550 lines
17 KiB
Go
550 lines
17 KiB
Go
package basic
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import (
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"fmt"
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"math"
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"strings"
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"time"
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)
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var defDeltaTFn = DefaultDeltaTv2
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/*
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@name: 儒略日计算
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@dec: 计算给定时间的儒略日，1582年改力后为格里高利历，之前为儒略历
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@ 请注意，传入的时间在天文计算中一般为力学时，应当注意和世界时的转化
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*/
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func JDECalc(Year, Month int, Day float64) float64 {
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if Month == 1 || Month == 2 {
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Year--
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Month += 12
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}
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var tmpvarB int
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tmpvar := fmt.Sprintf("%04d-%02d-%2d", Year, Month, int(math.Floor(Day)))
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if strings.Compare(tmpvar, `1582-10-04`) != 1 {
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tmpvarB = 0
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} else {
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tmpvarA := int(Year / 100)
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tmpvarB = 2 - tmpvarA + int(tmpvarA/4)
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}
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return (math.Floor(365.25*(float64(Year)+4716.0)) + math.Floor(30.6001*float64(Month+1)) + Day + float64(tmpvarB) - 1524.5)
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}
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/*
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@name: 获得当前儒略日时间：当地世界时，非格林尼治时间
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*/
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func GetNowJDE() (NowJDE float64) {
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Time := float64(time.Now().Second())/3600.0/24.0 + float64(time.Now().Minute())/60.0/24.0 + float64(time.Now().Hour())/24.0
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NowJDE = JDECalc(time.Now().Year(), int(time.Now().Month()), float64(time.Now().Day())+Time)
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return
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}
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func dt_ext(y, jsd float64) float64 { // 二次曲线外推，用于数值外插
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dy := (y - 1820) / 100.00
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return -20 + jsd*dy*dy
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}
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func dt_cal(y float64) float64 { //传入年， 返回世界时UT与原子时（力学时 TD）之差, ΔT = TD - UT
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dt_at := []float64{
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-4000, 108371.7, -13036.80, 392.000, 0.0000,
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-500, 17201.0, -627.82, 16.170, -0.3413,
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-150, 12200.6, -346.41, 5.403, -0.1593,
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150, 9113.8, -328.13, -1.647, 0.0377,
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500, 5707.5, -391.41, 0.915, 0.3145,
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900, 2203.4, -283.45, 13.034, -0.1778,
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1300, 490.1, -57.35, 2.085, -0.0072,
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1600, 120.0, -9.81, -1.532, 0.1403,
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1700, 10.2, -0.91, 0.510, -0.0370,
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1800, 13.4, -0.72, 0.202, -0.0193,
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1830, 7.8, -1.81, 0.416, -0.0247,
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1860, 8.3, -0.13, -0.406, 0.0292,
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1880, -5.4, 0.32, -0.183, 0.0173,
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1900, -2.3, 2.06, 0.169, -0.0135,
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1920, 21.2, 1.69, -0.304, 0.0167,
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1940, 24.2, 1.22, -0.064, 0.0031,
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1960, 33.2, 0.51, 0.231, -0.0109,
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1980, 51.0, 1.29, -0.026, 0.0032,
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2000, 63.87, 0.1, 0, 0,
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2005, 64.7, 0.4, 0, 0, //一次项记为x,则 10x=0.4秒/年*(2015-2005),解得x=0.4
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2015, 69,
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}
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y0 := dt_at[len(dt_at)-2] //表中最后一年
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t0 := dt_at[len(dt_at)-1] //表中最后一年的 deltatT
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if y >= y0 {
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jsd := float64(31) // sjd是y1年之后的加速度估计
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// 瑞士星历表jsd=31, NASA网站jsd=32, skmap的jsd=29
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if y > y0+100.00 {
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return dt_ext(y, jsd)
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}
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v := dt_ext(y, jsd) //二次曲线外推
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dv := dt_ext(y0, jsd) - t0 // ye年的二次外推与te的差
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return (v - dv*(y0+100.00-y)/100.00)
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}
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d := dt_at
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var i int
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for i = 0; i < len(d); i += 5 {
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if float64(y) < d[i+5] {
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break
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// 判断年所在的区间
