Chinese New Year (CNY) falls on 19th February this year. That's an unusually late date; CNY generally falls around the beginning of February.
CNY can also fall on 20th February, though that's only happened once in my lifetime.
a. When will CNY next fall on 20th February?
b. Can CNY ever fall on 21st February? If so, when will that happen next?
(In reply to
computer solution by Charlie)
The calculations:
// Series on new window
function chSeries(form) {
var year0 = form.year.value;
var numb = form.numYears.value;
newWindow = window.open('','newWin','scrollbars=yes,resizable=yes,location=yes,width=300,height=300')
newWindow.document.writeln('<html><head><title>Chinese New Years<\/title><\/head><body>');
newWindow.document.write("<table>")
for (year=year0; year<1*year0+1*numb && year<4100;year++) {
if (year >= 1644 && year <= 4099) {
result = chNYCalc(year);
if (result.month == 2 && (result.day > 19))
{
if (result.month == 1)
month = "January";
else
month = "February";
newWindow.document.write("<tr><td>"+month+"<\/td>")
newWindow.document.write("<td>"+result.day+"<\/td>")
newWindow.document.write("<td>"+year+"<\/td>")
newWindow.document.write("<td>"+result.animal+"<\/td>")
newWindow.document.writeln("<\/tr>")
}
} /* if */
} /* for */
newWindow.document.writeln("<\/table><\/body><\/html>")
newWindow.document.close()
}
function clrTxt(form){
form.day.value = "";
form.month.value = "";
form.animal.value = "";
form.animalPrev.value = "";
}
// Truncate an integer.
function trunc(num) {
if (num > 0)
return Math.floor(num);
else
return Math.ceil(num);
}
// Normalize a degree measure
function fnnm(x) {
return (x - 360 * Math.floor(x/360));
}
// trig functions in degrees
function fnsn(x) {
return Math.sin(x*dr)}
function fncs(x) {
return Math.cos(x*dr)}
// Chinese New Year CALCULATION
function chNYCalc(y) {
/*
* y is a 4 digit year
* d returns the day of the month of Chinese New Year
* m returns the month of Chinese New Year
*
*/
var chTZ; // Chinese Time Zone -- hours
var s1, s2; // preceding and contained winter solstice jd
var solT1, solT2; // solar terms 1 and 2 - begin and end Aquarius
var m1, m2, m3, m12; // new moons
var NY; // Proposed JD of new year
var m,d,y;
var cw0, cw1, cw2, cw3;
var c; // animal number
a = new Array (
"Rat", "Ox", "Tiger", "Rabbit(Hare)",
"Dragon", "Snake", "Horse", "Sheep(Goat)",
"Monkey", "Rooster", "Dog", "Boar(Pig)")
var animal,animalPrev;
if (y < 1928)
chTZ = -(465+40/60)/60;
else
chTZ = -8;
s1 = wSolst(y-1,chTZ);
s2 = wSolst(1*y,chTZ);
solT1 = solTerm(y, chTZ, 300);
solT2 = solTerm(y, chTZ, 330);
m1 = nextNewMoon(s1, chTZ);
m2 = nextNewMoon(m1, chTZ);
m3 = nextNewMoon(m2, chTZ);
m12 = nextNewMoon(s2, chTZ);
NY = m2
if (Math.floor((m12 - m1)/ 29.530588 + .5) == 13)
if (solT1 >= m2 || solT2 >= m3) {
NY = m3;
/* alert("delay") */
}
if (NY > 2299160)
{cw0= Math.floor((NY - 1867216.25)/36524.25);
cw0= NY + 1 + cw0 - Math.floor(cw0/4);
} else
{cw0= NY};
cw0 += 1524;
cw1 = Math.floor((cw0 - 122.1)/365.25);
cw2 = Math.floor(365.25*cw1);
cw3 = Math.floor((cw0 - cw2)/30.6001);
d = cw0 - cw2 - Math.floor(30.61*cw3);
y = cw1 - 4716;
