Rama physics Appendix

As specified in the Introduction, we suppose that Rama is an infinitely long cylinder with translation invariance. This means that all physical quantities stay the same when moving along the axis. For instance, in this model, the surface temperature or lighting only depend on an angle around the axis, and are independent of the abscissa along this axis. This greatly simplifies their computation. In this context, a basic need for lighting and temperature profile models is to be able to compute:

• the transmittance of the atmosphere between two points, i.e. the proportion of light emitted at one point that reaches the other.
• the "surface irradiance", i.e. the amount of light received at a point on the surface from all the other points of the surface.
• the "average surface radiance", i.e. the amount of light received at a point in the atmosphere, from all the points of the surface, divided $4\pi$.
• the "volume irradiance", i.e. the amount of light received at a point on the surface from all the points inside the atmosphere.
• the "average volume radiance", i.e. the amount of light received at a point in the atmosphere, from all its other points, divided by $4\pi$.

These quantities are computed in the following sections:

• transmittance
• surface irradiance
• average surface radiance
• volume irradiance
• average volume radiance

This appendix also provides the implementation details for the radiative transfer algorithm described in the Coupled lighting and temperature profiles section, and for the numerical fluid simulation method described in the Natural convection and wind speed section:

• radiative transfer
• natural convection

© Eric Bruneton