From d20d989f5495492f1258c8313db7c19b429111a3 Mon Sep 17 00:00:00 2001
From: ulrich
Date: Thu, 23 Mar 2023 17:55:43 +0000
Subject: [PATCH] Chinesischer Kalender implementiert
---
src/de/uhilger/zeitrechnung/kalender/BasisKalender.java | 115 ++++++++++++++++++++++++++++++++++++++++++++++++++++-----
1 files changed, 104 insertions(+), 11 deletions(-)
diff --git a/src/de/uhilger/zeitrechnung/kalender/BasisKalender.java b/src/de/uhilger/zeitrechnung/kalender/BasisKalender.java
index 7a726f2..bd70083 100644
--- a/src/de/uhilger/zeitrechnung/kalender/BasisKalender.java
+++ b/src/de/uhilger/zeitrechnung/kalender/BasisKalender.java
@@ -22,10 +22,12 @@
import de.uhilger.zeitrechnung.Zeit;
/**
- * Abstrakte Basisklasse fuer Klassen, die ein Kalendersystem implementieren
+ * Abstrakte Basisklasse fuer Klassen, die ein Kalendersystem implementieren.
+ *
+ * Hier sind neben allerlei relevanten Rechenmethoden die grundlegenden
+ * astronomischen Algorithmen für die Zeit- und Kalenderrechnung implementiert.
*
* @author Ulrich Hilger
- * @version 2, 1.10.2022
*/
public abstract class BasisKalender implements Zeitrechnung {
@@ -82,6 +84,12 @@
return nterTag(-1, t, datum);
}
+ /* ----- */
+
+ public double moduloAngepasst(double x, double y) {
+ return y + modulo(x, -y);
+ }
+
/* ---- Zeit ----- */
public double zuMoment(int stunde, int minute, double sekunde) {
@@ -100,7 +108,10 @@
return z;
}
- /* ----------- Mondphase ----------- */
+ /* ----------- Mond ----------- */
+
+ /** durchschnittliche Dauer eines Mondphasenzyklus (synodischer Monat) in Tagen */
+ public static final double MITTLERER_SYNODISCHER_MONAT = 29.530588853;
public double mondphase(double t) {
return modulo(mondLaenge(t) - solareLaenge(t), 360);
@@ -109,7 +120,7 @@
public double mondHoehe(double t, Ort ort) {
double phi = ort.getBreite();
double psi = ort.getLaenge();
- double varepsilon = obliquity(t);
+ double varepsilon = schiefstand(t);
double lambda = mondLaenge(t);
double beta = mondBreite(t);
double alpha = arcTanGrad(
@@ -266,6 +277,80 @@
private static final double[] siderealCoeff = new double[] {280.46061837, 36525 * 360.98564736629, 0.000387933, 1d/38710000};
}
+ public double neumondNach(double tee) {
+ return nterNeumond(1 + Math.round(tee / MITTLERER_SYNODISCHER_MONAT - mondphase(tee) / (double) (360)));
+ }
+
+ public double neumondVor(double tee) {
+ return nterNeumond(Math.round(tee / MITTLERER_SYNODISCHER_MONAT - mondphase(tee) / (double) (360)));
+ }
+
+ public double nterNeumond(long n) {
+ double k = n - 24724;
+ double c = k / 1236.85;
+ double approx = poly(c, nm.coeffApprox);
+ double capE = poly(c, nm.coeffCapE);
+ double solarAnomaly = poly(c, nm.coeffSolarAnomaly);
+ double lunarAnomaly = poly(c, nm.coeffLunarAnomaly);
+ double moonArgument = poly(c, nm.coeffMoonArgument);
+ double capOmega = poly(c, nm.coeffCapOmega);
+ double correction = -0.00017 * sinGrad(capOmega);
+ for(int ix = 0; ix < nm.sineCoeff.length; ++ix) {
+ correction += nm.sineCoeff[ix] * Math.pow(capE, nm.EFactor[ix]) *
+ sinGrad(nm.solarCoeff[ix] * solarAnomaly +
+ nm.lunarCoeff[ix] * lunarAnomaly +
+ nm.moonCoeff[ix] * moonArgument);
+ }
+ double additional = 0;
+ for(int ix = 0; ix < nm.addConst.length; ++ix) {
+ additional += nm.addFactor[ix] *
+ sinGrad(nm.addConst[ix] + nm.addCoeff[ix] * k);
+ }
+ double extra = 0.000325 * sinGrad(poly(c, nm.extra));
+ return universalVonDynamisch(approx + correction + extra + additional);
+ }
+ private static class nm {
+ private static final double[] coeffApprox = new double[] {730125.59765, MITTLERER_SYNODISCHER_MONAT * 1236.85, 0.0001337, -0.000000150, 0.00000000073};
+ private static final double[] coeffCapE = new double[] {1, -0.002516, -0.0000074};
+ private static final double[] coeffSolarAnomaly = new double[] {2.5534, 29.10535669 * 1236.85, -0.0000218, -0.00000011};
+ private static final double[] coeffLunarAnomaly = new double[] {201.5643, 385.81693528 * 1236.85, 0.0107438, 0.00001239, -0.000000058};
+ private static final double[] coeffMoonArgument = new double[] {160.7108, 390.67050274 * 1236.85, -0.0016341, -0.00000227, 0.000000011};
+ private static final double[] coeffCapOmega = new double[] {124.7746, -1.56375580 * 1236.85, 0.0020691, 0.00000215};
+ private static final byte[] EFactor = new byte[] {0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
+ private static final byte[] solarCoeff = new byte[] {0, 1, 0, 0, -1, 1, 2, 0, 0, 1, 0, 1, 1, -1, 2, 0, 3, 1, 0, 1, -1, -1, 1, 0};
+ private static final byte[] lunarCoeff = new byte[] {1, 0, 2, 0, 1, 1, 0, 1, 1, 2, 3, 0, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 4};
