Disclaimer: this question is a little vague and lacks some necessary details, but any help is appreciated! Background: The James Webb Space Telescope has a 5-layer sunshield that absorbs solar radiation allowing the telescope to cool (with the help of a crycooler) to its operating temperature of 7K. Mirrors within the telescope are composed of beryllium which has a long thermal time constant. Question: what is the rate of cooling, either for the sun shield, telescope, or beryllium mirrors? I.e., I'd like to find out how rapidly either component cools. My only ideass are to use either the Stefan-Boltzmann law, Newton's Law of Cooling, or a thermodynamic identity, becuase the answer to this problem must involve a differential. Any help/ideas are appreciated, thank you.

Disclaimer: this question is a little vague and lacks some necessary details, but any help is appreciated! Background: The James Webb Space Telescope has a 5-layer sunshield that absorbs solar radiation allowing the telescope to cool (with the help of a crycooler) to its operating temperature of 7K. Mirrors within the telescope are composed of beryllium which has a long thermal time constant. Question: what is the rate of cooling, either for the sun shield, telescope, or beryllium mirrors? I.e., I'd like to find out how rapidly either component cools. My only ideass are to use either the Stefan-Boltzmann law, Newton's Law of Cooling, or a thermodynamic identity, becuase the answer to this problem must involve a differential. Any help/ideas are appreciated, thank you.