Radiative Transfer: Nuclear Winter on Caprica

Second Author - Eric

Abstract

Caprica is a fictional Earth-like planet.  N bombs are dropped randomly across the surface of the planet, each sending a mass M of particles into the atmosphere, each with density ρ and radius r.  Our goal is to find out how this affects the surface temperature and habitability of the planet.

Methods

Let's begin by finding the total number of particles, Np ejected into the atmosphere of Caprica.  We calculate this by dividing the total mass ejected by a single bomb, M, by the mass of the individual particle, given by the product of its density and its volume.  We then multiply by N, the number of bombs dropped across the surface of the planet.  We get the total number of particles to be:

Next, we need to determine what fraction of the total flux at the surface of the planet is blocked by the particles in the atmosphere.  Provided that the particles are sufficiently large and that the thickness of the atmosphere is negligible, we can do this by multiplying the number of particles, Np, by the area of each of them to get the total area blocked by the debris, which is:

We divide this area from the total area under sunlight to get the fraction of the flux that is blocked by the particles, and then subtract from 1 to give us the fraction of light that makes it through to the surface of the planet,

where R is the radius of Caprica.

Now, we can use the equation

to determine how the surface temperature of the planet is affected by the debris in the atmosphere.  We determine that the new temperature is given by the following expression:

where T is the normal average temperature of the planet, or about 287K.

Let's now plug values into this expression and calculate the new temperature of Caprica.

Using N = 5000, M = 10E10 kg, r = 0.1 mm, and ρ = 1000 kg/m^3, and assuming that all other values are the same as Earth, we get that the new surface temperature is 276K.

Conclusions

How hospitable would Caprica be at its new temperature?  276K is almost at the freezing point of water, and considering the economic and agricultural effects of such a temperature shift, there would likely be a mass extinction as a result of the nuclear winter (radiation aside).