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koreader/plugins/autowarmth.koplugin/suntime.lua

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Lua

--[[--
-- Author: Martin Zwicknagl (zwim)
-- Date: 2021-10-29
-- The current source code of this file can be found on https://github.com/zwim/suntime.
Module to calculate ephemeris and other times depending on the sun position.
Maximal errors from 2020-2050 (compared to https://midcdmz.nrel.gov/spa/) are:
* -43.52° Christchurch 66s
* -20.16° Mauritius: 25s
* 20.30° Honolulu: 47s
* 33.58° Casablanca: 24s
* 35.68° Tokio: 50s
* 37.97° Athene: 24s
* 38° Sacramento: 67s
* 41.91° Rome: 27s
* 47.25° Innsbruck: 13s
* 52.32° Berlin: 30s
* 59.92° Oslo: 42s
* 64.14° Reykjavik: 69s
* 65.69° Akureyri: <24s (except *)
* 70.67° Hammerfest: <105s (except **)
*) A few days around beginning of summer (error <290s)
**) A few days after and befor midnight sun (error <1200s)
@usage
local SunTime = require("suntime")
time_zone = 0
altitude = 50
degree = true
SunTime:setPosition("Reykjavik", 64.14381, -21.92626, timezone, altitude, degree)
SunTime:setAdvanced()
SunTime:setDate()
SunTime:calculateTimes()
print(SunTime.rise, SunTime.set, SunTime.set_civil) -- or similar see calculateTime()
@module suntime
--]]--
-- math abbrevations
local pi = math.pi
local pi_2 = pi/2
local abs = math.abs
local floor = math.floor
local sin = math.sin
local cos = math.cos
local tan = math.tan
local asin = math.asin
local acos = math.acos
local atan = math.atan
local toRad = pi/180
local toDeg = 1/toRad
local function Rad(x)
return x*toRad
end
--------------------------------------------
local speed_of_light = 2.99792E8
local sun_radius = 6.96342e8
local average_earth_radius = 6371e3
local semimajor_axis = 149598022.96E3 -- earth orbit's major semi-axis in meter
local average_speed_earth = 29.7859e3
local aberration = asin(average_speed_earth/speed_of_light) -- Aberration relativistic
-- local average_speed_equator = (2*pi * average_earth_radius) / (24*3600)
--------------------------------------------
-- minimal twillight times in hours
local min_civil_twilight = 20/60
local min_nautic_twilight = 45/60 - min_civil_twilight
local min_astronomic_twilight = 20/60 - min_nautic_twilight
local SunTime = {
astronomic = Rad(-18),
nautic = Rad(-12),
civil = Rad(-6),
-- eod = Rad(-49/60), -- approx. end of day
earth_flatten = 1 / 298.257223563, -- WGS84
average_temperature = 10, -- °C
times = {},
}
----------------------------------------------------------------
-- simple 'Equation of time' good for dates between 2008-2027
-- errors for latitude 20° are within 1min
-- 47° are within 1min 30sec
-- 65° are within 5min
-- https://www.astronomie.info/zeitgleichung/#Auf-_und_Untergang (German)
function SunTime:getZglSimple()
local T = self.date.yday
return -0.171 * sin(0.0337 * T + 0.465) - 0.1299 * sin(0.01787 * T - 0.168)
end
-- more advanced 'Equation of time' good for dates between 1800-2200
-- errors are better than with the simple method
-- https://de.wikipedia.org/wiki/Zeitgleichung (German) and
-- more infos on http://www.hlmths.de/Scilab/Zeitgleichung.pdf (German)
function SunTime:getZglAdvanced()
local e = self.num_ex
local e2 = e*e
local e3 = e2*e
local e4 = e3*e
local e5 = e4*e
-- https://de.wikibooks.org/wiki/Astronomische_Berechnungen_f%C3%BCr_Amateure/_Himmelsmechanik/_Sonne
local C = (2*e - e3/4 + 5/96*e5) * self.sin_M
+ (5/4*e2 + 11/24*e4) * self.sin_2M
+ (13/12*e3 - 43/64*e5) * self.sin_3M
+ 103/96*e4 * self.sin_4M
+ 1097/960*e5 * self.sin_5M -- rad
local lamb = self.L + C
local tanL = tan(self.L)
local tanLamb = tan(lamb)
local cosEps = cos(self.epsilon)
local zgl = atan( (tanL - tanLamb*cosEps) / (1 + tanL*tanLamb*cosEps) ) --rad
return zgl*toDeg/15 -- to hours *4'/60
end
-- set current date or year/month/day daylightsaving hh/mm/ss
