#!/usr/bin/env python3
# Copyright © 2014 Mattias Andrée (maandree@member.fsf.org)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
# This module implements algorithms for calculating information about the Sun.
from math import *
import time
SOLAR_ELEVATION_SUNSET_SUNRISE = 0.0
'''
:float The Sun's elevation at sunset and sunrise,
measured in degrees
'''
SOLAR_ELEVATION_CIVIL_DUSK_DAWN = -6.0
'''
:float The Sun's elevation at civil dusk and civil
dawn, measured in degrees
'''
SOLAR_ELEVATION_NAUTICAL_DUSK_DAWN = -12.0
'''
:float The Sun's elevation at nautical dusk and
nautical dawn, measured in degrees
'''
SOLAR_ELEVATION_ASTRONOMICAL_DUSK_DAWN = -18.0
'''
:float The Sun's elevation at astronomical dusk
and astronomical dawn, measured in degrees
'''
SOLAR_ELEVATION_RANGE_TWILIGHT = (-18.0, 0.0)
'''
:(float, float) The Sun's lowest and highest elevation during
all periods of twilight, measured in degrees
'''
SOLAR_ELEVATION_RANGE_CIVIL_TWILIGHT = (-6.0, 0.0)
'''
:(float, float) The Sun's lowest and highest elevation
during civil twilight, measured in degrees
'''
SOLAR_ELEVATION_RANGE_NAUTICAL_TWILIGHT = (-12.0, -6.0)
'''
:(float, float) The Sun's lowest and highest elevation
during nautical twilight, measured in degrees
'''
SOLAR_ELEVATION_RANGE_ASTRONOMICAL_TWILIGHT = (-18.0, -12.0)
'''
:(float, float) The Sun's lowest and highest elevation during
astronomical twilight, measured in degrees
'''
def sun(latitude, longitude, t = None, low = -6.0, high = 3.0):
'''
Get the visibility of the Sun
@param latitude:float The latitude component of your GPS coordinate
@param longitude:float The longitude component of your GPS coordinate
@param t:float? The time in Julian Centuries, `None` for current time
@param low:float The 100 % night limit elevation of the Sun (highest when not visible)
@param high:float The 100 % day limit elevation of the Sun (lowest while fully visible)
@return :float The visibilty of the Sun, 0 during the night, 1 during the day,
between 0 and 1 during twilight. Other values will not occur
'''
t = julian_centuries() if t is None else t
e = solar_elevation(latitude, longitude, t)
e = (e - low) / (high - low)
return min(max(0, e), 1)
# The following functions are used to calculate the result for `sun`
# (most of them) but could be used for anything else. There name is
# should tell you enough, `t` (and `noon`) is in Julian centuries
# except for in the convertion methods.
def julian_day_to_epoch(t):
'''
Converts a Julian Day timestamp to a POSIX time timestamp
@param t:float The time in Julian Days
@return :float The time in POSIX time
'''
return (t - 2440587.5) * 86400.0
def epoch_to_julian_day(t):
'''
Converts a POSIX time timestamp to a Julian Day timestamp
@param t:float The time in POSIX time
@return :float The time in Julian Days
'''
return t / 86400.0 + 2440587.5
def julian_day_to_julian_centuries(t):
'''
Converts a Julian Day timestamp to a Julian Centuries timestamp
@param t:float The time in Julian Days
@return :float The time in Julian Centuries
'''
return (t - 2451545.0) / 36525.0
def julian_centuries_to_julian_day(t):
'''
Converts a Julian Centuries timestamp to a Julian Day timestamp
@param t:float The time in Julian Centuries
@return :float The time in Julian Days
'''
return t * 36525.0 + 2451545.0
def epoch_to_julian_centuries(t):
'''
Converts a POSIX time timestamp to a Julian Centuries timestamp
@param t:float The time in POSIX time
@return :float The time in Julian Centuries
'''
return julian_day_to_julian_centuries(epoch_to_julian_day(t))
def julian_centuries_to_epoch(t):
'''
Converts a Julian Centuries timestamp to a POSIX time timestamp
@param t:float The time in Julian Centuries
@return :float The time in POSIX time
'''
return julian_day_to_epoch(julian_centuries_to_julian_day(t))
def epoch():
'''
Get current POSIX time
@return :float The current POSIX time
'''
return time.time()
def julian_day():
'''
Get current Julian Day time
@return :float The current Julian Day time
'''
return epoch_to_julian_day(epoch())
def julian_centuries():
'''
Get current Julian Centuries time (100 Julian days since J2000)
@return :float The current Julian Centuries time
'''
return epoch_to_julian_centuries(epoch())
def radians(deg):
'''
Convert an angle from degrees to radians
@param deg:float The angle in degrees
@return :float The angle in radians
'''
return deg * pi / 180
def degrees(rad):
'''
Convert an angle from radians to degrees
@param rad:float The angle in radians
@return :float The angle in degrees
'''
return rad * 180 / pi
def sun_geometric_mean_longitude(t):
'''
Calculates the Sun's geometric mean longitude
@param t:float The time in Julian Centuries
@return :float The Sun's geometric mean longitude in radians
'''
return radians((0.0003032 * t ** 2 + 36000.76983 * t + 280.46646) % 360)
