Add time stepping naked planet model

Time-Stepping Naked Planet Model/naked_planet.py

@@ -0,0 +1,51 @@
+import numpy
+import matplotlib.pyplot
+
+
+# Inputs
+timeDuration = 2000                    # years
+timeStep = 10                          # years
+waterDepth = 4000                          # meters
+initialTemp = 400
+
+# Constants
+secondToYear = 60*60*24*365
+specificWaterHeatCapacity  = 4.2E3      # kg/m^3
+waterDensity = 1000                     # J/kg*m^3
+L = 1350                                # Watts/m2
+albedo = 0.3
+epsilon = 1
+sigma = 5.67E-8                         # W/m2 K4
+
+
+# Calc amount of steps for given duration and resolution
+nSteps = int(timeDuration/timeStep)
+
+initialHeat = initialTemp * (waterDepth*waterDensity*specificWaterHeatCapacity)
+initialRadiatedHeat = epsilon * sigma * pow(initialTemp,4)
+T = [initialTemp]               # K
+Q = [initialHeat]               # Watt/m^2
+time = [0]                      # years
+heatOut = [initialRadiatedHeat] # Watt/m^2
+# print(initialRadiatedHeat)
+
+for i in range(nSteps):
+    # Calculate the heat change rate 
+    dQ_dt = (L * (1 - albedo)/4) - epsilon * sigma * pow(T[-1],4)
+    # Add heat change over step period to total heat in system   
+    Q.append(Q[-1] + dQ_dt * timeStep * secondToYear)
+    # Calculate temperature of planet based on heat in system
+    T.append(Q[-1] / (waterDepth*waterDensity*specificWaterHeatCapacity))
+    # Calculate only the outgoing heat
+    heatOut.append(epsilon * sigma * pow(T[-1],4)) 
+    # Save timestep for plotting
+    time.append(time[-1] + timeStep)
+
+print(T[-1])
+
+
+matplotlib.pyplot.plot(time, T)
+matplotlib.pyplot.title("Time-dependent temperature of a naked planet")
+matplotlib.pyplot.xlabel('Time (years)')
+matplotlib.pyplot.ylabel('Temperature (K)')
+matplotlib.pyplot.show()