Solar luminosity is estimated to have been 30% lower than today at the time when the solar system formed, 4.6 billion years ago.

Question

(a) If Earth's albedo was the same as it is now (A=0.3), what would have been its effective radiating temperature Te at that time?
(b) If the magnitude of the greenhouse effect had also remained unchanged (Delta Tg = 33K), what would Earth's average surface temperature have been?

Answer 1

I highly recommend this reference for assistance:
http://www.atmos.washington.edu/2001Q1/211/notes_for_011001_lecture.html

(a) Earth's effective radiation temperature now is 255 K. (See above reference)
If the solar luminosity were 30% of what it is now, the effective radiating temperature would be lower by a factor (0.3)^(1/4) = 0.74, because of the Stefan-Boltzmann T^4 law.

That would make the effective radiating temperature 189 K.

(b) Sorry, but I don't understand the delta Tg concept. The reference quoted above has some discussion of the greenhouse effect, which may be helpful to you.