# CANNIBALISERS:
# The result of this function should always be positive, this
# means that after division modulo 360 but before `radians`,
# you will need to add 360 if the value is negative. This can
# only happen if `t` is negative, which can only happen for date
# times before 2000-(01)Jan-01 12:00:00 UTC par division modulo
# implementations with the signess of atleast the left operand.
# More precively, it happens between cirka 1970-(01)Jan-11
# 16:09:02 UTC and cirka -374702470660351740 seconds before
# January 1, 1970 00:00 UTC, which is so far back in time
# it cannot be reliable pinned down to the right year, but it
# is without a shadow of a doubt looooong before the Earth
# was formed, is right up there with the age of the Milky Way
# and the universe itself.
def sun_geometric_mean_anomaly(t):
'''
Calculates the Sun's geometric mean anomaly
@param t:float The time in Julian Centuries
@return :float The Sun's geometric mean anomaly in radians
'''
return radians(-0.0001537 * t ** 2 + 35999.05029 * t + 357.52911)
def earth_orbit_eccentricity(t):
'''
Calculates the Earth's orbit eccentricity
@param t:float The time in Julian Centuries
@return :float The Earth's orbit eccentricity
'''
return -0.0000001267 * t ** 2 - 0.000042037 * t + 0.016708634
def sun_equation_of_centre(t):
'''
Calculates the Sun's equation of the centre, the difference between
the true anomaly and the mean anomaly
@param t:float The time in Julian Centuries
@return :float The Sun's equation of the centre, in radians
'''
a = sun_geometric_mean_anomaly(t)
rc = sin(1 * a) * (-0.000014 * t ** 2 - 0.004817 * t + 1.914602)
rc += sin(2 * a) * (-0.000101 * t + 0.019993)
rc += sin(3 * a) * 0.000289
return radians(rc)
def sun_real_longitude(t):
'''
Calculates the Sun's real longitudinal position
@param t:float The time in Julian Centuries
@return :float The longitude, in radians
'''
rc = sun_geometric_mean_longitude(t)
return rc + sun_equation_of_centre(t)
def sun_apparent_longitude(t):
'''
Calculates the Sun's apparent longitudinal position
@param t:float The time in Julian Centuries
@return :float The longitude, in radians
'''
rc = degrees(sun_real_longitude(t)) - 0.00569
rc -= 0.00478 * sin(radians(-1934.136 * t + 125.04))
return radians(rc)
def mean_ecliptic_obliquity(t):
'''
Calculates the mean ecliptic obliquity of the Sun's
apparent motion without variation correction
@param t:float The time in Julian Centuries
@return :float The uncorrected mean obliquity, in radians
'''
rc = 0.001813 * t ** 3 - 0.00059 * t ** 2 - 46.815 * t + 21.448
rc = 26 + rc / 60
rc = 23 + rc / 60
return radians(rc)
def corrected_mean_ecliptic_obliquity(t):
'''
Calculates the mean ecliptic obliquity of the Sun's
apparent motion with variation correction
@param t:float The time in Julian Centuries
@return :float The mean obliquity, in radians
'''
rc = -1934.136 * t + 125.04
rc = 0.00256 * cos(radians(rc))
rc += degrees(mean_ecliptic_obliquity(t))
return radians(rc)
def solar_declination(t):
'''
Calculates the Sun's declination
@param t:float The time in Julian Centuries
@return :float The Sun's declination, in radians
'''
rc = sin(corrected_mean_ecliptic_obliquity(t))
rc *= sin(sun_apparent_longitude(t))
return asin(rc)
def equation_of_time(t):
'''
Calculates the equation of time, the discrepancy
between apparent and mean solar time
@param t:float The time in Julian Centuries
@return :float The equation of time, in degrees
'''
l = sun_geometric_mean_longitude(t)
e = earth_orbit_eccentricity(t)
m = sun_geometric_mean_anomaly(t)
y = corrected_mean_ecliptic_obliquity(t)
y = tan(y / 2) ** 2
rc = y * sin(2 * l)
rc += (4 * y * cos(2 * l) - 2) * e * sin(m)
rc -= 0.5 * y ** 2 * sin(4 * l)
rc -= 1.25 * e ** 2 * sin(2 * m)
