esi.py

from __future__ import division

from operator import mul
from math import pi, sqrt

NUM_TERMS = 4 # Number of properties used in computing ESI
G = 6.674e-11 # m**3/(kg * s**2) (Gravitational constant)

TERM_WEIGHTS = {
    'radius': 0.57,
    'density': 1.07,
    'escape_velocity': 0.70,
    'temperature': 5.58
}

EARTH_VALUES = {
    'radius': 1, # the Earth is 1 earth in radius
    'density': 1, # the Earth is 1 earth in density
    'escape_velocity': 1, # the Earth is 1 earth in escape velocity
    'temperature': 288, # Kelvins
}


def calculate_term(other_val, earth_val, term_weight):
    abs_diff = abs((other_val - earth_val)/(other_val + earth_val))
    return (1 - abs_diff)**(term_weight/NUM_TERMS)


def calculate_esi(**kwargs):
    """
    kwargs must contain:
    radius (in meters)
    density (in kilograms/meter**3)
    escape_velocity (in meters/second)
    temperature (in degrees Kelvin)
    """
    terms = [calculate_term(v, EARTH_VALUES[k], TERM_WEIGHTS[k])
             for k,v in kwargs.items()]
    return reduce(mul, terms)


# Le petit test
assert (1.0 - calculate_esi(**EARTH_VALUES)) < 0.0000001

# Values will be used to compute value of chucks
# in reference units from EARTH_VALUES
earth = {
    'radius': 6371000, # m
    'density': 5514.0, # kg/m**3
    'escape_velocity': 11186000, # m/s
    'temperature': 288, # K
}

chuck = {
    'mass': 88.45, # kg
    'density': 1062.0, # kg/m**3
    'temperature': 310.15, # K
}

chuck['volume'] = chuck['mass'] / chuck['density'] # kg/(kg/m**3) => m**3
chuck['radius'] = 3 * (chuck['volume']/(4*pi))**(1/3) # m
chuck['escape_velocity'] = sqrt(2 * G * chuck['mass'] / chuck['radius']) # sqrt((m**3)/(kg * s**2) * kg * m**-1) = sqrt(m**2/kg**2) = m/s

# values for chuck, measured in EARTH_VALUES units
earth_chuck = {
    'density': chuck['density'] / earth['density'],
    'radius': chuck['radius'] / earth['radius'],
    'escape_velocity': chuck['escape_velocity'] / earth['escape_velocity'],
    'temperature': chuck['temperature']
}

print calculate_esi(**earth_chuck)