#!/usr/bin/pyton3
# ====================================================================
# earth's rotational speed at latitude 45
# ====================================================================
import math
description = '''\
+-----------------------------------------------------------------------+
| calculate the earth's rotational (eastward) speed at a given latitude |
+-----------------------------------------------------------------------+'''
print(description)
deg = 45.0 # ---- earth's latitude in degrees
print()
print(f'latitude = {deg:.2f} degrees')
# ---- calculate earth's radius at the equator
er = 24_901.0/(math.pi*2.0)s
print()
print(f'earth\'s radius at the equator = {er:.2f} miles')
# ---- calculate earth's rotational speed at equator
es = 24_901.0/24.0
print()
print(f'earth\'s rotational speed at the equator = {es:.2f} mph')
# ---- calculate earth's radius at latitude ? degrees
lr = er * math.cos(math.radians(deg))
print()
print(f'earth\'s radius at latitude {deg:.2f} degrees = {lr:.2f} miles')
# ---- calculate circumference at latitude ? degrees
lc = 2.0 * math.pi * lr
print()
print(f'earth\'s circumference at latitude {deg:.2f} degrees = {lc:.2f} miles')
r = lc/24_901.0
print()
print(f'ratio of latitude to earth\'s circumference = {r:.2f}')
print('(surprise, it is the cos of the latitude angle)')
print(f'(cos of {deg:.2f} degrees = {math.cos(math.radians(deg)):.2f})')
# ---- calculate miles/hour at latitude ? degrees
es = lc/24.0
print()
print(f'earth\'s rotational speed at latitude {deg:.2f} degrees = {es:.2f} mph')