-- if dst == nil use curent daylight saving of the system
local days_in_month = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}
function SunTime:setDate(year, month, day, dst, hour, min, sec)
self.date = os.date("*t") -- get current day
if year and month and day then
self.date.year = year
self.date.month = month
self.date.day = day
if year % 4 == 0 and (year % 100 ~= 0 or year % 400 == 0) then
days_in_month[2] = 29
else
days_in_month[2] = 28
end
self.date.yday = day
for i = 1, month-1 do
self.date.yday = self.date.yday + days_in_month[i]
end
self.date.hour = hour or 12
self.date.min = min or 0
self.date.sec = sec or 0
if dst ~= nil then
self.date.isdst = dst
end
end
end
--[[--
Set position for later calculations
@param name Name of the location
@param latitude Geographical latitude, North is positive
@param longitude Geographical longitude, West is negative
@param time_zone Timezone e.g. CET = +1; if nil try to autodetect the current zone
@param altitude Altitude of the location above the sea level
@param degree if `nil` latitude and longitue are in radian, else in decimal degree
--]]--
function SunTime:setPosition(name, latitude, longitude, time_zone, altitude, degree)
altitude = altitude or 200
if degree then
latitude = latitude * toRad
longitude = longitude * toRad
end
-- check for sane values
-- latitudes are from -90° to +90°
if latitude > pi_2 then
latitude = pi_2
elseif latitude < -pi_2 then
latitude = -pi_2
end
-- longitudes are from -180° to +180°
if longitude > pi then
longitude = pi
elseif longitude < -pi then
longitude = -pi
end
latitude = atan((1-self.earth_flatten)^2 * tan(latitude))
self.pos = {name = name, latitude = latitude, longitude = longitude, altitude = altitude}
self.time_zone = time_zone or self:getTimezoneOffset()
-- self.refract = Rad(36.35/60 * .5 ^ (altitude / 5538)) -- constant temperature
self.refract = Rad(36.20/60 * (1 - 0.0065*altitude/(273.15+self.average_temperature)) ^ 5.255 )
self.sin_latitude = sin(self.pos.latitude)
self.cos_latitude = cos(self.pos.latitude)
end
--[[--
Use a simple equation of time (valid for the years 2008-2027)
--]]--
function SunTime:setSimple()
self.getZgl = self.getZglSimple
end
--[[--
Use an advanced equation of time (valid for the years 1800-2200 at least)
--]]--
function SunTime:setAdvanced()
self.getZgl = self.getZglAdvanced
end
--[[--
Function to get the equation of time, can be set by setSimple() or setAdvanced()
--]]--
SunTime.getZgl = SunTime.getZglAdvanced
function SunTime:daysSince2000(hour)
local delta = self.date.year - 2000
local leap = floor((delta-1)/4)
return 365 * delta + leap + self.date.yday + (hour-12)/24 -- WMO No.8, rebased for 2000-01-01 12:00
end
-- more accurate parameters of earth orbit from
-- Title: Numerical expressions for precession formulae and mean elements for the Moon and the planets
-- Authors: Simon, J. L., Bretagnon, P., Chapront, J., Chapront-Touze, M., Francou, G., & Laskar, J., ,
-- Journal: Astronomy and Astrophysics (ISSN 0004-6361), vol. 282, no. 2, p. 663-683
-- Bibliographic Code: 1994A&A...282..663S
function SunTime:initVars(hour)
if not hour then
hour = 12
end
local after_noon = hour > 12
local T = self:daysSince2000(hour)/36525 -- in Julian centuries form 2000-01-01 12:00
-- self.num_ex = 0.0167086342 - 0.000042 * T
-- numerical eccentricity of earth's orbit
-- see wikipedia: https://de.wikipedia.org/wiki/Erdbahn-> Meeus
-- and Numerical expressions for preccession formulae
-- time is in Julian centuries
self.num_ex = 0.0167086342 + T*(-0.0004203654e-1
+ T*(-0.0000126734e-2 + T*( 0.0000001444e-3
+ T*(-0.0000000002e-4 + T* 0.0000000003e-5))))
-- self.epsilon = (23 + 26/60 + 21/3600 - 46.82/3600 * T) * toRad
-- earth's obliquity to the ecliptic
-- see Numerical expressions for precession formulae ...
