + "\n"; alpha = sunpos(jd)[10]; //document.debug.log.value += "alpha = " + alpha + "\n"; deltaPsi = nutation(jd)[0]; //document.debug.log.value += "deltaPsi = " + deltaPsi + "\n"; epsilon = obliqeq(jd) + nutation(jd)[1]; //document.debug.log.value += "epsilon = " + epsilon + "\n"; E = L0 + (-0.0057183) + (-alpha) + (deltaPsi * dcos(epsilon)); //document.debug.log.value += "E = " + E + "\n"; E = E - 20.0 * (Math.floor(E / 20.0)); //document.debug.log.value += "Efixed = " + E + "\n"; E = E / (24 * 60); //document.debug.log.value += "Eday = " + E + "\n"; return E; }