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https://github.com/koreader/koreader
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597 lines
20 KiB
Lua
597 lines
20 KiB
Lua
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-- Author: Martin Zwicknagl (zwim)
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-- Date: 2021-10-29
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-- The current source code of this file can be found on https://github.com/zwim/suntime.
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--[[--
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Module to calculate ephemeris and other times depending on the sun position.
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Maximal errors from 2020-2050 (compared to https://midcdmz.nrel.gov/spa/) are:
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* -43.52° Christchurch 66s
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* -20.16° Mauritius: 25s
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* 20.30° Honolulu: 47s
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* 33.58° Casablanca: 24s
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* 35.68° Tokio: 50s
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* 37.97° Athene: 24s
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* 38° Sacramento: 67s
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* 41.91° Rome: 27s
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* 47.25° Innsbruck: 13s
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* 52.32° Berlin: 30s
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* 59.92° Oslo: 42s
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* 64.14° Reykjavik: 66s
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* 65.69° Akureyri: <24s (except *)
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* 70.67° Hammerfest: <105s (except **)
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*) A few days around beginning of summer (error <290s)
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**) A few days after and befor midnight sun (error <1200s)
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@usage
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local SunTime = require("suntime")
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time_zone = 0
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altitude = 50
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degree = true
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SunTime:setPosition("Reykjavik", 64.14381, -21.92626, timezone, altitude, degree)
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SunTime:setAdvanced()
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SunTime:setDate()
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SunTime:calculateTimes()
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print(SunTime.rise, SunTime.set, SunTime.set_civil) -- or similar see calculateTime()
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@module suntime
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--]]--
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-- math abbrevations
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local pi = math.pi
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local pi_2 = pi/2
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local abs = math.abs
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local floor = math.floor
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local sin = math.sin
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local cos = math.cos
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local tan = math.tan
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local asin = math.asin
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local acos = math.acos
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local atan = math.atan
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local toRad = pi/180
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local toDeg = 1/toRad
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local function Rad(x)
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return x*toRad
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end
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--------------------------------------------
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local speed_of_light = 2.99792E8
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local sun_radius = 6.96342e8
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local average_earth_radius = 6371e3
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local semimajor_axis = 149598022.96E3 -- earth orbit's major semi-axis in meter
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local average_speed_earth = 29.7859e3
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local aberration = asin(average_speed_earth/speed_of_light) -- Aberration relativistic
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--local average_speed_equator = (2*pi * average_earth_radius) / (24*3600)
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--------------------------------------------
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-- minimal twillight times in hours
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local min_civil_twilight = 20/60
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local min_nautic_twilight = 45/60 - min_civil_twilight
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local min_astronomic_twilight = 20/60 - min_nautic_twilight
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local SunTime = {
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astronomic = Rad(-18),
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nautic = Rad(-12),
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civil = Rad(-6),
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-- eod = Rad(-49/60), -- approx. end of day
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earth_flatten = 1 / 298.257223563, -- WGS84
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average_temperature = 10, -- °C
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times = {},
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}
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----------------------------------------------------------------
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-- simple 'Equation of time' good for dates between 2008-2027
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-- errors for latitude 20° are within 1min
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-- 47° are within 1min 30sec
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-- 65° are within 5min
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-- https://www.astronomie.info/zeitgleichung/#Auf-_und_Untergang (German)
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function SunTime:getZglSimple()
