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Surface Simulation

1,308 bytes removed, 1 year ago
Moved temperature model from here to the Temperature Calculation page
===Temperature===
 
ForThe eachTemperature pointlayer onrepresents the surface maptemperature of theeach object,point Universeon Sandboxthe performsmap of the followingobject's calculationssurface. inThe each[[Temperature timeCalculation|temperature step.calculations]] First,consider Universethe Sandboxeffects calculates theof incoming energyheat from heat sources like nearby stars. Some of, the energyeffects willof be reflected back into spacecooling, and somethe will be absorbed. The fractionspread of incomingheat energyacross absorbedthe issurface calculated usingof the object's. [[Average Albedo]].
 
The Temperature is displayed using the following units:
Some of this absorbed energy will be re-radiated back into space. If the object has no atmosphere, the output power, or the rate at which energy is radiated away, is calculated from the temperature of the point using the [[https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law|Stefan-Boltzmann law]]. If the object does have an atmosphere, the output power is calculated from the temperature of the point and the [[Greenhouse Effect]] of the object <ref name="Kleeman">Kleeman, Richard (2017).[https://math.nyu.edu/faculty/kleeman/zero_dim_ebm.html Zero-Dimensional Energy Balance Model]</ref>.
 
* Kelvin (K) is the [https://en.wikipedia.org/wiki/International_System_of_Units SI] base unit for temperature
The change in the temperature of the point, Δ''T'', is then calculated using the incoming power, ''P<sub>in</sub>'', the output power, ''P<sub>out</sub>'', the time step, Δ''t'', and the [https://en.wikipedia.org/wiki/Heat_capacity heat capacity] of silicate, ''C'' = 2.08×10<sup>8</sup> J/K, using
* Degrees Fahrenheit (°F)
:<math>\Delta T = (P_{in} - P_{out})\Delta T / C. </math>
* Degrees Celsius (°C)
 
Conversions between these three units are as follows:
Heat flows from areas of high temperature to areas of low temperature, so the heat in a single point on the surface map of an object may spread or [https://en.wikipedia.org/wiki/Diffusion diffuse] into nearby points, and the heat in those points may spread to the first point. Universe Sandbox calculates this diffusion by using the [https://en.wikipedia.org/wiki/FTCS_scheme FTCS method] to solve the [https://en.wikipedia.org/wiki/Heat_equation heat equation]. The temperatures of each point on the surface map are then corrected based on the results of this diffusion calculation.
 
°C = K - 273
 
°F = (9/5)°C + 32
 
===Elevation and Displacement===

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