b612
044f2f4381
- 新增半解析、旧模型、自定义与多源堆叠星历实例，提供 Context、Instance、SPK 读取及状态与视位置计算 - 统一太阳、月球和行星实例接口，扩展黄经穿越、留、相位、最近角距、偕日可见、任意高度升落、轨道节点及凌日等天象查询 - 完善日月食、月掩与凌日的月缘剖面、有限盘面接触、站心修正、局地可见性、全球路径和地图输出 - 新增 SVG、GeoJSON、KML 天象输出及凌日、月掩和月缘地形相关缓存与几何求解 - 新增恒星星表导入与查询，支持 CSV、Hipparcos、BSC5、Stellarium 等格式及名称、交叉标识、锥面检索和星等过滤 - 补充 IAU 2006、地球定向、折射消光、大气观测、轨道传播及半解析行星/月球数据支持 - 将默认未来民用时标切换为 TimeScaleLeapHour，更新 2027–2400 农历速查表、中文日期解析和时区边界处理 - 增加事件基线、跨模型回归、几何边界、月缘地形和输出契约测试，完善中英文手册、示例资源、NOTICE 与忽略规则
200 lines
7.5 KiB
Go
200 lines
7.5 KiB
Go
package basic
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import "math"
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// Uranus 北极 J2000 赤经、赤纬与扁率。
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const (
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uranusPoleRA = 257.311
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uranusPoleDec = -15.175
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uranusFlattening = 0.02293
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j2000ObliquityDeg = 23.4392911
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)
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// planetMagnitude2018 用 Mallama & Hilton 2018 模型求视星等；index 为 1..7（水星..海王星）。
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// 超出模型相位角范围返回 NaN。
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func planetMagnitude2018(index int, jde float64, inst *Instance) float64 {
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r := planetRWithInstance(index, jde, inst)
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delta := planetEarthAwayWithInstance(index, jde, inst)
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earthR := planetRWithInstance(-1, jde, inst)
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if !(r > 0) || !(delta > 0) || !(earthR > 0) {
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return math.NaN()
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}
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cosPhase := (r*r + delta*delta - earthR*earthR) / (2 * r * delta)
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a := math.Acos(math.Max(-1, math.Min(1, cosPhase))) * 180 / math.Pi
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distance := 5 * math.Log10(r*delta)
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switch index {
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case 1:
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return -0.613 + a*(6.3280e-2+a*(-1.6336e-3+a*(3.3644e-5+a*(-3.4265e-7+a*(1.6893e-9-3.0334e-12*a))))) + distance
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case 2:
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if a <= 163.7 {
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return -4.384 + a*(-1.044e-3+a*(3.687e-4+a*(-2.814e-6+8.938e-9*a))) + distance
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}
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return 236.05828 + a*(-2.81914+8.39034e-3*a) + distance
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case 3:
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phys := MarsPhysicalNWithInstance(jde, -1, inst)
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lon := PlanetCoordinateNWithInstance(3, 0, jde, -1, inst)
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return marsMagnitude2018(r, delta, a, phys.SubEarthLongitude, phys.SubSolarLongitude, lon)
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case 4:
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if a <= 12 {
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return -9.395 + a*(-3.7e-4+6.16e-4*a) + distance
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}
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x := a / 180
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albedo := 1 + x*(-1.507+x*(-0.363+x*(-0.062+x*(2.809-1.876*x))))
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if !(albedo > 0) {
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return math.NaN()
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}
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return -9.428 - 2.5*math.Log10(albedo) + distance
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case 5:
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if a > 6.5 {
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return math.NaN()
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}
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earthLat, sunLat, _, _, _, _ := saturnRingParametersWithInstance(jde, inst)
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be, bs := earthLat*rad, sunLat*rad
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tilt := 0.0
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if be*bs > 0 {
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tilt = math.Abs(math.Sin(math.Sqrt(be * bs)))
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}
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return -8.914 - 1.825*tilt + 0.026*a - 0.378*tilt*math.Exp(-2.25*a) + distance
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case 6:
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phase := 0.0
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if a > 3.1 {
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phase = a * (6.587e-3 + 1.045e-4*a)
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}
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return -7.110 - 0.00084*uranusEffectiveSubLatitude(jde, inst) + phase + distance
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case 7:
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year := 2000 + (jde-2451545)/365.25