return 4 * degrees(rc)
def hour_angle_from_elevation(latitude, declination, elevation):
'''
Calculates the solar hour angle from the Sun's elevation
@param longitude:float The longitude in degrees eastwards
from Greenwich, negative for westwards
@param declination:float The declination, in degrees
@param hour_angle:float The Sun's elevation, in degrees
@return :float The solar hour angle, in degrees
'''
if elevation == 0:
return 0
rc = cos(abs(elevation))
rc -= sin(radians(latitude)) * sin(declination)
rc /= cos(radians(latitude)) * cos(declination)
rc = acos(rc)
return -rc if (rc < 0) == (elevation < 0) else rc;
def elevation_from_hour_angle(latitude, declination, hour_angle):
'''
Calculates the Sun's elevation from the solar hour angle
@param longitude:float The longitude in degrees eastwards
from Greenwich, negative for westwards
@param declination:float The declination, in degrees
@param hour_angle:float The solar hour angle, in degrees
@return :float The Sun's elevation, in degrees
'''
rc = cos(radians(latitude))
rc *= cos(hour_angle) * cos(declination)
rc += sin(radians(latitude)) * sin(declination)
return asin(rc)
def time_of_solar_noon(t, longitude):
'''
Calculates the time of the closest solar noon
@param t:float A time close to the seeked time,
in Julian Centuries
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@return :float The time, in Julian Centuries,
of the closest solar noon
'''
t, rc = julian_centuries_to_julian_day(t), longitude
for (k, m) in ((-360, 0), (1440, -0.5)):
rc = julian_day_to_julian_centuries(t + m + rc / k)
rc = 720 - 4 * longitude - equation_of_time(rc)
return rc
def time_of_solar_elevation(t, noon, latitude, longitude, elevation):
'''
Calculates the time the Sun has a specified apparent
elevation at a geographical position
@param t:float A time close to the seeked time,
in Julian Centuries
@param noon:float The time of the closest solar noon
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@param elevation:float The solar elevation, in degrees
@return :float The time, in Julian Centuries,
of the specified elevation
'''
rc = noon
rc, et = solar_declination(rc), equation_of_time(rc)
rc = hour_angle_from_elevation(latitude, rc, elevation)
rc = 720 - 4 * (longitude + degrees(rc)) - et
rc = julian_day_to_julian_centuries(julian_centuries_to_julian_day(t) + rc / 1440)
rc, et = solar_declination(rc), equation_of_time(rc)
rc = hour_angle_from_elevation(latitude, rc, elevation)
rc = 720 - 4 * (longitude + degrees(rc)) - et
return rc
def solar_elevation_from_time(t, latitude, longitude):
'''
Calculates the Sun's elevation as apparent
from a geographical position
@param t:float The time in Julian Centuries
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@return :float The Sun's apparent at the specified time
as seen from the specified position,
measured in degrees
'''
rc = julian_centuries_to_julian_day(t)
rc = (rc - float(int(rc + 0.5)) - 0.5) * 1440
rc = 720 - rc - equation_of_time(t)
rc = radians(rc / 4 - longitude)
return elevation_from_hour_angle(latitude, solar_declination(t), rc)
def solar_elevation(latitude, longitude, t = None):
'''
Calculates the Sun's elevation as apparent
from a geographical position
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float The Sun's apparent at the specified time
as seen from the specified position,
measured in degrees
'''
rc = julian_centuries() if t is None else t
rc = solar_elevation_from_time(rc, latitude, longitude)
return degrees(rc)
# TODO document
def have_sunrise_and_sunset(latitude, t = None):
'''
Determine whether solar declination currently is
so that there can be sunrises and sunsets. If not,
you either have 24-hour daytime or 24-hour nighttime.
