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Consider an asteroid with an iron core (pc = 8000kg/m^3) covered by a thin silicate mantle (pm = 3400kg/m^3) with a thickness of 20% of the radius R of the asteroid. Assume that the internal temperature Ti = 600K is constant throughout the core. The thermal energy of the core is 3*k*Ti per atom(where k is Boltzmann's constant) and assume that the thermal conductivity of the silicate mantle is about kc = 2 W/ (m*K). Ignore the heat capacity of the mantle. If the surface of the asteroid has a temperature of Ts = 200K find the value of R such that the asteroid has a cooling rate of 1 K / 1 million years.
I really don't know where to start with this question. Any help would be appreciated.
I really don't know where to start with this question. Any help would be appreciated.