-- Time is here in Julian centuries
-- local epsilon = 23 + 26/60 + (21.412 + T*(-468.0927E-1
-- + T*(-0.0152E-2 + T*(1.9989E-3
-- + T*(-0.0051E-4 - T*0.0025E-5)))))/3600 --°
-- Astronomical Almanac 2010, p. B52
-- Time is here in Julian centuries
local epsilon = 23 + 26/60 + (21.406 - T*(46.836769
- T*( 0.0001831 + T*(0.00200340
+ T*(-5.76E-7 - T* 4.34E-8)))))/3600 --°
self.epsilon = epsilon * toRad
-- see Numerical expressions for precession formulae ...
-- mean longitude
local nT = T * (36000.7690/35999.3720) -- convert from equinox to date
local L = 100.46645683 + (nT*(1295977422.83429E-1
+ nT*(-2.04411E-2 - nT* 0.00523E-3)))/3600 --°
self.L = (L - floor(L/360)*360) * toRad
-- see Numerical expressions for precession formulae ...
-- Time is here in Julian centuries
local omega = 102.93734808 + nT*(11612.35290e-1
+ nT*(53.27577e-2 + nT*(-0.14095e-3
+ nT*( 0.11440e-4 + nT* 0.00478e-5))))/3600 --°
-- mean anomaly
local M = L - omega --°
self.M = (M - floor(M/360)*360) * toRad
self.sin_M = sin(self.M)
self.cos_M = cos(self.M)
-- sin(2x)=2 sin(x) cos(x)
self.sin_2M = 2 * self.sin_M * self.cos_M
-- sin(3x) = 3 sin(x) 4 sin(x)^3
self.sin_3M = 3 * self.sin_M - 4 * self.sin_M^3
-- sin(4x) = 8 sin(x) cos(x)^3 - 4 sin(x) cos(x)
self.sin_4M = 8 * self.sin_M * self.cos_M^3 - 4 * self.sin_M * self.cos_M
-- sin(5x) = 5 sin(x) - 20 sin(x)^3+ 16 sin(x)^5
self.sin_5M = 5 * self.sin_M - 20 * self.sin_M^3 + 16 * self.sin_M^5
-- Deklination nach astronomie.info
-- local decl = 0.4095 * sin(0.016906 * (self.date.yday - 80.086))
--Deklination nach Brodbeck (2001)
-- local decl = 0.40954 * sin(0.0172 * (self.date.yday - 79.349740))
-- Deklination WMO-No.8 page I-7-37
--local T = self.days_since_2000
--local L = 280.460 + 0.9856474 * T
--L = (L - floor(L/360)*360) * toRad
--local g = 357.528 + 0.9856003 * T -- mean anomaly
--g = (g - floor(g/360)*360) * toRad
--local l = L + (1.915 * sin (g) + 0.020 * sin (2*g))*toRad
--local ep = self.epsilon
-- -- sin(decl) = sin(ep)*sin(l)
--self.decl = asin(sin(ep)*sin(l))
-- Deklination WMO-No.8 page I-7-37
local l = self.L + pi + (1.915 * self.sin_M + 0.020 * self.sin_2M)*toRad
self.decl = asin(sin(self.epsilon)*sin(l))
-- Nutation see https://de.wikipedia.org/wiki/Nutation_(Astronomie)
local A = { 2.18243920 - 33.7570460 * T,
-2.77624462 + 1256.66393 * T,
7.62068856 + 16799.4182 * T,
4.36487839 - 67.5140919 * T}
local B = {92025e-4 + 8.9e-4 * T,
5736e-4 - 3.1e-4 * T,
977e-4 - 0.5e-4 * T,
-895e-4 + 0.5e-4 * T}
local delta_epsilon = 0 --"
for i = 1, #A do
delta_epsilon = delta_epsilon + B[i]*cos(A[i])
end
-- add nutation to declination
self.decl = self.decl + delta_epsilon/3600*toRad
-- https://de.wikipedia.org/wiki/Kepler-Gleichung#Wahre_Anomalie
self.E = self.M + self.num_ex * self.sin_M + self.num_ex^2 / 2 * self.sin_2M
self.r = semimajor_axis * (1 - self.num_ex * cos(self.E))
-- self.eod = -atan(sun_radius/self.r) - self.refract
-- ^- astronomical refraction (at altitude)
if after_noon then
self.eod = -atan((sun_radius-average_earth_radius*self.cos_latitude)/self.r) - self.refract
self.eod = self.eod + aberration
else
self.eod = -atan((sun_radius+average_earth_radius*self.cos_latitude)/self.r) - self.refract
self.eod = self.eod - aberration
end
self.zgl = self:getZgl()
end
function SunTime:getTimeDiff(height)
local val = (sin(height) - self.sin_latitude*sin(self.decl))
/ (self.cos_latitude*cos(self.decl))
if abs(val) > 1 then
return
end
return 12/pi * acos(val)
end
-- get the sun height for a given time
