#! /usr/bin/python3
# ===================================================================
# Given the circumference of a sphere (the earth) and a great circle
# distance on the sphere (the earth), calculate the great circle
# angle with the center of the sphere (the earth)
# ===================================================================
# FYI: pi = 3.141592653589793
# ===================================================================

from math import pi, radians, cos, sin, asin, sqrt

# -------------------------------------------------------------------
# given a great circle distance and circumference,
# calculate its angle with the center of the earth
#   gs   great circle distance
#   cr   circumference of circle
# return angle in (degrees, radians)
# -------------------------------------------------------------------

def great_circle_angle(gs,cr):

    a1 = 360.0 * (gs/cr)       # degrees

    a2 = (pi/180.0) * a1       # radians

    return (a1,a2)             # return degrees and radials


# -------------------------------------------------------------------
# ---- main
# -------------------------------------------------------------------

if '__main__' == __name__:

    # ---- earth

    radm = 3959                # earth radius in miles
    radk = 6371                # earth radius in kilometers

    cirm = 24875.11            # earth circumference in miles
    cirk = 40030.14            # earth circumference in kilometers

    gcd1 = cirm / 8.0          # great circle distance (45 degrees)
    gcd2 = gcd1 * 2            # great circle distance (90 degrees)
    gcd3 = gcd1 * 3            # great circle distance (135 degrees)
    gcd4 = gcd1 * 4            # great circle distance (180 degrees)

    for gs in [ gcd1, gcd2, gcd3, gcd4 ]:

       deg,rad = great_circle_angle(gs,cirm)

       print(f'Great Circle Angle: {deg} (degrees)')

    print()