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}
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}
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t1 := (y - d[i]) / (d[i+5] - d[i]) * 10.00 //////// 三次插值， 保证精确性
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t2 := t1 * t1
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t3 := t2 * t1
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res := d[i+1] + d[i+2]*t1 + d[i+3]*t2 + d[i+4]*t3
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return (res)
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}
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func DeltaT(date float64, isJDE bool) float64 {
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return defDeltaTFn(date, isJDE)
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}
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func SetDeltaTFn(fn func(float64, bool) float64) {
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if fn != nil {
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defDeltaTFn = fn
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}
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}
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func GetDeltaTFn() func(float64, bool) float64 {
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return defDeltaTFn
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}
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func OldDefaultDeltaT(Date float64, IsJDE bool) (Result float64) { //传入年或儒略日，传出为秒
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var Year float64
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if IsJDE {
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dates := JDE2Date(Date)
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Year = float64(dates.Year()) + float64(dates.YearDay())/365.0
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} else {
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Year = Date
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}
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if Year < 2100 && Year >= 2010 {
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return dt_cal(Year)
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}
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return DefaultDeltaT(Date, IsJDE)
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}
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func DefaultDeltaT(Date float64, IsJDE bool) (Result float64) { //传入年或儒略日，传出为秒
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var Year float64
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if IsJDE {
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dates := JDE2Date(Date)
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Year = float64(dates.Year()) + float64(dates.YearDay())/365.0
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} else {
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Year = Date
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}
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if Year < 2010 {
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Result = dt_cal(Year)
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return
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}
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if Year < 2100 && Year >= 2010 {
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var t = (Year - 2000.0)
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Result = 62.92 + 0.32217*t + 0.005589*t*t
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return
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}
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if Year >= 2100 && Year <= 2150 {
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Result = -20 + 32*(((Year-1820.0)/100.0)*((Year-1820.0)/100.0)) - 0.5628*(2150-Year)
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return
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}
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if Year > 2150 {
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//tmp=(Year-1820)/100;
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//Result= -20 + 32 * tmp*tmp;
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Result = dt_cal(Year)
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return
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}
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return
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}
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func DefaultDeltaTv2(date float64, isJd bool) float64 { //传入年或儒略日，传出为秒
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if !isJd {
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date = JDECalc(int(date), int((date-math.Floor(date))*12)+1, (date-math.Floor(date))*365.25+1)
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}
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return DeltaTv2(date)
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}
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// 使用Stephenson等人(2016)和Morrison等人(2021)的拟合和外推公式计算Delta T
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// http://astro.ukho.gov.uk/nao/lvm/
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// 2010年后的系数已修改以包含2019年后的数据
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// 返回Delta T，单位为秒
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func DeltaTSplineY(y float64) float64 {
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// 积分lod（平均太阳日偏离86400秒的偏差）方程：
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// 来自 http://astro.ukho.gov.uk/nao/lvm/：
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// lod = 1.72 t − 3.5 sin(2*pi*(t+0.75)/14) 单位ms/day，其中 t = (y - 1825)/100
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// 是从1825年开始的世纪数
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// 使用 1ms = 1e-3s 和 1儒略年 = 365.25天，
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// lod = 6.2823e-3 * Delta y - 1.278375*sin(2*pi/14*(Delta y /100 + 0.75) 单位s/year
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// 其中 Delta y = y - 1825。积分该方程得到
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// Integrate[lod, y] = 3.14115e-3*(Delta y)^2 + 894.8625/pi*cos(2*pi/14*(Delta y /100 + 0.75)
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// 单位为秒。积分常数设为0。
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integratedLod := func(x float64) float64 {
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u := x - 1825
