# Calculating 30% less solar energy. Provided the math is right, would there have been liquid water on Earth?

The Sun is estimated to have had a solar luminosity about 30% lower when the solar system was formed.

Now if I assumed that Earth's albedo was the same as it is today, what would have been the effective radiating temperature of the Earth at that time.

My solution: T_e = S/4*(1 - A)

I know that Earth's current albedo is A = 0.3.

Hence,

T_e = S/4*(1 - 0.3)

T_e = ( (0.7)*(1370) ) / (4 (5.67*10^-8)) * (1-0.3) = 233K

233K <- would have been Earth's effective radiating temperature

Now if one assumes the magnitude of the greenhouse effect was the same then (now it is 33k) Earth's temperature would be:

233K + 33K = 266K

Assuming the math is right between those two would there have been liquid water on Earth? If there would be, how does one resolve this paradox? that is, given that albedo was the same, what element of the climate system could explain this?

Thanks

• This also sounds like a homework question. A bit better, since you explained some of your starting math. But, still, what are you thinking towards the final answer and why? And also please include the homework tag when asking homework questions. We aren't against homework questions done well, but this is not a place to come and get magic answers, as the homework policy explains fairly well :-) – JeopardyTempest Feb 16 '18 at 9:12
• If there are water formed canyons and seas on mars (do we know?) then there would have been, and there would have been liquid water in the groundwater and deep seas, but the earth would be at least 10 degrees colder on average. unless plants found a way to regulate a favorable greenhouse effect using methane or something. – DeltaEnfieldWaid Feb 22 '18 at 17:51