File:Brightness of the moon disc by phase angle 1 v 1.svg

1. 1. 1. Relationship between phase angle (Sun-Moon-observer) and normalised, disc-integrated brightness of the moon
      2. Data extracted from a plot and interpolation function created for further use in the model
      3. Source: Buratti, Bonnie J., John K. Hillier, and Michael Wang. 1996. "The
      4. Lunar Opposition Surge: Observations by Clementine." Icarus 124 (December):
      5. 490-99. https://doi.org/10.1006/icar.1996.0225.

1. 1. brightness of the Moon
   2. by phase angle
2. 1. python3 source code
   3. 20.8.2023 0000.0000

import math import numpy as np import matplotlib.pyplot as plt

1. 2. uses data from
   4. https://github.com/msmielak/moonlit

1. https://github.com/msmielak/moonlit

1. 1. 1. Relationship between phase angle (Sun-Moon-observer) and normalised, disc-integrated brightness of the moon
      2. Data extracted from a plot and interpolation function created for further use in the model
      3. Source: Buratti, Bonnie J., John K. Hillier, and Michael Wang. 1996. "The
      4. Lunar Opposition Surge: Observations by Clementine." Icarus 124 (December):
      5. 490-99. https://doi.org/10.1006/icar.1996.0225.

phase_angles=np.array([0.367186581,0.561328356,0.755753776,1.017911051,1.343778816,1.638020082,1.9321973,2.201542706,2.446200869,2.690859033,2.960111111,3.304228275,3.798169858,4.566540124,5.659518624,6.926950784,8.294080819,9.760921815,11.2775818,12.86918679,14.51056309,16.15193939,17.79332234,19.43470363,21.07608991,22.71746788,24.55846678,26.59940044,28.6403448,30.68133202,32.72256159,34.76382063,36.805081,38.84640163,40.88817885,42.93016095,44.97243897,47.01472501,49.05701374,51.09936005,53.14188578,55.18442088,57.22695599,59.2695018,61.3123181,63.35526696,65.39821581,67.44116333,69.48411219,71.52711193,73.57035938,75.61364299,77.65692793,79.7002102,81.74354871,83.78698764,85.8304172,87.87385613,89.91732854,91.961129,94.00502721,96.04892543,98.09282096,100.1367821,102.1807767,104.2247874,106.2687927,108.3127874,110.3568141,112.4010042,114.4452425,116.4894862,118.5337607,120.5781851,122.6226792,124.6673768,126.7121119,128.7568778,130.8016611,132.8463627,134.8910482,136.9357699,138.9805559,141.0253124,143.0700395,145.1147611,147.1594494,149.2040787,151.2487227,153.2933882,155.3381112,157.382853,159.4275827,161.4723968,163.517239,165.5620973,167.6069529,169.6517964,171.6966668,173.7414943,175.786378,177.8311961,179.5020253])

illum_fraction=1+ np.cos(phase_angles*math.pi/180)/2

1. brightness of visible part of moon disc

phase_relative_brightness=np.array([0.981495601,0.957317682,0.93441936,0.911719223,0.887147319,0.864543232,0.841650203,0.819234668,0.797948808,0.776662948,0.753826384,0.731224944,0.709518906,0.688329272,0.669028531,0.649231859,0.629197232,0.608983672,0.588516023,0.568644051,0.54830288,0.52796171,0.50765056,0.487331904,0.467035764,0.446702099,0.426908396,0.409070349,0.391280626,0.373684202,0.357181123,0.340810937,0.324446792,0.308354473,0.294321992,0.281213721,0.269440419,0.25770336,0.245978382,0.234513149,0.223857355,0.213243844,0.202630334,0.192065148,0.18272016,0.17397319,0.165226219,0.156473208,0.147726238,0.139208809,0.131808889,0.124572064,0.11734128,0.110098415,0.103109254,0.096573137,0.089994736,0.083458618,0.077073516,0.072168356,0.067704159,0.063239962,0.058763683,0.054583393,0.050554118,0.04659733,0.042616379,0.038587104,0.034702802,0.031555452,0.028625563,0.025719836,0.022953043,0.020862794,0.019086656,0.018228687,0.017539854,0.016989954,0.016518582,0.015678735,0.0147664,0.014017161,0.013557871,0.012965687,0.01224061,0.011491371,0.010591118,0.009425079,0.008325486,0.007322543,0.006579345,0.005920715,0.005207719,0.004875281,0.004669694,0.004536595,0.004391414,0.004191868,0.004113134,0.003841101,0.003822773,0.003508456,0.003536722])

fit1=np.polyfit(phase_angles,phase_relative_brightness,20) poly1=np.poly1d(fit1)

phase_angles_2=np.linspace(0,180,180*5)

phase_relative_brightness_2=poly1(phase_angles_2)

phase_relative_brightness_2=np.where(phase_relative_brightness_2>1,1, phase_relative_brightness_2 )

phase_absolute_brighness_lux=phase_relative_brightness_2*0.25

fig = plt.figure() ax = fig.gca() ax.set_xticks(np.arange(0, 195, 15)) ax.set_yticks(np.arange(0, 1,0.1))

plt.xlabel("Phase angle of moon", size=18) plt.ylabel("Relative brightness", size=18)

plt.yticks(fontsize=18) plt.xticks(fontsize=18)

plt.suptitle("Relative brightness of the Moon", fontsize=22) plt.title("sum of whole visible moon disc", fontsize=18)

plt.grid()

plt.plot(phase_angles_2, phase_relative_brightness_2, color="#7f7f00")

plt.scatter(phase_angles, phase_relative_brightness, marker="+", color="#7f0000")

1. plt.plot(phase_angles, illum_fraction)

plt.show()