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local T = self.date.yday
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return -0.171 * sin(0.0337 * T + 0.465) - 0.1299 * sin(0.01787 * T - 0.168)
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end
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-- more advanced 'Equation of time' good for dates between 1800-2200
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-- errors are better than with the simple method
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-- https://de.wikipedia.org/wiki/Zeitgleichung (German) and
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-- more infos on http://www.hlmths.de/Scilab/Zeitgleichung.pdf (German)
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function SunTime:getZglAdvanced()
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local e = self.num_ex
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local e2 = e*e
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local e3 = e2*e
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local e4 = e3*e
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local e5 = e4*e
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-- https://de.wikibooks.org/wiki/Astronomische_Berechnungen_f%C3%BCr_Amateure/_Himmelsmechanik/_Sonne
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local C = (2*e - e3/4 + 5/96*e5) * self.sin_M
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+ (5/4*e2 + 11/24*e4) * self.sin_2M
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+ (13/12*e3 - 43/64*e5) * self.sin_3M
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+ 103/96*e4 * self.sin_4M
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+ 1097/960*e5 * self.sin_5M -- rad
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local lamb = self.L + C
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local tanL = tan(self.L)
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local tanLamb = tan(lamb)
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local cosEps = cos(self.epsilon)
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local zgl = atan( (tanL - tanLamb*cosEps) / (1 + tanL*tanLamb*cosEps) ) --rad
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return zgl*toDeg/15 -- to hours *4'/60
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end
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-- set current date or year/month/day daylightsaving hh/mm/ss
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-- if dst == nil use curent daylight saving of the system
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local days_in_month = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}
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function SunTime:setDate(year, month, day, dst, hour, min, sec)
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self.date = os.date("*t") -- get current day
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if year and month and day then
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self.date.year = year
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self.date.month = month
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self.date.day = day
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if year % 4 == 0 and (year % 100 ~= 0 or year % 400 == 0) then
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days_in_month[2] = 29
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else
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days_in_month[2] = 28
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end
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self.date.yday = day
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for i = 1, month-1 do
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self.date.yday = self.date.yday + days_in_month[i]
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end
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self.date.hour = hour or 12
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self.date.min = min or 0
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self.date.sec = sec or 0
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if dst ~= nil then
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self.date.isdst = dst
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end
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end
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end
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--[[--
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Set position for later calculations
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@param name Name of the location
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@param latitude Geographical latitude, North is positive
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@param longitude Geographical longitude, West is negative
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@param time_zone Timezone e.g. CET = +1
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@param altitude Altitude of the location above the sea level
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@param degree if `nil` latitude and longitue are in radian, else in decimal degree
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--]]--
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function SunTime:setPosition(name, latitude, longitude, time_zone, altitude, degree)
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altitude = altitude or 200
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if degree then
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latitude = latitude * toRad
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longitude = longitude * toRad
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end
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-- check for sane values
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-- latitudes are from -90° to +90°
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if latitude > pi_2 then
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latitude = pi_2
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elseif latitude < -pi_2 then
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latitude = -pi_2
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end
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-- longitudes are from -180° to +180°
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if longitude > pi then
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longitude = pi
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elseif longitude < -pi then
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longitude = -pi
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end
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latitude = atan((1-self.earth_flatten)^2 * tan(latitude))
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self.pos = {name = name, latitude = latitude, longitude = longitude, altitude = altitude}
