The Planet Mean Surface Temperature Equation: Tmean=[Φ(1-a)S(β*N*cp)¹∕ ⁴ /4σ]¹∕ ⁴

What was the Earth's mean temperature 3,5 billion years ago (3,5 Bya ) ?

Lets see:

Sun's irradiating intensity was weaker.

It was only 75 % of the present,

S = 0,75*So

And Earth rotated twice as fast then,

1 rotation in 12 hours.

Lets calculate:

Earth’s Without-Atmosphere Surface Mean Temperature calculation Tmean.earth.3,5 Bya

So = 1.362 W/m² ( "So" is the present Solar constant )

Earth’s albedo: aearth = 0,30

Φearth = 0,47

β = 150 days*gr*oC/rotation*cal – is a Rotating Planet Surface Solar Irradiation Absorbing-Emitting Universal Law constant

N = 2 rotations /per day, was Earth’s sidereal rotation spin at 3,5 Bya

cp.earth = 1 cal/gr*oC

σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant

Earth’s Without-Atmosphere Surface Mean Temperature Equation Tmean.earth is:

Tmean.earth = [ Φ (1-a) So (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴

Τmean.earth.3,5 Bya = [ 0,47(1-0,30)*0,75*1.362 W/m²(150 days*gr*oC/rotation*cal *2rotations/day*1 cal/gr*oC)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τmean.earth.3,5 Bya = [ 0,47(1-0,30)*0,75*1.362 W/m²(150*2*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =

Τmean.earth.3.5 Bya = ( 6.167.274.722,0 )¹∕ ⁴ = 280,23 K

Tmean.earth.3.5 Bya = 280,23 Κ

or Tmean.earth.3,5 Bya = 7 oC.

Conclusion:

3,5 billion years ago planet Earth had a sustainable for life mean temperature of 7 oC.

From Wikipedia: " Among the earliest fossil evidence for life is microbial mat fossils found in 3.48 billion-year-old sandstone in Western Australia,[63]".