List of top Atmospheric and Ocean Science Questions on Blackbody Radiation and Radiation Balance

A spherical asteroid, revolving around the sun in a circular orbit, is in radiative balance. Suddenly, the asteroid enters the shadow of a planet and solar radiation is cut off. Assuming that the asteroid emits as a blackbody in the longwave regime, the time taken to reduce the average temperature of the asteroid by 0.5 K is \(\underline{\hspace{1cm}}\) seconds (rounded off to the nearest integer).
Consider a layer of atmosphere between 5 and 6 km height. The downwelling longwave radiation at 5 and 6 km is 240 and 230 Wm\(^{-2}\), respectively. The upwelling longwave radiation at these heights is 260 and 240 Wm\(^{-2}\), respectively. The longwave heating rate in this layer is \(\underline{\hspace{1cm}}\) K per day. (Round off to one decimal place.)