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Just wanted to point out that saying this planet has no atmosphere at all may not be true-some believe that it may be possible the planet harbors clouds of silicate material, essentially giving it an atmosphere of vaporized rock.
one little errata: sin(0) = 0 — for “perfectly aligned” I think you mean that the orbit axis is 90 degrees from our line of sight so i = 90 and sin(i) = 1.