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I would like help in designing a manned craft for exploration and mining activities on Ceres.
The sunlight reaching Ceres is approx 10% of that in LEO. Does this mean the spacecraft would have trouble keeping warm, or cool? Would spacecraft around Ceres need to use reflective foil covers, thermal blankets, white paint etc? Or will they be black, to absorb and heat up as much as they can?
Would they also require radiators to give off excess heat? Assume a present-day level of technology.
In short: the answer is yes to all of the above and the amount of each depends on details.
Thermal design of spacecraft usually starts out with assumptions regarding the size, total heat loads, and temperature limits of components. Manned spacecraft have an additional level of complexity due to the requirements needed for comfortable living in cramped quarters. Adding even more complexity comes from the reduced insolation leading to a design trade between large solar panels or an RTG that typical deep space craft use for electricity.
No matter which approach is used, avionics, humans, and a possible RTG will produce waste heat which will have to be radiated out to space meaning that, yes radiators will be needed. This is true for all spacecraft; heat can only be removed by radiation. The specific coating of the radiator is always up for trade (white paint, silver-coated Teflon, optical solar reflectors are a few examples). A black radiator emits heat roughly as well as it absorbs sunlight, so as the spacecraft travels further away from the sun, it'll absorb less solar heat.
As far as reflective foil and thermal blankets, these are typically made from multi-layered insulation (MLI) which are generally used for a two-fold purpose: to reflect incoming solar radiation and to keep heat inside. For such a cold target environment as Ceres, a significant portion of the spacecraft will likely need to be covered in blankets to keep the heat in while a few target areas will act as radiators. Heat from the air conditioning and system avionics systems would likely be routed to those radiators conductively or through heat pipes.
