To maintain a spacecraft$$s main components at an operational range of $0-10$C$,$ the bus can

be internally insulated. Typical insulation materials have a thermal conductivity of $0\mathrm{.}035$

$0\mathrm{.}16$ W

mK $.$ Assuming a spherical spacecraft has an external radius of $2\mathrm{.}5$ m$,$ and its internal

electronics generate a $/$ of $200,400,$ and $600$ W of internal heat during different times in

the mission. For each power level, calculate the insulation layer thickness $($that is$,)$ to

maintain the inner temperature within the acceptable range. Assume a thermal conductivity

of $=0\mathrm{.}12$ W

mK for the insulation and the spacecraft outer surface temperature is $8$C$.$