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self.time_zone = time_zone
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-- self.refract = Rad(36.35/60 * .5 ^ (altitude / 5538)) -- constant temperature
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self.refract = Rad(36.20/60 * (1 - 0.0065*altitude/(273.15+self.average_temperature)) ^ 5.255 )
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self.sin_latitude = sin(self.pos.latitude)
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self.cos_latitude = cos(self.pos.latitude)
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end
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--[[--
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Use a simple equation of time (valid for the years 2008-2027)
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--]]--
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function SunTime:setSimple()
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self.getZgl = self.getZglSimple
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end
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--[[--
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Use an advanced equation of time (valid for the years 1800-2200 at least)
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--]]--
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function SunTime:setAdvanced()
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self.getZgl = self.getZglAdvanced
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end
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--[[--
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Function to get the equation of time, can be set by setSimple() or setAdvanced()
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--]]--
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SunTime.getZgl = SunTime.getZglAdvanced
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function SunTime:daysSince2000(hour)
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local delta = self.date.year - 2000
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local leap = floor((delta-1)/4)
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return 365 * delta + leap + self.date.yday + (hour-12)/24 -- WMO No.8, rebased for 2000-01-01 12:00
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end
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-- more accurate parameters of earth orbit from
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-- Title: Numerical expressions for precession formulae and mean elements for the Moon and the planets
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-- Authors: Simon, J. L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., & Laskar, J., ,
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-- Journal: Astronomy and Astrophysics (ISSN 0004-6361), vol. 282, no. 2, p. 663-683
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-- Bibliographic Code: 1994A&A...282..663S
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function SunTime:initVars(hour)
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if not hour then
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hour = 12
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end
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local after_noon = hour > 12
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local T = self:daysSince2000(hour)/36525 -- in Julian centuries form 2000-01-01 12:00
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-- self.num_ex = 0.0167086342 - 0.000042 * T
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-- numerical eccentricity of earth's orbit
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-- see wikipedia: https://de.wikipedia.org/wiki/Erdbahn-> Meeus
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-- and Numerical expressions for preccession formulae
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-- time is in Julian centuries
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self.num_ex = 0.0167086342 + T*(-0.0004203654e-1
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+ T*(-0.0000126734e-2 + T*( 0.0000001444e-3
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+ T*(-0.0000000002e-4 + T* 0.0000000003e-5))))
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-- self.epsilon = (23 + 26/60 + 21/3600 - 46.82/3600 * T) * toRad
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-- earth's obliquity to the ecliptic
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-- see Numerical expressions for precession formulae ...
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-- Time is here in Julian centuries
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-- local epsilon = 23 + 26/60 + (21.412 + T*(-468.0927E-1
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-- + T*(-0.0152E-2 + T*(1.9989E-3
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-- + T*(-0.0051E-4 - T*0.0025E-5)))))/3600 --°
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-- Astronomical Almanac 2010, p. B52
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-- Time is here in Julian centuries
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local epsilon = 23 + 26/60 + (21.406 - T*(46.836769
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- T*( 0.0001831 + T*(0.00200340
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+ T*(-5.76E-7 - T* 4.34E-8)))))/3600 --°
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self.epsilon = epsilon * toRad
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-- see Numerical expressions for precession formulae ...
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-- mean longitude
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local nT = T * (36000.7690/35999.3720) -- convert from equinox to date
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local L = 100.46645683 + (nT*(1295977422.83429E-1
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+ nT*(-2.04411E-2 - nT* 0.00523E-3)))/3600 --°
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self.L = (L - floor(L/360)*360) * toRad
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-- see Numerical expressions for precession formulae ...
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-- Time is here in Julian centuries
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local omega = 102.93734808 + nT*(11612.35290e-1
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+ nT*(53.27577e-2 + nT*(-0.14095e-3
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+ nT*( 0.11440e-4 + nT* 0.00478e-5))))/3600 --°
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-- mean anomaly
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local M = L - omega --°
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self.M = (M - floor(M/360)*360) * toRad
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self.sin_M = sin(self.M)
