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461 lines
15 KiB
Lua
461 lines
15 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 are:
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* 33.58° Casablanca: 24s
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* 37.97° Athene: 25s
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* 41.91° Rome: 28s
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* 47.25° Innsbruck: 14s
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* 52.32° Berlin: 32s
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* 64.14° Reykjavik: 113s
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* 65.69° Akureyri: <110s (except *)
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* 70.67° Hammerfest: <105s (except **)
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*) A few days around beginning of summer (error <530s)
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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 toRad = math.pi/180
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local toDeg = 1/toRad
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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 function Rad(x)
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return x*toRad
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end
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--------------------------------------------
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local SunTime = {}
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SunTime.astronomic = Rad(-18)
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SunTime.nautic = Rad(-12)
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SunTime.civil = Rad(-6)
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-- SunTime.eod = Rad(-49/60) -- approx. end of day
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SunTime.earth_flatten = 1 / 298.257223563 -- WGS84
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SunTime.average_temperature = 10 -- °C
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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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local M = self.M
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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) * sin(M)
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+ (5/4*e2 + 11/24*e4) * sin(2*M)
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+ (13/12*e3 - 43/64*e5) * sin(3*M)
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+ 103/96*e4 * sin(4*M)
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+ 1097/960*e5 * sin(5*M) -- 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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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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local feb = 28
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if year % 4 == 0 and (year % 100 ~= 0 or year % 400 == 0) then
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feb = 29
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end
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local days_in_month = {31, feb, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}
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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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if not self.getZgl then
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self.getZgl = self.getZglAdvanced
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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 > math.pi/2 then
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latitude = math.pi/2
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elseif latitude < -math.pi/2 then
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latitude = -math.pi/2
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end
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-- longitudes are from -180° to +180°
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if longitude > math.pi then
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longitude = math.pi
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elseif longitude < -math.pi then
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longitude = -math.pi
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end
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self.pos = {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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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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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 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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-- 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 + math.pi + (1.915 * sin (self.M) + 0.020 * sin (2*self.M))*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 * sin(self.M) + self.num_ex^2 / 2 * sin(2*self.M)
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self.a = 149598022.96E3 -- große Halbachse in meter
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self.r = self.a * (1 - self.num_ex * cos(self.E))
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self.eod = -atan(6.96342e8/self.r) - self.refract
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-- ^--sun radius ^- astronomical refraction (at altitude)
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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) - sin(self.pos.latitude)*sin(self.decl))
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/ (cos(self.pos.latitude)*cos(self.decl))
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if math.abs(val) > 1 then
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return
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end
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return 12/math.pi * acos(val)
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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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-- Sed after_noon to true, if sunset 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)
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local dst = self.date.isdst and 1 or 0
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local timeDiff = self:getTimeDiff(height, 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/math.pi + dst - self.zgl
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if not after_noon then
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return 12 - timeDiff + local_correction
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else
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return 12 + timeDiff + local_correction
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end
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end
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-- If height is nil, use newly calculated self.eod
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function SunTime:calculateTimeIter(height, hour)
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local after_noon = hour > 12
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self:initVars(hour) -- calculate self.eod
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hour = self:calculateTime(height or self.eod, hour, after_noon)
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if hour ~= nil then
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self:initVars(hour) -- calculate self.eod
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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()
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self:initVars(12)
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if self.pos.latitude >= 0 then -- northern hemisphere
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if math.pi/2 - self.pos.latitude + self.decl > self.eod then
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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/math.pi + dst - self.zgl
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return 12 + local_correction
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end
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else -- sourthern hemisphere
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if math.pi/2 + self.pos.latitude - self.decl > self.eod then
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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/math.pi + dst - self.zgl
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return 12 + local_correction
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end
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end
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end
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function SunTime:calculateMidnight()
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-- 24 is the midnight at the end of the current day,
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-- 00 would be the beginning of the day
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self:initVars(24)
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if self.pos.latitude >= 0 then -- northern hemisphere
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if math.pi/2 - self.pos.latitude - self.decl > self.eod then
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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/math.pi + dst - self.zgl
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return 24 + local_correction
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end
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else -- southern hemisphere
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if math.pi/2 + self.pos.latitude + self.decl > self.eod then
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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/math.pi + dst - self.zgl
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return 24 + local_correction
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end
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end
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end
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--[[--
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Calculates the ephemeris and twilight times
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@usage
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SunTime:calculateTime()
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Times are in hours or `nil` if not applicable.
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You can then access:
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self.rise_astronomic
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self.rise_nautic
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self.rise_civil
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self.rise
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self.noon
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self.set
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self.set_civil
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self.set_nautic
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self.set_astronomic
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self.midnight
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Or as values in a table:
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self.times[1] midnight - 24h
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self.times[2] rise_astronomic
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self.times[3] rise_nautic
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self.times[4] rise_civil
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self.times[5] rise
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self.times[6] noon
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self.times[7] set
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self.times[8] set_civil
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self.times[9] set_nautic
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self.times[10] set_astronomic
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self.times[11] midnight
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--]]--
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function SunTime:calculateTimes()
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-- All or some the times can be nil at great latitudes
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-- but either noon or midnight is not nil!
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self.rise = self:calculateTimeIter(nil, 6)
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self.set = self:calculateTimeIter(nil, 18)
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self.rise_civil = self:calculateTimeIter(self.civil, 6)
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self.set_civil = self:calculateTimeIter(self.civil, 18)
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self.rise_nautic = self:calculateTimeIter(self.nautic, 6)
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self.set_nautic = self:calculateTimeIter(self.nautic, 18)
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self.rise_astronomic = self:calculateTimeIter(self.astronomic, 6)
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self.set_astronomic = self:calculateTimeIter(self.astronomic, 18)
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self.noon = self:calculateNoon()
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self.midnight = self:calculateMidnight()
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self.times = {}
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self.times[1] = self.midnight and (self.midnight - 24)
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self.times[2] = self.rise_astronomic
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self.times[3] = self.rise_nautic
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self.times[4] = self.rise_civil
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self.times[5] = self.rise
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self.times[6] = self.noon
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self.times[7] = self.set
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self.times[8] = self.set_civil
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self.times[9] = self.set_nautic
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self.times[10] = self.set_astronomic
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self.times[11] = self.midnight
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end
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-- Get time in seconds (either actual time in hours or date struct)
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function SunTime:getTimeInSec(val)
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if not val then
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val = os.date("*t")
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end
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if type(val) == "table" then
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return val.hour*3600 + val.min*60 + val.sec
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end
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return val*3600
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end
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return SunTime
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