+ private static final byte[] moonCoeff = new byte[] {0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 0, 2, -2, 0, 0, -2, 0, -2, 2, 2, 2, -2, 0, 0};
+ private static final double[] sineCoeff = new double[] {
+ -0.40720, 0.17241, 0.01608, 0.01039, 0.00739, -0.00514, 0.00208,
+ -0.00111, -0.00057, 0.00056, -0.00042, 0.00042, 0.00038, -0.00024,
+ -0.00007, 0.00004, 0.00004, 0.00003, 0.00003, -0.00003, 0.00003,
+ -0.00002, -0.00002, 0.00002
+ };
+ private static final double[] addConst = new double[] {
+ 251.88, 251.83, 349.42, 84.66, 141.74, 207.14, 154.84, 34.52, 207.19,
+ 291.34, 161.72, 239.56, 331.55
+ };
+ private static final double[] addCoeff = new double[] {
+ 0.016321, 26.641886, 36.412478, 18.206239, 53.303771, 2.453732,
+ 7.306860, 27.261239, 0.121824, 1.844379, 24.198154, 25.513099, 3.592518
+ };
+ private static final double[] addFactor = new double[] {
+ 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
+ };
+ private static final double[] extra = new double[] {
+ 299.77, 132.8475848, -0.009173
+ };
+ }
+
+ public double universalVonDynamisch(double tee) {
+ return tee - ephemeridenKorrektur(tee);
+ }
+
+ public double universalVonStandard(double teeS, Ort locale) {
+ return teeS - locale.getZeitzone() / 24;
+ }
+
/* ----------- Sonnenauf- und -untergang ----------- */
public double sonnenaufgang(long date, Ort ort) throws Exception {
@@ -312,7 +397,7 @@
public double zeitVonHorizont(double approx, Ort ort, double alpha) throws Exception {
double phi = ort.getBreite();
double t = universalVonLokal(approx, ort);
- double delta = arcSinGrad(sinGrad(obliquity(t)) * sinGrad(solareLaenge(t)));
+ double delta = arcSinGrad(sinGrad(schiefstand(t)) * sinGrad(solareLaenge(t)));
boolean morgen = modulo(approx, 1) < 0.5;
double sinusAbstand = tanGrad(phi) * tanGrad(delta) +
sinGrad(alpha) / (kosGrad(delta) * kosGrad(phi));
@@ -340,14 +425,14 @@
double laenge = poly(c, et.koeffLaenge);
double anomalie = poly(c, et.koeffAnomalie);
double exzentrizitaet = poly(c, et.koeffExzentrizitaet);
- double varepsilon = obliquity(t);
+ double varepsilon = schiefstand(t);
double y = quadrat(tanGrad(varepsilon / 2));
double equation = (1d / 2d / Math.PI) * (y * sinGrad(2 * laenge) +
-2 * exzentrizitaet * sinGrad(anomalie) +
4 * exzentrizitaet * y * sinGrad(anomalie) * kosGrad(2 * laenge) +
-0.5 * y * y * sinGrad(4 * laenge) +
-1.25 * exzentrizitaet * exzentrizitaet * sinGrad(2 * anomalie));
- return signum(equation) * Math.min(Math.abs(equation), stunde(12));
+ return vorzeichen(equation) * Math.min(Math.abs(equation), stunde(12));
}
private static class et {
private static final double[] koeffLaenge = new double[] {280.46645, 36000.76983, 0.0003032};
@@ -355,13 +440,13 @@
private static final double[] koeffExzentrizitaet = new double[] {0.016708617, -0.000042037, -0.0000001236};
}
- public double obliquity(double t) {
+ public double schiefstand(double t) {
double c = julJahrhunderte(t);
return winkel(23, 26, 21.448) + poly(c, coeffObliquity);
}
private final double[] coeffObliquity = new double[] {0, winkel(0, 0, -46.8150), winkel(0, 0, -0.00059), winkel(0, 0, 0.001813)};
- public int signum(double x) {
+ public int vorzeichen(double x) {
if(x < 0)
return -1;
else if(x > 0)
@@ -400,7 +485,8 @@
/* ---------------- Jahreszeiten ----- */
- public static final double TROPISCHES_JAHR = 365.242189;
+ /** durchschnittliche Dauer eines Umlaufs der Erde um die Sonne in Tagen */
+ public static final double MITTLERES_TROPISCHES_JAHR = 365.242189;
public double standardVonUniversal(double t, Ort ort) {
return t + ort.getZeitzone() / 24;
@@ -408,7 +494,7 @@
public double solareLaengeNach(double t, double phi) {
double varepsilon = 0.00001;
- double rate = TROPISCHES_JAHR / (double) 360;
+ double rate = MITTLERES_TROPISCHES_JAHR / (double) 360;
double tau = t + rate * modulo(phi - solareLaenge(t), 360);
double l = Math.max(t, tau - 5);
double u = tau + 5;
@@ -437,6 +523,13 @@
return modulo(laenge + aberration(t) + nutation(t), 360);
}
+ public double geschaetzteSolareLaengeVor(double tee, double phi) {
+ double rate = MITTLERES_TROPISCHES_JAHR / (double) (360);
+ double tau = tee - rate * modulo(solareLaenge(tee) - phi, 360);
+ double capDelta = modulo(solareLaenge(tau) - phi + (double) (180), 360) - (double) (180);
+ return Math.min(tee, tau - rate * capDelta);
+ }
+
public double julJahrhunderte(double t) {
return (dynamischVonUniversal(t) - j2000()) / 36525;
}
--
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