A preliminary design for an Earth$-$Mars mission using only passive thermal control is unable

to maintain the spacecraft bus within the $0-10$C range. To lower the temperature at Earth, a

deployable radiator panel with an outer white paint Z$93$ coating $($s $=0\mathrm{.}18,$ IR $=0\mathrm{.}92)$ is

suggested. Similarly, a heater can be used to increase the temperature at Mars. Based on the

preliminary design calculations, the total heat into the spacecraft $($Qin$)$ from the sun, albedo,

and S$/$C power systems $($NOT the heater$)$ will be $2000$ W and $1200$ W at Earth and Mars,

respectively. The spacecraft will start at a $200$ km altitude parking orbit and be captured at

Mars at an altitude of $150$ km$.$ The spacecraft emissivity is $0\mathrm{.}13$ and its surface area is $50$ m$2.$

Assume Earth is at $287$ K and Mars at $213$ K$.$ Find the radiator area and heater power

necessary to keep the spacecraft within the acceptable temperature range.