Trying to categorize moon phase using fraction illuminated I have a dataset with events that are occurring over a period of 5 years. I am trying to determine whether these events are related to moon phase. I downloaded the "fraction of moon illuminated" for the time period, but am struggling to define the cutpoints for crescent, quarter, and gibbous. These are defined by the USNO as 0.25, 0.5, and 0.75 (http://aa.usno.navy.mil/data/docs/MoonFraction.php) but I am seeking to divide the period into 8 bins of equal time. I think it is a sine function, where the period is 29.53059 days. If I divide this by 8, I get: 3.69132375 days.

Can anyone help me determine the fraction illuminated (y) that corresponds to these outpoints?

0 days

3.69132375 days

7.3826475 days

11.07397125 days

14.765295  days

18.45661875  days

22.1479425  days

25.83926625  days

???

Thanks
I used pyephem to calculate the fraction illuminated at each time

Program

import ephem
m = ephem.Moon
d1 = ephem.Moon('2017') # d1 is the date of the first new moon in 2017
days = [3.69132375*i for i in range(1,8)]
for day in days:
    m.compute(d1+day)
    print(day, m.moon_phase)


Output

3.69132375   0.1482372306829685
7.3826475    0.5259582805101828
11.07397125  0.8929835990614957
14.765295    0.9932503040700423
18.45661875  0.8004766309895268
22.1479425   0.4698580677294108
25.83926625  0.15043495343265506


Note that this is dependent on the particular month. There is an asymmetry as the motion of the moon is not perfectly even, it moves in an elliptical orbit.