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return 3.14115e-3*u*u + 284.8435805251424*math.Cos(0.4487989505128276*(0.01*u+0.75))
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}
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if y < -720 {
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// 使用积分lod + 常数
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const c = 1.007739546148514
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return integratedLod(y) + c
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}
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if y > 2025 {
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// 使用积分lod + 常数
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const c = -150.56787057979514
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return integratedLod(y) + c
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}
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// 使用三次样条拟合
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y0 := []float64{-720, -100, 400, 1000, 1150, 1300, 1500, 1600, 1650, 1720, 1800, 1810, 1820, 1830, 1840, 1850, 1855, 1860, 1865, 1870, 1875, 1880, 1885, 1890, 1895, 1900, 1905, 1910, 1915, 1920, 1925, 1930, 1935, 1940, 1945, 1950, 1953, 1956, 1959, 1962, 1965, 1968, 1971, 1974, 1977, 1980, 1983, 1986, 1989, 1992, 1995, 1998, 2001, 2004, 2007, 2010, 2013, 2016, 2019, 2022}
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y1 := []float64{-100, 400, 1000, 1150, 1300, 1500, 1600, 1650, 1720, 1800, 1810, 1820, 1830, 1840, 1850, 1855, 1860, 1865, 1870, 1875, 1880, 1885, 1890, 1895, 1900, 1905, 1910, 1915, 1920, 1925, 1930, 1935, 1940, 1945, 1950, 1953, 1956, 1959, 1962, 1965, 1968, 1971, 1974, 1977, 1980, 1983, 1986, 1989, 1992, 1995, 1998, 2001, 2004, 2007, 2010, 2013, 2016, 2019, 2022, 2025}
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a0 := []float64{20371.848, 11557.668, 6535.116, 1650.393, 1056.647, 681.149, 292.343, 109.127, 43.952, 12.068, 18.367, 15.678, 16.516, 10.804, 7.634, 9.338, 10.357, 9.04, 8.255, 2.371, -1.126, -3.21, -4.388, -3.884, -5.017, -1.977, 4.923, 11.142, 17.479, 21.617, 23.789, 24.418, 24.164, 24.426, 27.05, 28.932, 30.002, 30.76, 32.652, 33.621, 35.093, 37.956, 40.951, 44.244, 47.291, 50.361, 52.936, 54.984, 56.373, 58.453, 60.678, 62.898, 64.083, 64.553, 65.197, 66.061, 66.919, 68.130, 69.250, 69.296}
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a1 := []float64{-9999.586, -5822.27, -5671.519, -753.21, -459.628, -421.345, -192.841, -78.697, -68.089, 2.507, -3.481, 0.021, -2.157, -6.018, -0.416, 1.642, -0.486, -0.591, -3.456, -5.593, -2.314, -1.893, 0.101, -0.531, 0.134, 5.715, 6.828, 6.33, 5.518, 3.02, 1.333, 0.052, -0.419, 1.645, 2.499, 1.127, 0.737, 1.409, 1.577, 0.868, 2.275, 3.035, 3.157, 3.199, 3.069, 2.878, 2.354, 1.577, 1.648, 2.235, 2.324, 1.804, 0.674, 0.466, 0.804, 0.839, 1.005, 1.348, 0.594, -0.227}
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a2 := []float64{776.247, 1303.151, -298.291, 184.811, 108.771, 61.953, -6.572, 10.505, 38.333, 41.731, -1.126, 4.629, -6.806, 2.944, 2.658, 0.261, -2.389, 2.284, -5.148, 3.011, 0.269, 0.152, 1.842, -2.474, 3.138, 2.443, -1.329, 0.831, -1.643, -0.856, -0.831, -0.449, -0.022, 2.086, -1.232, 0.22, -0.61, 1.282, -1.115, 0.406, 1.002, -0.242, 0.364, -0.323, 0.193, -0.384, -0.14, -0.637, 0.708, -0.121, 0.21, -0.729, -0.402, 0.194, 0.144, -0.109, 0.275, 0.068, -0.822, 0.001}
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a3 := []float64{409.16, -503.433, 1085.087, -25.346, -24.641, -29.414, 16.197, 3.018, -2.127, -37.939, 1.918, -3.812, 3.25, -0.096, -0.539, -0.883, 1.558, -2.477, 2.72, -0.914, -0.039, 0.563, -1.438, 1.871, -0.232, -1.257, 0.72, -0.825, 0.262, 0.008, 0.127, 0.142, 0.702, -1.106, 0.614, -0.277, 0.631, -0.799, 0.507, 0.199, -0.414, 0.202, -0.229, 0.172, -0.192, 0.081, -0.165, 0.448, -0.276, 0.11, -0.313, 0.109, 0.199, -0.017, -0.084, 0.128, -0.069, -0.297, 0.274, 0.086}
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n := len(y0)
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var i int
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for i = n - 1; i >= 0; i-- {
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if y >= y0[i] {
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break
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}
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}
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t := (y - y0[i]) / (y1[i] - y0[i])
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dT := a0[i] + t*(a1[i]+t*(a2[i]+t*a3[i]))
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return dT
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}
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func DeltaTv2(jd float64) float64 {
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if jd > 2461041.5 || jd < 2441317.5 {
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var y float64
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if jd >= 2299160.5 {
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y = (jd-2451544.5)/365.2425 + 2000
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} else {
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y = (jd+0.5)/365.25 - 4712
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}
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return DeltaTSplineY(y)
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}
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// 闰秒JD值
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jdLeaps := []float64{2457754.5, 2457204.5, 2456109.5, 2454832.5,
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2453736.5, 2451179.5, 2450630.5, 2450083.5,
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2449534.5, 2449169.5, 2448804.5, 2448257.5,
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2447892.5, 2447161.5, 2446247.5, 2445516.5,
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2445151.5, 2444786.5, 2444239.5, 2443874.5,
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2443509.5, 2443144.5, 2442778.5, 2442413.5,
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2442048.5, 2441683.5, 2441499.5, 2441133.5}
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n := len(jdLeaps)
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DT := 42.184
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for i := 0; i < n; i++ {
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if jd > jdLeaps[i] {
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DT += float64(n - i - 1)
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break
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}
