Conside a spherical asteroid (radius 10km and constant mass density 3g/cm^3). The core extends to 3km and contains radioactive material. (The rest of the asteroid contains no radioactive material. The heating rate in the core is 10^-8 erg/s/g
1. Determine the temperature at the center of the asteroid
2. Determine the temperature at the surface of the asteroid
3. At what radius relative to the center of the asteroid, is the rate of outward directed flux of heat a maximum? Justify.