Compute the northern latitude where total daylight time is the same in May (31 days) and June (30 days).

main.py

#!/usr/bin/env python3


"""
Reference: https://twitter.com/djg98115/status/1333275207369277442

http://mathforum.org/library/drmath/view/56478.html

   D = daylength
   L = latitude
   J = day of the year

   P = asin[.39795*cos(.2163108 + 2*atan{.9671396*tan[.00860(J-186)]})]

                          _                                         _
                         / sin(0.8333*pi/180) + sin(L*pi/180)*sin(P) \
   D = 24 - (24/pi)*acos{  -----------------------------------------  }
                         \_          cos(L*pi/180)*cos(P)           _/
"""

import pint  # Not used just kept to show my good intention.
from math import asin, cos, atan, tan, sin, pi, acos
from datetime import date
from scipy import optimize


def daylength(latitude, day_of_year):
    P = p_helper(day_of_year)
    numerator = sin(0.8333 * pi / 180) + sin(latitude * pi / 180) * sin(P)
    denominator = cos(latitude * pi / 180) * cos(P)
    D = 24 - (24 / pi) * acos(numerator / denominator)
    return D


def p_helper(day_of_year):
    return asin(
        0.39795
        * cos(0.2163108 + 2 * atan(0.9671396 * tan(0.00860 * (day_of_year - 186))))
    )


def daylength_range(start, stop, latitude):
    return sum(daylength(latitude=latitude, day_of_year=d) for d in range(start, stop))


def daylength_may(latitude):
    jan1 = date(2021, 1, 1)
    start = (date(2021, 5, 1) - jan1).days
    end = (date(2021, 5, 31) - jan1).days
    return daylength_range(start, end, latitude=latitude)


def daylength_june(latitude):
    jan1 = date(2021, 1, 1)
    start = (date(2021, 6, 1) - jan1).days
    end = (date(2021, 6, 30) - jan1).days
    return daylength_range(start, end, latitude=latitude)


if __name__ == "__main__":

    def f(lat):
        if lat < 0.1 or lat > 90.0:
            return 100000
        diff = daylength_may(latitude=lat) - daylength_june(latitude=lat)
        return diff ** 2

    result = optimize.minimize_scalar(f)

    if result.success:
        latitude = result.x
        may = daylength_may(latitude=latitude)
        june = daylength_june(latitude=latitude)
        print(f"At latitude {latitude}")
        print(f"May has a total of \t{may} hours of daylight. Avg: {may/31}")
        print(f"June has a total of \t{june} hours of daylight. Avg: {june / 30}")

    else:
        print(f"Failed to find result. {result}")

Pipfile

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[requires]
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Pipfile.lock

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