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}
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return DT
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}
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func TD2UT(JDE float64, UT2TD bool) float64 { // true 世界时转力学时CC，false 力学时转世界时VV
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Deltat := DeltaT(JDE, true)
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if UT2TD {
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return JDE + Deltat/3600/24
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} else {
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return JDE - Deltat/3600/24
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}
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}
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/*
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* @name: JDE转日期，输出为数组
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*/
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func JDE2Date(JD float64) time.Time {
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JD = JD + 0.5
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Z := float64(int(JD))
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F := JD - Z
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var A, B, Years, Months, Days float64
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if Z < 2299161.0 {
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A = Z
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} else {
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alpha := math.Floor((Z - 1867216.25) / 36524.25)
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A = Z + 1 + alpha - math.Floor(alpha/4)
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}
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B = A + 1524
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C := math.Floor((B - 122.1) / 365.25)
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D := math.Floor(365.25 * C)
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E := math.Floor((B - D) / 30.6001)
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Days = B - D - math.Floor(30.6001*E) + F
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if E < 14 {
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Months = E - 1
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}
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if E == 14 || E == 15 {
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Months = E - 13
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}
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if Months > 2 {
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Years = C - 4716
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}
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if Months == 1 || Months == 2 {
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Years = C - 4715
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}
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tms := (Days - math.Floor(Days)) * 24 * 3600
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Days = math.Floor(Days)
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tz, _ := time.LoadLocation("Local")
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dates := time.Date(int(Years), time.Month(int(Months)), int(Days), 0, 0, 0, 0, tz)
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return time.Unix(dates.Unix()+int64(tms), int64((tms-math.Floor(tms))*1000000000))
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}
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// JDE2DateByZone JDE（儒略日）转日期
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// JD: 儒略日
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// tz: 目标时区
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// byZone: (true: 传入的儒略日视为目标时区当地时间的儒略日，false: 传入的儒略日视为UTC时间的儒略日)
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// 回参：转换后的日期，时区始终为目标时区
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func JDE2DateByZone(JD float64, tz *time.Location, byZone bool) time.Time {
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JD = JD + 0.5
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Z := float64(int(JD))
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F := JD - Z
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var A, B, Years, Months, Days float64
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if Z < 2299161.0 {
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A = Z
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} else {
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alpha := math.Floor((Z - 1867216.25) / 36524.25)
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A = Z + 1 + alpha - math.Floor(alpha/4)
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}
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B = A + 1524
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C := math.Floor((B - 122.1) / 365.25)
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D := math.Floor(365.25 * C)
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E := math.Floor((B - D) / 30.6001)
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Days = B - D - math.Floor(30.6001*E) + F
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if E < 14 {
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Months = E - 1
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}
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if E == 14 || E == 15 {
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Months = E - 13
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}
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if Months > 2 {
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Years = C - 4716
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}
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if Months == 1 || Months == 2 {
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Years = C - 4715
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}
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tms := (Days - math.Floor(Days)) * 24 * 3600
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Days = math.Floor(Days)
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var transTz = tz
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if !byZone {
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transTz = time.UTC
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}
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return time.Date(int(Years), time.Month(int(Months)), int(Days), 0, 0, 0, 0, transTz).
