Prints a circumference of astronomical sizes in miles-feet-inches

astro_circf.py

# Inspired by:
#   'How many digits of pi do we really need?'
#   (https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/)
#
# I wanted to see for myself that the difference between 15 digits and 16
# digits amounted to only half of an inch at the scale of Voyager 1's
# distance of ~12.5 billion miles

from decimal import Decimal, getcontext

getcontext().prec = 60


def pi_to_nth_decimal(n=15):
    # from https://oeis.org/A000796
    pi = (3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6,
          2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 6,
          9, 3, 9, 9, 3, 7, 5, 1, 0, 5, 8, 2, 0, 9, 7, 4, 9, 4, 4, 5, 9,
          2, 3, 0, 7, 8, 1, 6, 4, 0, 6, 2, 8, 6, 2, 0, 8, 9, 9, 8, 6, 2,
          8, 0, 3, 4, 8, 2, 5, 3, 4, 2, 1, 1, 7, 0, 6, 7, 9, 8, 2, 1, 4)
    return Decimal((0, pi[:n+1], -n))


def astro_circf(radius_in_miles, pi_decimals=15):
    pi = pi_to_nth_decimal(pi_decimals)
    r_inches = radius_in_miles * 5280 * 12
    d = r_inches * 2
    circ = pi * Decimal(d)
    return circ


def astro_dist(d):
    inches = d % 12
    feet = ((d - inches) / 12) % 5280
    miles = (d - feet - inches) / (5280 * 12)
    return '{:,} miles, {:,} feet, {:g} inches'.format(
        int(miles), int(feet), inches)

def inches_to_angstroms(d):
    return '{:g} angstroms'.format(d * Decimal(2.54e8))

getcontext().prec = 20
print('Circumference given V-ger1\'s distance of ~12.5 billion miles')
distance = 1.25e10
dist_15 = astro_circf(distance, 15)
dist_16 = astro_circf(distance, 16)
print('15:', astro_dist(dist_15))
print('16:', astro_dist(dist_16))

print()
print('Difference between 15 and 16 digits is')
print(astro_dist(dist_16-dist_15))
print()

getcontext().prec = 42
print('The radius of the universe is about 46 billion light years')
distance = 4.6e10 * 5.88e12  # 5.88 trillion miles per light year
dist_39 = astro_circf(distance, 39)
dist_40 = astro_circf(distance, 40)
print('39:', astro_dist(dist_39))
print('40:', astro_dist(dist_40))

print()
print('Difference between 39 and 40 digits is')
print(astro_dist(dist_40-dist_39))
print('or')
print(inches_to_angstroms(dist_40-dist_39))
print()

# Circumference given V-ger1's distance of ~12.5 billion miles
# 15: 78,539,816,339 miles, 3,932 feet, 8.1120 inches
# 16: 78,539,816,339 miles, 3,932 feet, 8.4288 inches

# Difference between 15 and 16 digits is
# 0 miles, 0 feet, 0.3168 inches

# The radius of the universe is about 46 billion light years
# 39: 1,699,475,961,885,934,368,891,522 miles, 32 feet, 3.622581225019 inches
# 40: 1,699,475,961,885,934,368,891,522 miles, 32 feet, 3.622581225023 inches

# Difference between 39 and 40 digits is
# 0 miles, 0 feet, 4e-12 inches
# or
# 0.001016000000 angstroms