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self.cos_M = cos(self.M)
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-- sin(2x)=2 sin(x) cos(x)
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self.sin_2M = 2 * self.sin_M * self.cos_M
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-- sin(3x) = 3 sin(x) − 4 sin(x)^3
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self.sin_3M = 3 * self.sin_M - 4 * self.sin_M^3
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-- sin(4x) = 8 sin(x) cos(x)^3 - 4 sin(x) cos(x)
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self.sin_4M = 8 * self.sin_M * self.cos_M^3 - 4 * self.sin_M * self.cos_M
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-- sin(5x) = 5 sin(x) - 20 sin(x)^3+ 16 sin(x)^5
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self.sin_5M = 5 * self.sin_M - 20 * self.sin_M^3 + 16 * self.sin_M^5
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-- Deklination nach astronomie.info
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-- local decl = 0.4095 * sin(0.016906 * (self.date.yday - 80.086))
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--Deklination nach Brodbeck (2001)
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-- local decl = 0.40954 * sin(0.0172 * (self.date.yday - 79.349740))
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-- Deklination WMO-No.8 page I-7-37
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--local T = self.days_since_2000
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--local L = 280.460 + 0.9856474 * T
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--L = (L - floor(L/360)*360) * toRad
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--local g = 357.528 + 0.9856003 * T -- mean anomaly
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--g = (g - floor(g/360)*360) * toRad
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--local l = L + (1.915 * sin (g) + 0.020 * sin (2*g))*toRad
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--local ep = self.epsilon
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-- -- sin(decl) = sin(ep)*sin(l)
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--self.decl = asin(sin(ep)*sin(l))
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-- Deklination WMO-No.8 page I-7-37
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local l = self.L + pi + (1.915 * self.sin_M + 0.020 * self.sin_2M)*toRad
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self.decl = asin(sin(self.epsilon)*sin(l))
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-- Nutation see https://de.wikipedia.org/wiki/Nutation_(Astronomie)
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local A = { 2.18243920 - 33.7570460 * T,
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-2.77624462 + 1256.66393 * T,
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7.62068856 + 16799.4182 * T,
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4.36487839 - 67.5140919 * T}
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local B = {92025e-4 + 8.9e-4 * T,
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5736e-4 - 3.1e-4 * T,
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977e-4 - 0.5e-4 * T,
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-895e-4 + 0.5e-4 * T}
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local delta_epsilon = 0 --"
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for i = 1, #A do
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delta_epsilon = delta_epsilon + B[i]*cos(A[i])
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end
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-- add nutation to declination
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self.decl = self.decl + delta_epsilon/3600*toRad
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-- https://de.wikipedia.org/wiki/Kepler-Gleichung#Wahre_Anomalie
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self.E = self.M + self.num_ex * self.sin_M + self.num_ex^2 / 2 * self.sin_2M
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self.r = semimajor_axis * (1 - self.num_ex * cos(self.E))
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-- self.eod = -atan(sun_radius/self.r) - self.refract
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-- ^- astronomical refraction (at altitude)
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if after_noon then
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self.eod = -atan((sun_radius-average_earth_radius*self.cos_latitude)/self.r) - self.refract
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self.eod = self.eod + aberration
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else
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self.eod = -atan((sun_radius+average_earth_radius*self.cos_latitude)/self.r) - self.refract
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self.eod = self.eod - aberration
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end
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self.zgl = self:getZgl()
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end
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function SunTime:getTimeDiff(height)
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local val = (sin(height) - self.sin_latitude*sin(self.decl))
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/ (self.cos_latitude*cos(self.decl))
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if abs(val) > 1 then
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return
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end
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return 12/pi * acos(val)
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end
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-- get the sun height for a given time
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-- eod for considering sun diameter and astronomic refraction
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function SunTime:getHeight(time, eod)
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time = time - 12 -- subtrace 12, because JD starts at 12:00
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local val = cos(self.decl)*self.cos_latitude*cos(pi/12*time)
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+ sin(self.decl)*self.sin_latitude
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if abs(val) > 1 then
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return
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end
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if eod then
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return asin(val) - eod -- self.eod might be a bit too small
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else
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return asin(val)
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end
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end