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param t:float? The time in Julian Centuries, `None`
for the current time
@return Whether there can be sunrises and
sunsets where you are located
'''
t = julian_centuries() if t is None else t
d = degrees(solar_declination(t))
## Covert everything to the Northern hemisphere
latitude = abs(latitude)
if d >= 0:
## Northern summer
return -90 + d < latitude < 90 - d
else:
## Northern winter
return -90 - d < latitude < 90 + d
# TODO document
def is_summer(latitude, t = None):
'''
Determine whether it is summer
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param t:float? The time in Julian Centuries, `None`
for the current time
@return Whether it is summer on the hemisphere
you are located on
'''
t = julian_centuries() if t is None else t
d = solar_declination(t)
return (d > 0) == (latitude > 0)
# TODO document
def is_winter(latitude, t = None):
'''
Determine whether it is winter
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param t:float? The time in Julian Centuries, `None`
for the current time
@return Whether it is winter on the hemisphere
you are located on
'''
t = julian_centuries() if t is None else t
d = solar_declination(t)
return not ((d > 0) == (latitude > 0))
# TODO document
def solar_prediction(delta, requested, fun, epsilon = 0.000001, span = 0.01, t = None):
'''
Predict the time point of the next or previous
time an arbitrary condition is meet
@param delta:float Iteration step size, negative for past
event, positive for future event
@param requested:float The value returned by `fun` for which to
calculate the time point of occurrence
@param fun:(t:float)→float Function that calculate the data of interest
@param epsilon:float Error tolerance for `requested`
@param span:float The number of Julian centuries (0,01 for
one year) to restrict the search to
@param t:float? The time in Julian Centuries, `None` for
the current time
@return :float? The calculated time point, `None` if none
were found within the specified time span
'''
t = julian_centuries() if t is None else t
t1 = t2 = t
v1 = v0 = fun(t)
while True:
if abs(t2 - t) > span:
return None
t2 += delta
v2 = fun(t2)
if (v1 <= requested <= v2) or ((requested >= v1 >= v2) and (requested <= v0)):
break
if (v1 >= requested >= v2) or ((requested <= v1 <= v2) and (requested >= v0)):
break
t1 = t2
v2 = v1
for _itr in range(1000):
tm = (t1 + t2) / 2
v1 = fun(t1)
v2 = fun(t2)
vm = fun(tm)
if abs(v1 - v2) < epsilon:
return tm if abs(vm) < epsilon else None
if v1 < v2:
if requested < vm:
t2 = tm
else:
t1 = tm
elif v1 > v2:
if requested > vm:
t2 = tm
else:
t1 = tm
return None
# TODO document
def future_past_equinox(delta, t = None):
'''
Predict the time point of the next or previous equinox
@param delta:float Iteration step size, negative for
past event, positive for future event
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float The calculated time point
'''
return solar_prediction(delta, 0, solar_declination, t = t)
# TODO document
def future_equinox(t = None):
'''
Predict the time point of the next equinox
@param delta:float Iteration step size, negative for
past event, positive for future event
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float The calculated time point
'''
return future_past_equinox(0.01 / 2000, t)
# TODO document
def past_equinox(t = None):
'''
Predict the time point of the previous equinox
@param delta:float Iteration step size, negative for
past event, positive for future event
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float The calculated time point
'''
return future_past_equinox(0.01 / -2000, t)
# TODO document
def future_past_solstice(delta, t = None):
'''
Predict the time point of the next or previous solstice
@param delta:float Iteration step size, negative for
past event, positive for future event
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float The calculated time point
'''
e = 0.00001
fun = solar_declination
dfun = lambda t : (fun(t + e) - fun(t - e)) / 2
return solar_prediction(delta, 0, dfun, t = t)
# TODO document
def future_solstice(t = None):
'''
Predict the time point of the next solstice
@param t:float? The time in Julian Centuries,
`None` for the current time
@return :float The calculated time point
'''
return future_past_solstice(0.01 / 2000, t)
# TODO document
def past_solstice(t = None):
'''
Predict the time point of the previous solstice
@param t:float? The time in Julian Centuries,
`None` for the current time
@return :float The calculated time point
'''
return future_past_solstice(0.01 / -2000, t)
def future_past_elevation(delta, latitude, longitude, elevation, t = None):
'''
Predict the time point of the next or previous time
the Sun reaches or reached a specific elevation
@param delta:float Iteration step size, negative for past
event, positive for future event
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@param elevation:float The elevation of interest