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unit := -7.00
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switch {
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case year < 1980:
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unit = -6.89
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case year <= 2000:
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unit = -6.89 - 0.0054*(year-1980)
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}
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if a > 1.9 && year > 2000 {
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unit += a * (7.944e-3 + 9.617e-5*a)
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}
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return unit + distance
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}
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return math.NaN()
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}
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// uranusEffectiveSubLatitude 天王星星下点与日下点行星面纬度绝对值的平均（度）。
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func uranusEffectiveSubLatitude(jde float64, inst *Instance) float64 {
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pole := eclipticUnitFromEquatorial(uranusPoleRA, uranusPoleDec)
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geoLon, geoLat := planetApparentLoBoWithInstance(6, jde, inst)
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helioLon, helioLat := planetLWithInstance(6, jde, inst), planetBWithInstance(6, jde, inst)
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sub := func(lon, lat float64) float64 {
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d := sphericalUnit(lon, lat)
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// 星下点方向自行星指向观测者，与视方向相反。
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centric := math.Asin(math.Max(-1, math.Min(1, -(pole[0]*d[0]+pole[1]*d[1]+pole[2]*d[2]))))
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graphic := math.Atan(math.Tan(centric) / ((1 - uranusFlattening) * (1 - uranusFlattening)))
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return math.Abs(graphic) * 180 / math.Pi
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}
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return (sub(geoLon, geoLat) + sub(helioLon, helioLat)) / 2
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}
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func sphericalUnit(lonDeg, latDeg float64) [3]float64 {
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lon, lat := lonDeg*rad, latDeg*rad
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return [3]float64{math.Cos(lat) * math.Cos(lon), math.Cos(lat) * math.Sin(lon), math.Sin(lat)}
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}
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func eclipticUnitFromEquatorial(raDeg, decDeg float64) [3]float64 {
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v := sphericalUnit(raDeg, decDeg)
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s, c := math.Sincos(j2000ObliquityDeg * rad)
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return [3]float64{v[0], v[1]*c + v[2]*s, -v[1]*s + v[2]*c}
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}
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// MercuryMag2018WithInstance 水星视星等（Mallama & Hilton 2018）/ Mercury magnitude, Mallama & Hilton 2018.
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func MercuryMag2018WithInstance(jde float64, inst *Instance) float64 {
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return planetMagnitude2018(1, jde, inst)
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}
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// VenusMag2018WithInstance 金星视星等（Mallama & Hilton 2018）/ Venus magnitude, Mallama & Hilton 2018.
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func VenusMag2018WithInstance(jde float64, inst *Instance) float64 {
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return planetMagnitude2018(2, jde, inst)
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}
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// MarsMag2018WithInstance 火星视星等（Mallama & Hilton 2018，含自转与季节修正）/ Mars magnitude, Mallama & Hilton 2018 with rotation and season terms.
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func MarsMag2018WithInstance(jde float64, inst *Instance) float64 {
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return planetMagnitude2018(3, jde, inst)
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}
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// JupiterMag2018WithInstance 木星视星等（Mallama & Hilton 2018）/ Jupiter magnitude, Mallama & Hilton 2018.
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func JupiterMag2018WithInstance(jde float64, inst *Instance) float64 {
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return planetMagnitude2018(4, jde, inst)
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}
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// SaturnMag2018WithInstance 土星视星等（Mallama & Hilton 2018，含环）/ Saturn magnitude with rings, Mallama & Hilton 2018.
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func SaturnMag2018WithInstance(jde float64, inst *Instance) float64 {
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return planetMagnitude2018(5, jde, inst)
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}
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// UranusMag2018WithInstance 天王星视星等（Mallama & Hilton 2018）/ Uranus magnitude, Mallama & Hilton 2018.
