59 lines
2.5 KiB
Go
59 lines
2.5 KiB
Go
|
package basic
|
||
|
|
|
||
|
|
import "math"
|
||
|
|
|
||
|
|
// MoonHorizon 返回 UT 儒略日下海平面几何月球中心地平圈（月球恰好在地平线上的观测者轨迹，
|
||
|
|
// 即月下点周围的地平圈）的 [经度, 纬度] 顶点，单位为度，不重复首点。视差与椭球口径同
|
||
|
|
// HMoonHeight，不含折射；与 HMoonHeight(经, 纬, ..., 0) 配合时该圈上的点高度角为 0。
|
||
|
|
// samples<=0 取 360，其余夹到 [12, 1440]。
|
||
|
|
// MoonHorizon returns sea-level geometric Moon-centre horizon vertices in degrees for a UT Julian
|
||
|
|
// day: the locus of observers that see the Moon exactly on the horizon. Parallax and the observer
|
||
|
|
// ellipsoid match HMoonHeight; refraction is excluded.
|
||
|
|
func MoonHorizon(jdUT float64, samples int) [][2]float64 {
|
||
|
|
if !finite(jdUT) {
|
||
|
|
return nil
|
||
|
|
}
|
||
|
|
if samples <= 0 {
|
||
|
|
samples = 360
|
||
|
|
}
|
||
|
|
if samples < 12 {
|
||
|
|
samples = 12
|
||
|
|
} else if samples > 1440 {
|
||
|
|
samples = 1440
|
||
|
|
}
|
||
|
|
tt := TD2UT(jdUT, true)
|
||
|
|
ra, dec := HMoonTrueRaDec(tt)
|
||
|
|
distanceAU := HMoonAway(tt) / angularDiameterAstronomicalUnitKM
|
||
|
|
parallax := math.Sin(0.0024427777777*rad) / distanceAU
|
||
|
|
longitude := (ra - ApparentSiderealTime(jdUT)*15) * rad
|
||
|
|
latitude := dec * rad
|
||
|
|
if !finite(parallax) || parallax <= 0 || parallax >= 1 || !finite(longitude) || !finite(latitude) {
|
||
|
|
return nil
|
||
|
|
}
|
||
|
|
center := [3]float64{math.Cos(latitude) * math.Cos(longitude), math.Cos(latitude) * math.Sin(longitude), math.Sin(latitude)}
|
||
|
|
north := [3]float64{-math.Sin(latitude) * math.Cos(longitude), -math.Sin(latitude) * math.Sin(longitude), math.Cos(latitude)}
|
||
|
|
east := [3]float64{-math.Sin(longitude), math.Cos(longitude), 0}
|
||
|
|
points := make([][2]float64, samples)
|
||
|
|
for index := range points {
|
||
|
|
bearing := 2 * math.Pi * float64(index) / float64(samples)
|
||
|
|
radius := math.Acos(parallax)
|
||
|
|
var point [3]float64
|
||
|
|
for iteration := 0; iteration < 8; iteration++ {
|
||
|
|
for axis := range point {
|
||
|
|
point[axis] = center[axis]*math.Cos(radius) +
|
||
|
|
(north[axis]*math.Cos(bearing)+east[axis]*math.Sin(bearing))*math.Sin(radius)
|
||
|
|
}
|
||
|
|
lat := math.Asin(math.Max(-1, math.Min(1, point[2]))) / rad
|
||
|
|
// The topocentric direction is horizontal when its dot product
|
||
|
|
// with the geodetic zenith vanishes: cos(radius)=observer/range.
|
||
|
|
next := math.Acos(parallax * (pcosi(lat, 0)*math.Cos(lat*rad) + psini(lat, 0)*math.Sin(lat*rad)))
|
||
|
|
if math.Abs(next-radius) < 1e-14 {
|
||
|
|
break
|
||
|
|
}
|
||
|
|
radius = next
|
||
|
|
}
|
||
|
|
points[index] = [2]float64{math.Atan2(point[1], point[0]) / rad, math.Asin(math.Max(-1, math.Min(1, point[2]))) / rad}
|
||
|
|
}
|
||
|
|
return points
|
||
|
|
}
|