-- eod for considering sun diameter and astronomic refraction
function SunTime:getHeight(time, eod)
time = time - 12 -- subtrace 12, because JD starts at 12:00
local val = cos(self.decl)*self.cos_latitude*cos(pi/12*time)
+ sin(self.decl)*self.sin_latitude
if abs(val) > 1 then
return
end
if eod then
return asin(val) - eod -- self.eod might be a bit too small
else
return asin(val)
end
end
-- Get time for a certain height
-- Set height to nil for sunset/rise
-- Set hour near to expected time
-- Set after_noon to true, if sunset is wanted
-- Set no_correct_dst if no daylight saving correction is wanted
-- Result rise or set time
-- nil sun does not reach the height
function SunTime:calculateTime(height, hour, after_noon, no_correct_dst)
if not no_correct_dst then
if self.date.isdst and hour then
hour = hour - 1
end
end
self:initVars(hour) -- calculate self.eod
local timeDiff = self:getTimeDiff(height or self.eod, hour)
if not timeDiff then
return
end
local local_correction = self.time_zone - self.pos.longitude*12/pi - self.zgl
if not after_noon then
hour = 12 - timeDiff + local_correction
else
hour = 12 + timeDiff + local_correction
end
if not no_correct_dst then
if self.date.isdst and hour then
hour = hour + 1
end
end
return hour
end
-- Calculates the hour, when the sun reaches height
-- If height is nil, use newly calculated self.eod
-- hour gives a start value, default is used when hour == nil
function SunTime:calculateTimeIter(height, hour, default_hour)
local after_noon = (hour and hour > 12) or (default_hour and default_hour > 12)
if not hour then -- do the iteration with the default value
hour = self:calculateTime(height, default_hour, after_noon, true)
elseif hour and not default_hour then -- do the full iteration with value
hour = self:calculateTime(height, hour, after_noon, true)
end -- if hour and default_hour are given don't do the first step
if hour ~= nil then -- do the last calculation step
hour = self:calculateTime(height, hour, hour > 12)
end
return hour
end
function SunTime:calculateNoon(hour)
hour = hour or 12
self:initVars(hour)
local aberration_time = aberration / pi * 12 -- aberration in hours (angle/(2pi)*24)
local dst = self.date.isdst and 1 or 0
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 + aberration_time
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 + aberration_time
end
end
end
end
function SunTime:calculateMidnight(hour)
-- hour:
-- 00 would be the beginning of the day
-- 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 fast_twilight If not nil, then exact twilight times will be calculated.
@usage
SunTime:calculateTimes(fast_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 and self.rise and self.set then
self.noon = (self.rise + self.set) / 2
end
if not self.midnight and self.noon then
self.midnight = self.noon + 12
end
if not self.midnight_beginning and self.midnight then
self.midnight_beginning = self.midnight - 24
elseif not self.midnight and self.midnight_beginning then
self.midnight = self.midnight_beginning + 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, rounded to ms (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
val = val.hour*3600 + val.min*60 + val.sec
else
val = val*3600
end
return math.floor(val * 1000) * (1/1000)
end
-- Get the timezone offset in hours (including dst).
function SunTime:getTimezoneOffset()
local now_ts = os.time()
local utcdate = os.date("!*t", now_ts)
local localdate = os.date("*t", now_ts)
return os.difftime(os.time(localdate), os.time(utcdate)) * (1/3600)
end
return SunTime