 Solution

For an Earth-mass planet with a nitrogen-carbon-dioxide-water atmosphere, commonly quoted conservative Solar boundaries are approximatelyThe inner edge is governed by moist-greenhouse water loss and ultimately the runaway greenhouse. The outer edge is the maximum greenhouse outer habitable-zone limit, where additional carbon dioxide condenses or increases reflected light faster than it increases infrared trapping. Optimistic empirical boundaries, based on recent Venus and early Mars, are broader, roughly $0.75$ to $1.77\mathrm{AU}$. The values depend on clouds, planetary mass, atmospheric inventory, and climate assumptions.