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Add(time.Duration(int64(1000000000 * tms))).In(tz)
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}
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// Date2JDE 日期转儒略日
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func Date2JDE(date time.Time) float64 {
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day := float64(date.Day()) + float64(date.Hour())/24.0 + float64(date.Minute())/24.0/60.0 + float64(date.Second())/24.0/3600.0 + float64(date.Nanosecond())/1000000000.0/3600.0/24.0
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return JDECalc(date.Year(), int(date.Month()), day)
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}
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func GetLunar(year, month, day int, tz float64) (lyear, lmonth, lday int, leap bool, result string) {
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julianDayEpoch := JDECalc(year, month, float64(day))
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// 确定农历年份
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lyear = year
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adjustedYear := year
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if month == 11 || month == 12 {
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winterSolsticeDay := GetJQTime(year, 270) + tz
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firstNewMoonDay := TD2UT(CalcMoonS(float64(year)+11.0/12.0+5.0/30.0/12.0, 0), true) + tz
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nextNewMoonDay := TD2UT(CalcMoonS(float64(year)+1.0, 0), true) + tz
|
||
|
||
firstNewMoonDay = normalizeTimePoint(firstNewMoonDay)
|
||
nextNewMoonDay = normalizeTimePoint(nextNewMoonDay)
|
||
|
||
if winterSolsticeDay >= firstNewMoonDay && winterSolsticeDay < nextNewMoonDay && julianDayEpoch <= firstNewMoonDay {
|
||
adjustedYear--
|
||
}
|
||
if winterSolsticeDay >= nextNewMoonDay && julianDayEpoch < nextNewMoonDay {
|
||
adjustedYear--
|
||
}
|
||
} else {
|
||
adjustedYear--
|
||
}
|
||
|
||
// 获取节气和朔望月数据
|
||
solarTerms := GetJieqiLoops(adjustedYear, 25)
|
||
newMoonDays := GetMoonLoops(float64(adjustedYear), 17)
|
||
|
||
// 计算冬至日期
|
||
winterSolsticeFirst := solarTerms[0] - 8.0/24 + tz
|
||
winterSolsticeSecond := solarTerms[24] - 8.0/24 + tz
|
||
|
||
// 规范化时间点
|
||
normalizeTimeArray(newMoonDays, tz)
|
||
normalizeTimeArray(solarTerms, tz)
|
||
|
||
// 计算朔望月范围
|
||
minMoonIndex, maxMoonIndex := 20, 0
|
||
moonCount := 0
|
||
for i := 0; i < 15; i++ {
|
||
if newMoonDays[i] >= winterSolsticeFirst && newMoonDays[i] < winterSolsticeSecond {
|
||
if i <= minMoonIndex {
|
||
minMoonIndex = i
|
||
}
|
||
if i >= maxMoonIndex {
|
||
maxMoonIndex = i
|
||
}
|
||
moonCount++
|
||
}
|
||
}
|
||
|
||
// 确定闰月位置
|
||
leapMonthPos := 20
|
||
if moonCount == 13 {
|
||
solarTermIndex, i := 2, 0
|
||
for i = minMoonIndex; i <= maxMoonIndex; i++ {
|
||
if !(newMoonDays[i] <= solarTerms[solarTermIndex] && newMoonDays[i+1] > solarTerms[solarTermIndex]) {
|
||
break
|
||
}
|
||
solarTermIndex += 2
|
||
}
|
||
leapMonthPos = i - minMoonIndex + 1
|
||
}
|
||
|
||
// 找到当前月相索引
|
||
currentMoonIndex := 0
|
||
for currentMoonIndex = minMoonIndex - 1; currentMoonIndex <= maxMoonIndex; currentMoonIndex++ {
|
||
if newMoonDays[currentMoonIndex] > julianDayEpoch {
|
||
break
|
||
}
|
||
}
|
||
|
||