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float? The calculated time point, `None` if
none were found within a year
'''
fun = lambda t : solar_elevation(latitude, longitude, t)
return solar_prediction(delta, elevation, fun, t = t)
def future_elevation(latitude, longitude, elevation, t = None):
'''
Predict the time point of the next time the Sun
reaches a specific elevation
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@param elevation:float The elevation of interest
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float? The calculated time point, `None` if
none were found within a year
'''
return future_past_elevation(0.01 / 2000, latitude, longitude, elevation, t)
def past_elevation(latitude, longitude, elevation, t = None):
'''
Predict the time point of the previous time the Sun
reached a specific elevation
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@param elevation:float The elevation of interest
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float? The calculated time point, `None` if
none were found within a year
'''
return future_past_elevation(0.01 / -2000, latitude, longitude, elevation, t)
# TODO document
def future_past_elevation_derivative(delta, latitude, longitude, derivative, t = None):
'''
Predict the time point of the next or previous time the
Sun reaches or reached a specific elevation derivative
@param delta:float Iteration step size, negative for past
event, positive for future event
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@param derivative:float The elevation derivative value of interest
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float? The calculated time point, `None` if
none were found within a year
'''
fun = lambda t : solar_elevation(latitude, longitude, t)
dfun = lambda t : (fun(t + e) - fun(t - e)) / 2
return solar_prediction(delta, derivative, dfun, t = t)
# TODO document
def future_elevation_derivative(latitude, longitude, derivative, t = None):
'''
Predict the time point of the next time the
Sun reaches a specific elevation derivative
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@param derivative:float The elevation derivative value of interest
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float? The calculated time point, `None` if
none were found within a year
'''
return future_past_elevation_derivative(0.01 / 2000, latitude, longitude, derivative, t)
# TODO document
def past_elevation_derivative(latitude, longitude, derivative, t = None):
'''
Predict the time point of the previous time
the Sun reached a specific elevation derivative
@param latitude:float The latitude in degrees northwards from
the equator, negative for southwards
@param longitude:float The longitude in degrees eastwards from
Greenwich, negative for westwards
@param derivative:float The elevation derivative value of interest
@param t:float? The time in Julian Centuries, `None`
for the current time
@return :float? The calculated time point, `None`
if none were found within a year
'''
return future_past_elevation_derivative(0.01 / -2000, latitude, longitude, derivative, t)
# TODO: This algorithm is imprecise, gives an incorrent sunrise and I do not fully know its behaviour
def sunrise_equation(latitude, longitude, t = None):
# Calculate Julian Cycle
j_cent = julian_centuries() if t is None else t
j_date = julian_centuries_to_julian_day(j_cent)
j_cycle = int(j_date - 2451545.0009 - longitude / 360 + 0.5)
# Calculate approximate solar noon and solar man anomaly
approx_solar_noon = 451545.0009 + longitude / 360 + j_cycle
solar_mean_anomaly = int(357.5291 + 0.98560028 * (j_cycle - 2451545)) % 360
# Calculate solar equation of centre
equation_of_centre = 1.9148 * sin(1 * solar_mean_anomaly)
equation_of_centre += 0.0200 * sin(2 * solar_mean_anomaly)
equation_of_centre += 0.0003 * sin(3 * solar_mean_anomaly)
# Calculate solar ecliptic longitude
ecliptic_longitude = (solar_mean_anomaly + 102.9372 + equation_of_centre + 180) % 360
# Calculate solar transit
solar_transit = approx_solar_noon + 0.0053 * sin(solar_mean_anomaly)
solar_transit -= 0.0069 * sin(2 * ecliptic_longitude)
# Calculate solar declination
declination = asin(sin(ecliptic_longitude) * sin(radians(23.45)))
# Calculate solar hour angle
hour_angle = sin(radians(-0.83))
hour_angle -= sin(latitude) * sin(declination)
hour_angle /= cos(latitude) * cos(declination)
hour_angle = degrees(acos(hour_angle))
# Calculate time of sunset and sunrise
sunset = 2451545.0009 + (hour_angle + longitude) / 360
sunset += j_cycle + solar_transit - approx_solar_noon
sunrise = 2 * solar_transit - sunset
# Convert to Julian Centuries
return (julian_day_to_julian_centuries(sunset),
julian_day_to_julian_centuries(sunrise))
# TODO document
def ptime(t):
'''
Print a time stamp in human-readable local time
This function is intended for testing
@param t The time stamp in Julian Centuries
'''
import datetime
print(str(datetime.datetime.fromtimestamp(int(julian_centuries_to_epoch(t)))))