m = cw3 - 1;
if (m > 12)
{m -= 12; y += 1;}
c = (y-4) % 12; cPrev= (y-5) % 12;
animal = a[c]; animalPrev = a[cPrev];
return {month: m, day: d, animal: animal,
animalPrev: animalPrev}; // object containing the results
}
function nextNewMoon (j1, chTZ) {
var d,j1,t,k,m,mp,F,jdNo
d = j1 - 2415020; t = d / 36525
k = (j1 - 2415020.759) / 29.53058868; k = Math.floor(k) - 1
jdNo = 0
while (jdNo <= j1){
m = fnnm(359.22 + 29.10535608 * k)
mp = fnnm(306.03 + 385.8169181 * k + .01073 * t * t + .00001236 * t * t * t)
F = fnnm(21.2964 + 390.67050646 * k - .0016528 * t * t)
jdNo = 2415020.75933 + 29.53058868 * k + .0001178 * t * t
jdNo = jdNo + .1734 * fnsn(m)
jdNo = jdNo + .0021 * fnsn(2 * m)
jdNo = jdNo - .4068 * fnsn(mp)
jdNo = jdNo + .0161 * fnsn(2 * mp)
jdNo = jdNo + .0104 * fnsn(2 * F)
jdNo = jdNo - .0051 * fnsn(m + mp)
jdNo = jdNo - .0074 * fnsn(m - mp)
jdNo = jdNo + .001 * fnsn(2 * F - mp)
jdNo = jdNo - (.41 + 1.2053 * t + .4992 * t * t) / 1440
jdNo = jdNo - chTZ / 24
jdNo = Math.floor(jdNo + .5)
k = k + 1
} // LOOP UNTIL jdNo > j1
return jdNo
}
function solTerm (y, chTZ, LO) {
var ys,t,PE,L,DT,m,chJD;
if (LO >= 270)
ys = y - 1;
else
ys = 1*y;
t = (365.2422 * (ys + LO / 360) - 693878.7) / 36525
PE = .00134 * fncs(22518.7541 * t + 153)
PE = PE + .00154 * fncs(45037.5082 * t + 217) + .002 * fncs(32964.3577 * t + 313) + .00178 * fnsn(20.2 * t + 231)
DT = 1
while (Math.abs(DT * 36525) > .001) {
L = 279.6967 + 36000.76892 * t + .0003025 * t * t
m = 358.476 + 35999.04975 * t - .00015 * t * t - .0000033 * t * t * t
L = L + (1.91946 - .004789 * t - .000014 * t * t) * fnsn(m) + (.020094 - .0001 * t) * fnsn(2 * m) + .000293 * fnsn(3 * m)
L = L - .00479 * fnsn(fnnm(259.18 - 1934.142 * t)) - .00569 + PE + .00179 * fnsn(351 + 445267.1142 * t - .00144 * t * t)
L = fnnm(L)
DT = (fnnm(LO - L + 180) - 180) / 36525
t = t + DT;
} // LOOP WHILE ABS(DT * 36525) > .001
chJD = t * 36525 + 2415020 - (.41 + 1.2053 * t + .4992 * t * t) / 1440 - chTZ / 24
return Math.floor(chJD + .5)
}
function wSolst (ys, chTZ) { //chTZ in hours; + = west
var LO,t,PE,L,DT,chJD
LO = 270
t = (365.2422 * (1*ys + LO / 360) - 693878.7) / 36525
PE = .00134 * fncs(22518.7541 * t + 153)
PE = PE + .00154 * fncs(45037.5082 * t + 217) + .002 * fncs(32964.3577 * t + 313) + .00178 * fnsn(20.2 * t + 231)
DT = 1
while (Math.abs(DT * 36525) > .001) {
L = 279.6967 + 36000.76892 * t + .0003025 * t * t
m = 358.476 + 35999.04975 * t - .00015 * t * t - .0000033 * t * t * t
L = L + (1.91946 - .004789 * t - .000014 * t * t) * fnsn(m) + (.020094 - .0001 * t) * fnsn(2 * m) + .000293 * fnsn(3 * m)
L = L - .00479 * fnsn(fnnm(259.18 - 1934.142 * t)) - .00569 + PE + .00179 * fnsn(351 + 445267.1142 * t - .00144 * t * t)
L = fnnm(L)
DT = (fnnm(LO - L + 180) - 180) / 36525
t = t + DT;
} // LOOP WHILE ABS(DT * 36525) > .001
chJD = t * 36525 + 2415020 - (.41 + 1.2053 * t + .4992 * t * t) / 1440 - chTZ / 24
return Math.floor(chJD + .5)
}
The term - (.41 + 1.2053 * t + .4992 * t * t) / 1440 is the adjustment for the slowing rotation rate of the earth.
|
|
Posted by Charlie
on 2015-01-16 20:38:08 |
re: computer solution -- the JavaScript code
