# 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 :-) Feb 16, 2018 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. Feb 22, 2018 at 17:51

Quick and simple answer: A greater greenhouse effect.

There is an equilibrium in place. CO2 weathering rates depend on temperature, so at lower temperatures, we see CO2 levels rise, warming the planet. At higher temperatures, higher weathering rates mean more CO 2 drawdown, so the planet cools.

This is a very long term process. But this CO2 thermometer effect is believed to be the reason why we have had liquid oceans for all of known earth history.

As far as the black body effect goes; this is correct - from the viewpoint of an observer at distance, Earth would 'appear' colder. However, this is because the emission height changes (see https://andthentheresphysics.wordpress.com/2014/03/05/effective-emission-height/ ) for more of an explanation. Think of it as 'the height at which the atmosphere becomes IR-opaque' (although this is a simplification); the temperature then follows the lapse rate down to the ground. So raising the emission height raises the surface temperature.

(NB late at night, add refs later..)

• Thanks. Trying to understand this. So the effective radiating temperature of Earth is essentially what Earth's surface temperature would be without an atmosphere. So if the math was right for calculating it, the temperature would be 233K which is -40.27F, and withe the GHE it would be 19.13F. Why would Earth be so cold I thought the idea was Earth would get hotter without an atmosphere not make it colder? Being exposed to the Suns rays. A bit confused here would there still be water?
– yre
Feb 16, 2018 at 0:33
• I see why it would be colder because the temperature is 30% less so that's why it would be colder. So the water would be there but a new equilibrium would take place, a greater greenhouse effect.
– yre
Feb 16, 2018 at 0:52