299 lines
12 KiB
Go
299 lines
12 KiB
Go
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package basic
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import (
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"math"
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"time"
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)
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// AltitudeLimb 日月取高度的位置；行星与恒星忽略 / limb used for Sun and Moon altitude.
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type AltitudeLimb int
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const (
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// AltitudeLimbUpper 上缘，与日出日落口径相同 / upper limb.
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AltitudeLimbUpper AltitudeLimb = iota
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// AltitudeLimbCenter 中心 / centre.
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AltitudeLimbCenter
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// AltitudeLimbLower 下缘 / lower limb.
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AltitudeLimbLower
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)
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// AltitudeCrossingOptions 任意高度升落选项；零值为上缘、标准气象（1010 hPa、10 °C）、计入折射 / options for altitude crossings.
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type AltitudeCrossingOptions struct {
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Limb AltitudeLimb
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// NoRefraction 为 true 时目标高度按几何高度比较 / compare geometric altitude when true.
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NoRefraction bool
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// PressureHPa 为 0 时用标准气压与气温 / zero selects the standard atmosphere.
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PressureHPa float64
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TemperatureC float64
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}
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// AltitudeCrossingState 一个民用日内的穿越状态 / crossing state over one civil day.
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type AltitudeCrossingState int
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const (
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// AltitudeCrosses 至少有一次升或落 / at least one crossing.
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AltitudeCrosses AltitudeCrossingState = iota
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// AltitudeAlwaysAbove 全天高于目标高度 / always above the target altitude.
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AltitudeAlwaysAbove
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// AltitudeAlwaysBelow 全天低于目标高度 / always below the target altitude.
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AltitudeAlwaysBelow
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// AltitudeTangent 极值与目标高度相差不足 1″，视为相切 / extremum within 1″ of the target.
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AltitudeTangent
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)
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// AltitudeCrossing 民用日内首次升、落（本地儒略日，无则为 NaN）与残差范围（度）/ first rise and set in local JD with residual range in degrees.
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type AltitudeCrossing struct {
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Rise, Set float64
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State AltitudeCrossingState
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MinResidual float64
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MaxResidual float64
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}
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// AltitudeCrossingResult date 所在民用日内首次升、落（无则为零值，对应 HasRise/HasSet 为 false）与残差范围（度）/ first rise and set on the civil day.
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type AltitudeCrossingResult struct {
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Rise, Set time.Time
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HasRise, HasSet bool
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State AltitudeCrossingState
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MinResidual float64
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MaxResidual float64
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}
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const (
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altitudeScanStepDays = 10.0 / 1440
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altitudeTangentDegrees = 1.0 / 3600
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)
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func (options AltitudeCrossingOptions) refraction(trueAltitude float64) float64 {
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if options.NoRefraction {
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return 0
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}
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if options.PressureHPa == 0 {
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return RefractionFromTrueAltitude(trueAltitude, refractionStandardPressureHPa, refractionStandardTemperatureC)
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}
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return RefractionFromTrueAltitude(trueAltitude, options.PressureHPa, options.TemperatureC)
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}
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func (options AltitudeCrossingOptions) limbOffset(semidiameterDeg float64) float64 {
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switch options.Limb {
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case AltitudeLimbUpper:
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return semidiameterDeg
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case AltitudeLimbLower:
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return -semidiameterDeg
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}
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return 0
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}
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func (options AltitudeCrossingOptions) valid() bool {
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if options.Limb < AltitudeLimbUpper || options.Limb > AltitudeLimbLower {
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return false
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}
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return options.NoRefraction || options.PressureHPa == 0 || !math.IsNaN(RefractionFromTrueAltitude(0, options.PressureHPa, options.TemperatureC))
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}
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// SkyAltitudeCrossingWithInstance 日、月或行星在本地民用日 julianDay 内穿过视高度 targetAltitude（度，相对天文地平）的时刻 /
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// Sun, Moon or planet crossings of an apparent altitude on the local civil day.
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//
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// height 只影响月球站心视差；需要以下沉地平为基准时由调用方从 targetAltitude 中减去地平俯角。
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//
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// 这是按儒略日窗口求解的低级接口：julianDay 与 timeZone（小时）由调用方拼出本地民用日，
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// 固定时区不处理夏令时切换。julianDay 须取本地零点（x.5），正午及之后的值会落到次日窗口。一般用途请用 SkyAltitudeCrossingOnDate，它从 time.Time 推出
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// 当天的真实时区窗口 / low-level julian-day window API; prefer SkyAltitudeCrossingOnDate.
