Distance to the horizon in Python

horizon.py

#!/usr/bin/env python3
# coding: utf8

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# Copyright © 2022, Matjaž Guštin <dev@matjaz.it> <https://matjaz.it>.
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"""Compute how far the horizon is from where you stand."""

import math
import unittest

EARTH_RADIUS_EQUATOR_M = 6_378_137.0
"""Distance from Earth's centre to the surface at the equator in metres.
Often written as ``a``"""

EARTH_RADIUS_POLES_M = 6_356_752.3
"""Distance from Earth's centre to the surface at the poles in metres.
Often written as ``a``"""


def earth_radius(latitude_deg: float = None) -> float:
    """Distance from Earth centre to the surface in metres based on
    your latitude (offset from equator).

    Source: https://en.wikipedia.org/wiki/Earth_radius, 2022-02-26

    Args:
        latitude_deg: degrees of offset from the Equator.
            ``0`` for the Equator, ``+/-90`` for the poles (north or south)
            but the sign is discarded. ``None`` or ``NaN`` for the average
            radius.
    """
    if latitude_deg is None or math.isnan(latitude_deg):
        # Arithmetic mean of the polar and equatorial radii
        return (2 * EARTH_RADIUS_EQUATOR_M + EARTH_RADIUS_POLES_M) / 3
    if latitude_deg < -90 or latitude_deg > 90:
        raise ValueError('Latitude must be in [-90, +90] degrees, '
                         f'{latitude_deg} found instead')
    latitude_rad = math.radians(latitude_deg)
    sin = math.sin(latitude_rad)
    cos = math.cos(latitude_rad)
    num = ((EARTH_RADIUS_EQUATOR_M ** 2 * cos) ** 2
           + (EARTH_RADIUS_POLES_M ** 2 * sin) ** 2)
    den = ((EARTH_RADIUS_EQUATOR_M * cos) ** 2
           + (EARTH_RADIUS_POLES_M * sin) ** 2)
    return math.sqrt(num / den)


def horizon_distance(height_above_surface_m: float,
                     latitude_deg: float = None,
                     correct_for_atmosphere: bool = False) -> float:
    """Distance of the visible horizon at the viewer's height.

    Source: https://en.wikipedia.org/wiki/Horizon, 2022-02-26

    Args:
        height_above_surface_m: height of the observer's eyes from Earth's
             surface in metres (height above sea level).
        latitude_deg:  degrees of offset from the Equator of the
            observer's position, used to compute the Earth's radius at the
            observer's position. ``0`` for the Equator, ``+/-90`` for the poles
            (north or south) but the sign is discarded. ``None`` or ``NaN``
            (default) will use the average Earth radius..
        correct_for_atmosphere: default is False. When True, the Young's
            approximate compensation for atmospheric refraction is applied.
            This increases the Earth's radius by 1/6, virtually bringing
            the horizon further away. Light further than the horizon
            is refracted downwards, allowing us to see behind the horizon
            to some extend. This correction only works in standard atmospheric
            conditions.

    Returns:
        Distance between observer's eyes and the furthest still-visible
        item on the horizon.
    """
    radius = earth_radius(latitude_deg)
    if correct_for_atmosphere:
        radius *= 7 / 6  # Young approximate correction method
    return math.sqrt(height_above_surface_m *
                     (2 * radius + height_above_surface_m))


class TestEarthRadius(unittest.TestCase):
    def test_earth_radius_default(self):
        self.assertAlmostEqual(6_371_008.8, earth_radius(), places=1)
        self.assertAlmostEqual(6_371_008.8, earth_radius(None), places=1)
        self.assertAlmostEqual(6_371_008.8, earth_radius(math.nan), places=1)

    def test_earth_radius_poles(self):
        self.assertAlmostEqual(EARTH_RADIUS_POLES_M, earth_radius(+90))
        self.assertAlmostEqual(EARTH_RADIUS_POLES_M, earth_radius(-90))

    def test_earth_radius_equator(self):
        self.assertAlmostEqual(EARTH_RADIUS_EQUATOR_M, earth_radius(+0))
        self.assertAlmostEqual(EARTH_RADIUS_EQUATOR_M, earth_radius(-0))

    def test_earth_radius_any(self):
        self.assertAlmostEqual(6367489.536800727, earth_radius(+45))
        self.assertAlmostEqual(6367489.536800727, earth_radius(-45))
        self.assertAlmostEqual(6372824.41677746, earth_radius(+30))
        self.assertAlmostEqual(6372824.41677746, earth_radius(-30))


class TestHorizonDistance(unittest.TestCase):
    def test_horizon_distance_default(self):
        # At 1.7 metres height (average eye height when on surface)
        self.assertAlmostEqual(math.sqrt(2 * 6_371_008.8 * 1.7 + 1.7 ** 2),
                               horizon_distance(1.7), places=3)
        # At 100 metres height
        self.assertAlmostEqual(math.sqrt(2 * 6_371_008.8 * 100 + 100 ** 2),
                               horizon_distance(100), places=3)

    def test_horizon_distance_known_latitude(self):
        # At 1.7 metres height (average eye height when on surface)
        self.assertAlmostEqual(
            math.sqrt(2 * EARTH_RADIUS_EQUATOR_M * 1.7 + 1.7 ** 2),
            horizon_distance(1.7, 0), places=3)
        self.assertAlmostEqual(
            math.sqrt(2 * EARTH_RADIUS_POLES_M * 1.7 + 1.7 ** 2),
            horizon_distance(1.7, -90), places=3)
        # At 100 metres height
        self.assertAlmostEqual(
            math.sqrt(2 * EARTH_RADIUS_EQUATOR_M * 100 + 100 ** 2),
            horizon_distance(100, 0), places=3)
        self.assertAlmostEqual(
            math.sqrt(2 * EARTH_RADIUS_POLES_M * 100 + 100 ** 2),
            horizon_distance(100, 90), places=3)

    def test_horizon_distance_known_latitude_with_correction(self):
        # At 1.7 metres height (average eye height when on surface)
        self.assertAlmostEqual(
            math.sqrt(2 * EARTH_RADIUS_EQUATOR_M * 7 / 6 * 1.7 + 1.7 ** 2),
            horizon_distance(1.7, 0, True), places=3)
        self.assertAlmostEqual(
            math.sqrt(2 * EARTH_RADIUS_POLES_M * 7 / 6 * 1.7 + 1.7 ** 2),
            horizon_distance(1.7, -90, True), places=3)
        # At 100 metres height
        self.assertAlmostEqual(
            math.sqrt(2 * EARTH_RADIUS_EQUATOR_M * 7 / 6 * 100 + 100 ** 2),
            horizon_distance(100, 0, True), places=3)
        self.assertAlmostEqual(
            math.sqrt(2 * EARTH_RADIUS_POLES_M * 7 / 6 * 100 + 100 ** 2),
            horizon_distance(100, 90, True), places=3)


if __name__ == '__main__':
    unittest.main()