$2.$ A spacecraft is in a circular orbit around the Sun, with a radius of $1$ AU $($astronomical unit$)$ and an albedo of $0\mathrm{.}3.$ The spacecrafts surface is made of a material with a thermal emissivity of $0\mathrm{.}9$ and a temperature of $300$ K$.$ The spacecraft is equipped with a radiator that can radiate heat to deep space with an emissivity of $0\mathrm{.}95.$ The spacecraft has a power output of $1000$ W and a surface area of $10$ m$^2.$ Assume that the spacecraft and radiator are in thermal equilibrium, and neglect any conductive or convective heat transferA$)$ Determine the rate at which the spacecraft radiates energy to deep space.b$)$ Determine the rate at which the spacecraft absorbs energy from the Sun.c$)$ Determine the temperature of the radiator.