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func SkyAltitudeCrossingWithInstance(body SkyBody, julianDay, longitude, latitude, timeZone, height, targetAltitude float64,
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options AltitudeCrossingOptions, inst *Instance) (AltitudeCrossing, error) {
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altitude, err := skyAltitudeFunc(body, longitude, latitude, timeZone, height, inst)
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if err != nil {
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return AltitudeCrossing{}, err
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}
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start := math.Floor(julianDay) + 0.5
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return altitudeCrossing(start, start+1, latitude, height, targetAltitude, options, altitude)
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}
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// SkyAltitudeCrossingOnDate 日、月或行星在 date 所在民用日内穿过视高度 targetAltitude 的时刻；夏令时切换日按实际日长搜索 /
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// Sun, Moon or planet crossings of an apparent altitude on the civil day of date.
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func SkyAltitudeCrossingOnDate(body SkyBody, date time.Time, longitude, latitude, height, targetAltitude float64,
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options AltitudeCrossingOptions, inst *Instance) (AltitudeCrossingResult, error) {
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start, end, timeZone := civilDayWindow(date)
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altitude, err := skyAltitudeFunc(body, longitude, latitude, timeZone, height, inst)
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if err != nil {
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return AltitudeCrossingResult{}, err
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}
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raw, err := altitudeCrossing(start, end, latitude, height, targetAltitude, options, altitude)
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return altitudeCrossingOnDate(date, timeZone, raw, err)
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}
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// StarAltitudeCrossing 恒星（视赤经、视赤纬，度）在本地民用日内穿过视高度 targetAltitude 的时刻 / star crossings of an apparent altitude.
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//
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// julianDay 须取本地零点（x.5），正午及之后的值会落到次日窗口；一般用途请用 StarAltitudeCrossingOnDate。
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func StarAltitudeCrossing(julianDay, ra, dec, longitude, latitude, timeZone, targetAltitude float64, options AltitudeCrossingOptions) (AltitudeCrossing, error) {
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if !isFiniteFloat(ra) || !isFiniteFloat(dec) {
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return AltitudeCrossing{}, ErrInvalidObservationInput
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}
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start := math.Floor(julianDay) + 0.5
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return altitudeCrossing(start, start+1, latitude, 0, targetAltitude, options, starAltitudeFunc(ra, dec, longitude, latitude, timeZone))
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}
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// StarAltitudeCrossingOnDate 恒星在 date 所在民用日内穿过视高度 targetAltitude 的时刻；夏令时切换日按实际日长搜索 /
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// star crossings of an apparent altitude on the civil day of date.
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func StarAltitudeCrossingOnDate(date time.Time, ra, dec, longitude, latitude, targetAltitude float64, options AltitudeCrossingOptions) (AltitudeCrossingResult, error) {
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if !isFiniteFloat(ra) || !isFiniteFloat(dec) {
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return AltitudeCrossingResult{}, ErrInvalidObservationInput
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}
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start, end, timeZone := civilDayWindow(date)
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raw, err := altitudeCrossing(start, end, latitude, 0, targetAltitude, options, starAltitudeFunc(ra, dec, longitude, latitude, timeZone))
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return altitudeCrossingOnDate(date, timeZone, raw, err)
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}
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// civilDayWindow 以当天零点的偏移固定本地时标，窗口为真实日长（夏令时切换日 23 或 25 小时）。
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func civilDayWindow(date time.Time) (start, end, timeZone float64) {
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year, month, day := date.Date()
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midnight := time.Date(year, month, day, 0, 0, 0, 0, date.Location())
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next := time.Date(year, month, day+1, 0, 0, 0, 0, date.Location())
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_, offset := midnight.Zone()
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start = Date2JD(midnight)
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return start, start + next.Sub(midnight).Hours()/24, float64(offset) / 3600
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}
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func altitudeCrossingOnDate(date time.Time, timeZone float64, raw AltitudeCrossing, err error) (AltitudeCrossingResult, error) {
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if err != nil {
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return AltitudeCrossingResult{}, err
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}
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convert := func(jd float64) (time.Time, bool) {
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if math.IsNaN(jd) {
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return time.Time{}, false
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}
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return JD2DateByZone(jd-timeZone/24, date.Location(), false), true
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}
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out := AltitudeCrossingResult{State: raw.State, MinResidual: raw.MinResidual, MaxResidual: raw.MaxResidual}
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out.Rise, out.HasRise = convert(raw.Rise)
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out.Set, out.HasSet = convert(raw.Set)
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return out, nil
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}
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func skyAltitudeFunc(body SkyBody, longitude, latitude, timeZone, height float64, inst *Instance) (func(jd float64) (float64, float64), error) {
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switch {
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case body == SkySun:
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return func(jd float64) (float64, float64) {
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state := sunObservationStateN(jd, longitude, latitude, timeZone, -1, inst)
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return state.altitude, angularSemidiameterFromAU(sunEquatorialRadiusKM, state.distanceAU) / 3600
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}, nil
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case body == SkyMoon:
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return func(jd float64) (float64, float64) {
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state := hMoonObservationStateN(jd, longitude, latitude, timeZone, height, -1, inst)
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return state.altitude, angularSemidiameterArcsec(moonEquatorialRadiusKM, state.distanceKM) / 3600
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}, nil
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case body.valid():
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heightFn := skyPlanetHeight(body)
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return func(jd float64) (float64, float64) { return heightFn(jd, longitude, latitude, timeZone, inst), 0 }, nil
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}
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return nil, ErrInvalidObservationInput
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}
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func starAltitudeFunc(ra, dec, longitude, latitude, timeZone float64) func(jd float64) (float64, float64) {