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func UranusMag2018WithInstance(jde float64, inst *Instance) float64 {
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return planetMagnitude2018(6, jde, inst)
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}
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// NeptuneMag2018WithInstance 海王星视星等（Mallama & Hilton 2018）/ Neptune magnitude, Mallama & Hilton 2018.
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func NeptuneMag2018WithInstance(jde float64, inst *Instance) float64 {
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return planetMagnitude2018(7, jde, inst)
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}
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// 火星自转（有效中央经线，0°..390° 每 10°，首两项为 −20°、−10°）与季节（Ls）星等修正表。
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var (
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marsRotationCorrection = [40]float64{
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0.024, 0.034, 0.036, 0.045, 0.038, 0.023, 0.015, 0.011,
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0.000, -0.012, -0.018, -0.036, -0.044, -0.059, -0.060, -0.055,
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-0.043, -0.041, -0.041, -0.036, -0.036, -0.018, -0.038, -0.011,
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0.002, 0.004, 0.018, 0.019, 0.035, 0.050, 0.035, 0.027,
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0.037, 0.048, 0.025, 0.022, 0.024, 0.034, 0.036, 0.045,
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}
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marsSeasonCorrection = [40]float64{
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-0.030, -0.017, -0.029, -0.017, -0.014, -0.006, -0.018, -0.020,
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-0.014, -0.030, -0.008, -0.040, -0.024, -0.037, -0.036, -0.032,
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0.010, 0.010, -0.001, 0.044, 0.025, -0.004, -0.016, -0.008,
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0.029, -0.054, -0.033, 0.055, 0.017, 0.052, 0.006, 0.087,
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0.006, 0.064, 0.030, 0.019, -0.030, -0.017, -0.029, -0.017,
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}
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)
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// marsStirling 四阶 Stirling 插值；angle 取 [0, 360)，表中 angle=10k 对应下标 k+2。
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func marsStirling(table *[40]float64, angle float64) float64 {
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angle = math.Mod(angle, 360)
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if angle < 0 {
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angle += 360
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}
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zero := int(angle / 10)
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p := angle/10 - float64(zero)
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var d1 [3]float64
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for i := range d1 {
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d1[i] = table[zero+i+1] - table[zero+i]
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}
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d2 := [2]float64{d1[1] - d1[0], d1[2] - d1[1]}
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// 四阶差分需要第 4 个一阶差分，表首尾各补两项即为此预留。
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d1b := table[zero+4] - table[zero+3]
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d2c := d1b - d1[2]
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d3 := [2]float64{d2[1] - d2[0], d2c - d2[1]}
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d4 := d3[1] - d3[0]
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a4 := d4 / 24
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a3 := (d3[0] + d3[1]) / 12
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a2 := d2[1]/2 - a4
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a1 := (d1[1]+d1[2])/2 - a3
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a0 := table[zero+2]
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return a0 + p*(a1+p*(a2+p*(a3+p*a4)))
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}
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// marsMagnitude2018 火星视星等：r、delta 为 AU，alpha 为相位角（度），子地、子日经度为西经（度），helioLon 为日心黄经（度）。
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func marsMagnitude2018(r, delta, alpha, subEarthLon, subSunLon, helioLon float64) float64 {
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distance := 5 * math.Log10(r*delta)
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base := -0.367 + alpha*(-0.02573+0.0003445*alpha)
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if alpha <= 50 {
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base = -1.601 + alpha*(0.02267-0.0001302*alpha)
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}
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cm := (subEarthLon + subSunLon) / 2
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if math.Abs(subEarthLon-subSunLon) > 180 {
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cm += 180
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}
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// Ls 由日心黄经平移 −85° 得到。
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return base + distance + marsStirling(&marsRotationCorrection, cm) + marsStirling(&marsSeasonCorrection, helioLon-85)
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}
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