Add time stepping naked planet model

Time-Stepping Naked Planet Model/Grading/naked_planet_tosubmit.py

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+# %%
+
+
+# %%
+import numpy as np
+import matplotlib.pyplot as plt 
+
+# Set up constants as given:
+timeStep_years = 100           # years
+waterDepth = 4000              # meters
+L = 1350                       # W/m²
+albedo = 0.3
+epsilon = 1
+sigma = 5.67e-8                # W/m² K^4
+
+# The incoming solar flux is constant:
+incoming_flux = L * (1 - albedo) / 4   # W/m²
+
+# Calculate the heat capacity (J/m² K)
+# (water density = 1000 kg/m³, specific heat = 4184 J/(kg·K))
+heat_capacity = waterDepth * 1000 * 4184
+
+# Read the number of time steps from stdin
+nSteps = int(input(""))
+
+# Set the initial conditions.
+# (Initial temperature is chosen in Kelvins; 0 K is allowed though not physical.)
+initial_temperature = 0.0  # Kelvin
+heatContent = initial_temperature * heat_capacity  # in J/m²
+
+# Prepare lists for time and temperature (for plotting, if desired)
+time_list = [0]
+temperature_list = [initial_temperature]
+
+# Convert the time step to seconds.
+dt = timeStep_years * 365 * 24 * 3600
+
+# Integration loop: update heat content and temperature each step.
+for i in range(nSteps):
+    # Current temperature in Kelvin:
+    T = heatContent / heat_capacity
+    
+    # Differential equation: dHeat/dt = incoming_flux - ε·σ·(T)⁴
+    dH_dt = incoming_flux - epsilon * sigma * (T**4)
+    
+    # Update the heat content over the time step:
+    heatContent = heatContent + dH_dt * dt
+    
+    # Append new time and temperature to lists:
+    time_list.append((i+1) * timeStep_years)
+    temperature_list.append(heatContent / heat_capacity)
+
+# Compute the final temperature (in Kelvin) and the corresponding outgoing heat flux.
+final_temperature = heatContent / heat_capacity
+final_heat_flux = epsilon * sigma * (final_temperature**4)
+
+# Output only the final temperature and heat flux.
+print(final_temperature, final_heat_flux)
+
+# Plotting code
+plt.plot(time_list, temperature_list)
+plt.show()
+
+
+# %%
+
+
+