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-- Get time for a certain height
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-- Set hour near to expected time
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-- Set after_noon to true, if sunset is wanted
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-- Set no_correct_dst if no daylight saving correction is wanted
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-- Result rise or set time
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-- nil sun does not reach the height
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function SunTime:calculateTime(height, hour, after_noon, no_correct_dst)
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if not no_correct_dst then
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if self.date.isdst and hour then
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hour = hour - 1
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end
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end
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self:initVars(hour) -- calculate self.eod
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local timeDiff = self:getTimeDiff(height or self.eod, hour)
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if not timeDiff then
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return
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end
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local local_correction = self.time_zone - self.pos.longitude*12/pi - self.zgl
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if not after_noon then
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hour = 12 - timeDiff + local_correction
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else
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hour = 12 + timeDiff + local_correction
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end
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if not no_correct_dst then
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if self.date.isdst and hour then
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hour = hour + 1
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end
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end
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return hour
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end
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-- Calculates the hour, when the sun reaches height
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-- If height is nil, use newly calculated self.eod
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-- hour gives a start value, default is used when hour == nil
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function SunTime:calculateTimeIter(height, hour, default_hour)
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local after_noon = (hour and hour > 12) or (default_hour and default_hour > 12)
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if not hour then -- do the iteration with the default value
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hour = self:calculateTime(height or self.eod, default_hour, after_noon, true)
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elseif hour and not default_hour then -- do the full iteration with value
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hour = self:calculateTime(height or self.eod, hour, after_noon, true)
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end -- if hour and default_hour are given don't do the first step
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if hour ~= nil then -- do the last calculation step
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hour = self:calculateTime(height or self.eod, hour, after_noon)
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end
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return hour
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end
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function SunTime:calculateNoon(hour)
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hour = hour or 12
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self:initVars(hour)
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local aberration_time = aberration / pi * 12 -- aberration in hours (angle/(2pi)*24)
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local dst = self.date.isdst and 1 or 0
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local local_correction = self.time_zone - self.pos.longitude*12/pi + dst - self.zgl
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if self.pos.latitude >= 0 then -- northern hemisphere
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if pi_2 - self.pos.latitude + self.decl > self.eod then
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if self:getHeight(hour) > 0 then
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return hour + local_correction + aberration_time
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end
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end
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else -- sourthern hemisphere
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if pi_2 + self.pos.latitude - self.decl > self.eod then
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if self:getHeight(hour) > 0 then
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return hour + local_correction + aberration_time
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end
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end
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end
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end
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function SunTime:calculateMidnight(hour)
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-- hour:
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-- 00 would be the beginning of the day
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-- 24 is the midnight at the end of the current day,
|
||
hour = hour or 24
|
||
self:initVars(hour)
|
||
local dst = self.date.isdst and 1 or 0
|
||
-- no aberration correction here, as you can't see the sun on her nadir ;-)
|
||
local local_correction = self.time_zone - self.pos.longitude*12/pi + dst - self.zgl
|
||
if self.pos.latitude >= 0 then -- northern hemisphere
|
||
if pi_2 - self.pos.latitude - self.decl > self.eod then
|
||
if self:getHeight(hour) < 0 then
|
||
return hour + local_correction
|
||
end
|
||
end
|
||
else -- sourthern hemisphere
|
||
if pi_2 + self.pos.latitude + self.decl > self.eod then
|
||
if self:getHeight(hour) < 0 then
|
||
return hour + local_correction
|
||
end
|
||
end
|
||
end
|
||
end
|
||
|
||
--[[--
|
||
Calculates the ephemeris and twilight times
|
||
|
||
@param exact_twilight If not nil, then exact twilight times will be calculated.
|
||
|
||
@usage
|
||
SunTime:calculateTimes(exact_twilight)
|
||
|
||
|
||
Times are in hours or `nil` if not applicable.