// 计算农历月份
|
||
lmonth = currentMoonIndex - minMoonIndex
|
||
shouldAdjustLeap := false
|
||
leap = false
|
||
|
||
if lmonth >= leapMonthPos {
|
||
shouldAdjustLeap = true
|
||
}
|
||
if lmonth == leapMonthPos {
|
||
leap = true
|
||
}
|
||
if lmonth < 2 {
|
||
lmonth += 11
|
||
} else {
|
||
lmonth--
|
||
}
|
||
if shouldAdjustLeap {
|
||
lmonth--
|
||
}
|
||
if lmonth <= 0 {
|
||
lmonth += 12
|
||
}
|
||
|
||
// 计算农历日期
|
||
lday = int(julianDayEpoch-newMoonDays[currentMoonIndex-1]) + 1
|
||
|
||
// 生成农历日期字符串
|
||
result = formatLunarDateString(lmonth, lday, leap)
|
||
if lmonth >= 10 && month < 3 {
|
||
lyear--
|
||
}
|
||
return
|
||
}
|
||
|
||
func GetSolar(year, month, day int, leap bool, tz float64) float64 {
|
||
adjustedYear := year
|
||
if month < 11 {
|
||
adjustedYear--
|
||
}
|
||
|
||
// 获取节气和朔望月数据
|
||
solarTerms := GetJieqiLoops(adjustedYear, 25)
|
||
newMoonDays := GetMoonLoops(float64(adjustedYear), 17)
|
||
|
||
// 计算冬至日期
|
||
winterSolsticeFirst := solarTerms[0] - 8.0/24 + tz
|
||
winterSolsticeSecond := solarTerms[24] - 8.0/24 + tz
|
||
|
||
// 规范化时间点
|
||
normalizeTimeArray(newMoonDays, tz)
|
||
normalizeTimeArray(solarTerms, tz)
|
||
|
||
// 计算朔望月范围
|
||
minMoonIndex, maxMoonIndex := 20, 0
|
||
moonCount := 0
|
||
for i := 0; i < 15; i++ {
|
||
if newMoonDays[i] >= winterSolsticeFirst && newMoonDays[i] < winterSolsticeSecond {
|
||
if i <= minMoonIndex {
|
||
minMoonIndex = i
|
||
}
|
||
if i >= maxMoonIndex {
|
||
maxMoonIndex = i
|
||
}
|
||
moonCount++
|
||
}
|
||
}
|
||
|
||
// 确定闰月位置
|
||
leapMonthPos := 20
|
||
if moonCount == 13 {
|
||
solarTermIndex, i := 2, 0
|
||
for i = minMoonIndex; i <= maxMoonIndex; i++ {
|
||
if !(newMoonDays[i] <= solarTerms[solarTermIndex] && newMoonDays[i+1] > solarTerms[solarTermIndex]) {
|
||
break
|
||
}
|
||
solarTermIndex += 2
|
||
}
|
||
leapMonthPos = i - minMoonIndex + 1
|
||
}
|
||
|
||
// 计算实际月份索引
|
||
actualMonth := month
|
||
if leap {
|
||
actualMonth++
|
||
}
|
||
if actualMonth > 10 {
|
||
actualMonth -= 11
|
||
} else {
|
||
actualMonth++
|
||
}
|
||
if actualMonth >= leapMonthPos && !leap {
|
||
actualMonth++
|
||
}
|
||
|
||
return newMoonDays[minMoonIndex-1+actualMonth] + float64(day) - 1
|
||
}
|
||
|
||
func normalizeTimeArray(timeArray []float64, tz float64) {
|
||
for idx, timeValue := range timeArray {
|
||
adjustedTime := timeValue
|
||
if tz != 8.0/24 {
|
||
adjustedTime = timeValue - 8.0/24 + tz
|
||
}
|
||
timeArray[idx] = normalizeTimePoint(adjustedTime)
|
||
}
|
||
}
|
||
|
||
func normalizeTimePoint(timePoint float64) float64 {
|
||
if timePoint-math.Floor(timePoint) > 0.5 {
|
||
return math.Floor(timePoint) + 0.5
|
||
}
|
||
return math.Floor(timePoint) - 0.5
|
||
}
|
||
|
||
func formatLunarDateString(lunarMonth, lunarDay int, isLeap bool) string {
|
||
monthNames := []string{"十", "一", "二", "三", "四", "五", "六", "七", "八", "九", "十", "冬", "腊"}
|
||
dayPrefixes := []string{"初", "十", "廿", "三"}
|
||
|
||
var dateString string
|
||
|
||
if isLeap {
|
||
dateString += "闰"
|
||
}
|
||
|
||
if lunarMonth == 1 {
|
||
dateString += "正月"
|
||
} else {
|
||
dateString += monthNames[lunarMonth] + "月"
|
||
}
|
||
|
||
if lunarDay == 20 {
|
||
dateString += "二十"
|
||
} else if lunarDay == 10 {
|
||
dateString += "初十"
|
||
} else {
|
||
dateString += dayPrefixes[lunarDay/10] + monthNames[lunarDay%10]
|
||
}
|
||
|
||
return dateString
|
||
}
|