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return func(jd float64) (float64, float64) {
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return StarHeight(jd, ra, dec, longitude, latitude, timeZone), 0
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}
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}
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func skyPlanetHeight(body SkyBody) func(localJD, lon, lat, timezone float64, inst *Instance) float64 {
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switch body {
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case SkyMercury:
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return MercuryHeightWithInstance
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case SkyVenus:
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return VenusHeightWithInstance
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case SkyMars:
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return MarsHeightWithInstance
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case SkyJupiter:
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return JupiterHeightWithInstance
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case SkySaturn:
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return SaturnHeightWithInstance
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case SkyUranus:
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return UranusHeightWithInstance
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}
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return NeptuneHeightWithInstance
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}
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func altitudeCrossing(start, end, latitude, height, targetAltitude float64, options AltitudeCrossingOptions,
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altitude func(jd float64) (float64, float64)) (AltitudeCrossing, error) {
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if !isFiniteFloat(start) || !isFiniteFloat(end) || !(end > start) || !isFiniteFloat(latitude) || math.Abs(latitude) > 90 ||
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!isFiniteFloat(height) || !isFiniteFloat(targetAltitude) || math.Abs(targetAltitude) > 90 || !options.valid() {
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return AltitudeCrossing{}, ErrInvalidObservationInput
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}
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residual := func(jd float64) float64 {
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alt, semidiameter := altitude(jd)
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return alt + options.refraction(alt) + options.limbOffset(semidiameter) - targetAltitude
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}
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result := AltitudeCrossing{Rise: math.NaN(), Set: math.NaN(), MinResidual: math.Inf(1), MaxResidual: math.Inf(-1)}
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prevT, prevR := start, residual(start)
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if math.IsNaN(prevR) {
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return AltitudeCrossing{}, ErrInvalidObservationInput
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}
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track := func(t, r float64) {
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result.MinResidual = math.Min(result.MinResidual, r)
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result.MaxResidual = math.Max(result.MaxResidual, r)
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}
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track(prevT, prevR)
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record := func(root float64, rising bool) {
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if rising && math.IsNaN(result.Rise) {
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result.Rise = root
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} else if !rising && math.IsNaN(result.Set) {
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result.Set = root
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}
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}
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// 同号区间内朝目标一侧的极值可能越过目标高度，采样点看不到这两次穿越。
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refine := func(a, b, ra float64) {
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peak, rp := orbitalGoldenExtremum(residual, a, b, ra < 0)
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if math.IsNaN(rp) {
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return
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}
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track(peak, rp)
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if (rp < 0) == (ra < 0) || peak <= a || peak >= b {
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return
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}
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record(orbitalBisect(residual, a, peak, ra), ra < 0)
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record(orbitalBisect(residual, peak, b, rp), ra >= 0)
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}
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prev2T, prev2R, samples := prevT, prevR, 1
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for t := start + altitudeScanStepDays; prevT < end; t += altitudeScanStepDays {
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t = math.Min(t, end)
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r := residual(t)
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if math.IsNaN(r) {
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return AltitudeCrossing{}, ErrInvalidObservationInput
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}
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track(t, r)
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sameSign := (prevR < 0) == (r < 0)
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switch {
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case !sameSign:
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record(orbitalBisect(residual, prevT, t, prevR), r >= 0)
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case samples == 1:
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refine(prevT, t, prevR)
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case (prev2R < 0) == (prevR < 0) && altitudeTowardTarget(prev2R, prevR, r):
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refine(prev2T, t, prev2R)
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}
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prev2T, prev2R = prevT, prevR
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prevT, prevR = t, r
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samples++
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}
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if samples > 2 && (prev2R < 0) == (prevR < 0) {
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refine(prev2T, prevT, prev2R)
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}
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switch {
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case !math.IsNaN(result.Rise) || !math.IsNaN(result.Set):
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result.State = AltitudeCrosses
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case math.Abs(result.MinResidual) < altitudeTangentDegrees || math.Abs(result.MaxResidual) < altitudeTangentDegrees:
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result.State = AltitudeTangent
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case result.MinResidual > 0:
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result.State = AltitudeAlwaysAbove
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default:
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result.State = AltitudeAlwaysBelow
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}
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return result, nil
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}
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// altitudeTowardTarget 报告中间样本是否为朝零点一侧的局部极值：负残差取极大，正残差取极小。
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func altitudeTowardTarget(left, middle, right float64) bool {
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if middle < 0 {
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return middle >= left && middle >= right
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}
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return middle <= left && middle <= right
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}
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