Dwarf Planets

The code is based on finding volume, density and orbit radius of some dwarf planets. Further we tried to match these densities with one's calculated for different mixtures of granite and ice. Based on the results following conclusions can be drawn. Eris is a "rock star"—likely over 70% of granite rock. Pluto is the "balanced" one—roughly a 50/50 split. Ceres is surprisingly light—suggesting either more ice or a lot of trapped salts and clays (brines).

Here is the code

import math

# 1. Helper Functions
def vol_sphere(r):
    """Calculates volume of a sphere given radius."""
    return (4/3) * math.pi * r**3

def calc_density(rock_frac):
    """Calculates theoretical density based on rock/ice mix."""
    rho_rock = 3000  # kg/m3 (Granite-like)
    rho_ice = 900    # kg/m3 (Water ice)
    return rock_frac * rho_rock + (1 - rock_frac) * rho_ice

def orbit(period_yrs):
    """Calculates semi-major axis using Kepler's Third Law."""
    period_secs = period_yrs * secs_in_year
    kepler_const = 4 * math.pi**2 / (G * m_sun)
    return math.pow(period_secs**2 / kepler_const, 1/3)

# 2. Constants & Data
G = 6.674e-11
secs_in_year = 365.25 * 24 * 60 * 60
m_sun = 1.989e30
m_moon = 7.342e22
dia_moon = 3.474e06

dwarfs = {
    # Name: (diameter_%_moon, mass_%_moon, orbit_period_yrs)
    "Ceres": (27, 1.3, 4.6),
    "Pluto": (66, 17.8, 248),
    "Haumea": (36, 5.5, 283),
    "Makemake": (46, 5.4, 310),
    "Eris": (67, 22.7, 557)
}

# 3. Conversions and Calculations
# Convert relative moon data to absolute SI units
dwarfs_actual = {
    name: (
        (dia_moon / 2) * (d_pct / 100), # Radius (m)
        m_moon * (m_pct / 100),         # Mass (kg)
        p                               # Period (yrs)
    ) for name, (d_pct, m_pct, p) in dwarfs.items()
}

# Calculate Volume, Mass, Actual Density, and Orbital Distance
dwarfs_calc = {
    name: (
        vol_sphere(rad), 
        m, 
        m / vol_sphere(rad), 
        orbit(tp)
    ) for name, (rad, m, tp) in dwarfs_actual.items()
}

# 4. Output Physical Data
print(f"{'Name':<10} | {'Density':>8} | {'Distance (AU)':>12}")
print("-" * 40)
for dwarf, (vol, m, d, a) in dwarfs_calc.items():
    # Convert meters to Astronomical Units (AU) for readability
    dist_au = a / 1.496e11
    print(f"{dwarf:<10} | {d:>6.0f} kg/m³ | {dist_au:>10.2f} AU")

# 5. Composition Simulation
simulation = []  
print("\n--- Running Composition Simulation ---")

for rf in range(0, 101, 10):
    rock_p = rf / 100
    theo_den = calc_density(rock_p)
    
    for nm, (vol, m, dens, orb) in dwarfs_calc.items():
        diff = abs(dens - theo_den)
        simulation.append((nm, rf, diff))

# 6. Analyze Results (Find Best Fit)
print("\n--- Most Likely Composition (Best Fit) ---")
for name in dwarfs.keys():
    # Find the rock percentage with the smallest density difference
    planet_data = [item for item in simulation if item[0] == name]
    best_fit = min(planet_data, key=lambda x: x[2])
    
    print(f"{name:<10}: Approximately {best_fit[1]}% Rock / {100-best_fit[1]}% Ice")