|
||
|
||
You can then access:
|
||
self.midnight_beginning
|
||
|
||
self.rise_astronomic
|
||
self.rise_nautic
|
||
self.rise_civil
|
||
self.rise
|
||
|
||
self.noon
|
||
|
||
self.set
|
||
self.set_civil
|
||
self.set_nautic
|
||
self.set_astronomic
|
||
|
||
self.midnight
|
||
|
||
Or as values in a table:
|
||
self.times[1] midnight_beginning
|
||
self.times[2] rise_astronomic
|
||
self.times[3] rise_nautic
|
||
self.times[4] rise_civil
|
||
self.times[5] rise
|
||
self.times[6] noon
|
||
self.times[7] set
|
||
self.times[8] set_civil
|
||
self.times[9] set_nautic
|
||
self.times[10] set_astronomic
|
||
self.times[11] midnight
|
||
--]]--
|
||
function SunTime:calculateTimes(fast_twilight)
|
||
-- All or some the times can be nil at great latitudes
|
||
-- but either noon or midnight is not nil
|
||
|
||
if not fast_twilight then
|
||
-- The canonical way is to calculate everything from scratch
|
||
self.rise = self:calculateTimeIter(nil, 6)
|
||
self.set = self:calculateTimeIter(nil, 18)
|
||
|
||
self.rise_civil = self:calculateTimeIter(self.civil, 6)
|
||
self.set_civil = self:calculateTimeIter(self.civil, 18)
|
||
self.rise_nautic = self:calculateTimeIter(self.nautic, 6)
|
||
self.set_nautic = self:calculateTimeIter(self.nautic, 18)
|
||
self.rise_astronomic = self:calculateTimeIter(self.astronomic, 6)
|
||
self.set_astronomic = self:calculateTimeIter(self.astronomic, 18)
|
||
else
|
||
-- Calculate rise and set from scratch, use these values for twilight times
|
||
self.rise = self:calculateTimeIter(nil, 6)
|
||
self.rise_civil = self:calculateTimeIter(self.civil, self.rise - min_civil_twilight, 6)
|
||
self.rise_nautic = self:calculateTimeIter(self.nautic, self.rise_civil - min_nautic_twilight, 6)
|
||
self.rise_astronomic = self:calculateTimeIter(self.astronomic, self.rise_nautic - min_astronomic_twilight, 6)
|
||
|
||
self.set = self:calculateTimeIter(nil, 18)
|
||
self.set_civil = self:calculateTimeIter(self.civil, self.set + min_civil_twilight, 18)
|
||
self.set_nautic = self:calculateTimeIter(self.nautic, self.set_civil + min_nautic_twilight, 18)
|
||
self.set_astronomic = self:calculateTimeIter(self.astronomic, self.set_nautic + min_astronomic_twilight, 18)
|
||
end
|
||
|
||
self.midnight_beginning = self:calculateMidnight(0)
|
||
self.noon = self:calculateNoon()
|
||
self.midnight = self:calculateMidnight()
|
||
|
||
-- Sometimes at high latitudes noon or midnight does not get calculated.
|
||
-- Maybe there is a minor bug in the calculateNoon/calculateMidnight functions.
|
||
if self.rise and self.set then
|
||
if not self.noon then
|
||
self.noon = (self.rise + self.set) / 2
|
||
end
|
||
if not self.midnight then
|
||
self.midnight = self.noon + 12
|
||
end
|
||
if not self.midnight_beginning then
|
||
self.midnight_beginning = self.midnight - 24
|
||
end
|
||
elseif self.rise and not self.set then -- only sunrise on that day
|
||
self.midnight = nil
|
||
self.midnight_beginning = nil
|
||
elseif self.set and not self.rise then -- only sunset on that day
|
||
self.noon = nil
|
||
end
|
||
|
||
self.times[1] = self.midnight_beginning
|
||
self.times[2] = self.rise_astronomic
|
||
self.times[3] = self.rise_nautic
|
||
self.times[4] = self.rise_civil
|
||
self.times[5] = self.rise
|
||
self.times[6] = self.noon
|
||
self.times[7] = self.set
|
||
self.times[8] = self.set_civil
|
||
self.times[9] = self.set_nautic
|
||
self.times[10] = self.set_astronomic
|
||
self.times[11] = self.midnight
|
||
end
|
||
|
||
-- Get time in seconds (either actual time in hours or date struct)
|
||
function SunTime:getTimeInSec(val)
|
||
if not val then
|
||
val = os.date("*t")
|
||
end
|
||
|
||
if type(val) == "table" then
|
||
return val.hour*3600 + val.min*60 + val.sec
|
||
end
|
||
|
||
return val*3600
|
||
end
|
||
|
||
return SunTime
|