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diff --git a/src/solar_python.py b/src/solar_python.py new file mode 100644 index 0000000..bce8beb --- /dev/null +++ b/src/solar_python.py @@ -0,0 +1,796 @@ +# solar-python — Solar data calculation and prediction library for Python +# 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/>. + +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 +''' + + + +# 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) + + + +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)) + ## Convert 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 + + +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) + + +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)) + + + +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 + + + +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) + + +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) + + +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) + + + +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) + + +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) + + +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) + + + +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) + + +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) + + +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)) + |