Question No $1$: A$.$ Problem statement A university group designs a $1$kg cylindrical pico$-$satellite $10$ cm in diameter and $20$ cm height. The satellite has an internal power dissipation of $2\mathrm{.}4$W and specific heat capacity of $880$Jkg$-1$K$-1.$ The two circular ends are polished with aluminium while the cylindrical surface is all covered with solar cells. The thermos$-$optical properties of the surfaces are as follows $$ Solar absorptivity of aluminium $=10\%$ Infra$-$red emissivity of aluminium $=5\%$ Solar absorptivity of solar cells $=90\%$ Infra$-$red emissivity of solar cells $=95\%$ Maximum solar flux $=1400$ Wm$2$ Find the maximum equilibrium temperature of the spacecraft due to the sum of insolation and internal power dissipation alone $1.$ Firstly, with the sun shining orthogonally to the long axis of cylinder $2.$ Secondly, with the sun shining directly along the long axis of the cylinder Given that the satellite has reached its maximum temperature, calculate the initial rate of change immediately after entering the Earth$$s shadow B$.$ Propose solutions to maintain the temperature within operational limits $($e$.$g$.,$ thermal coatings, heat sinks$,$ radiators, or multi$-$layer insulation$).$ Justify your choices with calculations or relevant reasoning.