Thread by @nix_bit

Sₛᵤₙ = σ Tₛᵤₙ⁴
Sₛᵤₙ = (5,67 × 10⁻⁸ Wm⁻² K⁻⁴)(5800 K)⁴ = 64 × 10⁶ Wm⁻²
Sₛᵤₙ 4π(rₛᵤₙ )² = Sₑₐᵣₜₕ 4π(dₑₐᵣₜₕ)²
Sₑₐᵣₜₕ = Sₛᵤₙ (rₛᵤₙ/dₑₐᵣₜₕ)²
Sₑₐᵣₜₕ = 64 × 10⁶ Wm⁻² (695.510 km/149.600.000 km)²
= 1383,32 Wm⁻²

Sₑₐᵣₜₕ πrₑₐᵣₜₕ² = Sₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ4πrₑₐᵣₜₕ²
Sₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ = Sₑₐᵣₜₕ /4
Sₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ = 1383,32 Wm⁻²/4
= 345,83 Wm⁻²

Sₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ (1 – α ) = σ Tₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ⁴
Tₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ = ₄√(Sₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ (1 – α )/σ )
Tₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ = ₄√( 345,83 Wm⁻² (1 – 0,30 )/ 5,67 × 10⁻⁸ Wm⁻² K⁻⁴) = 255,62° K or -17.53° C

The oldest rocks on Earth found to date are the Acasta Gneiss in northwestern Canada near the Great Slave Lake, which are 4.03 billion years old.
space.com/24854-how-old-…

The atmosphere and the oceans accumulated gradually over millions of years with the continual degassing of the Earth's interior. Water remained a gas until the Earth cooled below 212 degrees Fahrenheit. (or 256°K or -17°C)
oceanservice.noaa.gov/facts/why_ocea…

The inorganic carbonate–silicate cycle.

source picture : researchgate.net/figure/The-car…

Methanogenesis, a biochemical process strictly carried out by anaerobic bacteria at hydro-thermal vents in earth's first oceans.
Acetic acid CH₃COOH => CO2 + CH4
csegrecorder.com/articles/view/…

"Our new data show that the chemical composition of the atmosphere was dynamic and, at least in the prelude to the Great Oxidation Event, hypersensitive to biological regulation."
phys.org/news/2017-03-e…

"Empirical measurements of pCO2 remain critical to understanding the long-term evolution of Earth’s atmosphere, late Mesoproterozoic (ca. 1.2 Ga) pCO2 levels to have been ≤0.36% (~10 times present atmospheric level)." eps.utk.edu/faculty/kah/pu…

Paleotemperature trend for Precambrian life inferred from resurrected proteins drop from 80°C to 40°C
(~353 K to ~ 353 K) from ~ 3.8 billion year ago till the Great oxidation event changed the atmosphere.

researchgate.net/publication/55…

Here we describe putative fossilized microorganisms that are at least 3.77 billion and possibly 4.28 billion years old in ferruginous sedimentary rocks, interpreted as seafloor-hydrothermal vent-related precipitates. nature.com/articles/natur…

After Hydrogen (H), Helium (He) and Oxygen (O) is Carbon (C) the most abundant element in space, also the most abundant element on the early scorched earth, the first anaerobic bacteria used this as food.
CH₃COOH => CO₂ + CH₄

Helium (He) is a Noble gas, a mono atomic gas that doesn't makes bounds with other elements easily ~100 substances compared to Carbon (C) with million substances. It evaporates to space away from the sun, gas till 4.2 K liquid till 0.95 K.

Hydrogen (H) is an element that bounds more easily like methane (CH₄) what reacted with the Carbon (C) , but due to it's abundance in space and earth it still evaporates to space away from sun. It still a gas ( 20.27K )on Pluto with ~ 37 K

Oxygen (O) evaporates at 90.2 K forming compounds with the Carbon (C), Carbon dioxide (CO₂) and Hydrogen (H), water H₂O in the early earth's atmosphere which is the first rain Carbonic acid (H₂CO₃) that erodes earth's crust and starts the inorganic carbonate–silicate cycle.

Between 3.85 a 1.85 billion year ago there was no surplus of oxygen in the atmosphere, it first bounds with earth's weathered crust then enriches the oceans.

source : en.wikipedia.org/wiki/Great_Oxi…

Anaerobic bacteria that produced CO₂ and CH₄ before the oxidation needed CO₂ that was dropping since earth creation, the next evolution of life used CO₂ and produced a toxic byproduct that was deadly for 99% of anaerobic bacteria, Oxygen O₂.
researchgate.net/figure/Cladogr…

The atmosphere of earth around 2.5 billion years ago with CH₄ and CO₂ was further disrupted making place for more O₂ in the atmosphere following the graph above.

"Artist's impression of early Earth (Hadeano)"
sci-news.com/geology/early-…

Just as Hydrogen and Helium, Oxygen O₂ evaporates to space.
At the stratosphere due to sun's energy (first tweet)
(Sₑₐᵣₜₕ_ₐᵥₑᵣₐ𝓰ₑ = 1383,32 Wm⁻²/4 = 345,83 Wm⁻²)
they split
O₂ => 2O
which form ozone
O₂ + O => O₃
which start the ozone cycle.
O₃ => O₂ + O

The ozone cycle not only protects earth from ultraviolet light from the sun, but is also a thermal blanket, warmth that traps H, He and free O in the high atmosphere this creates a more stable atmospheric volume, creating a more stable atmosphere.

This is not an ideal closed volume as we can see in the yearly loss of mass, 95.000 metric tons of Hydrogen (H) and 1.600 metric tons Helium (He)
scitechdaily.com/earth-loses-50…

But if we ignore the 0.000000000000001% yearly change, we can see the earth atmospheric volume as an unchanged volume which we can calculate with the "Ideal gas law".
PV=nRT

PV=nRT
Pressure (P),
Volume (V),
the number of substance in gas (n),
Gas constant (R),
Temperature (T)

The number of substance in gas (n) is found by dividing the total mass of the gas (earth's atmosphere) by the mass of that gas per mol.

n = m/M

Mass atmosphere of Earth (m) = 5,1 x 10¹⁸ kg
Molar mass atmosphere (M) = 28,97 g/mol
n = m/M
= 5,1×10²¹ g ÷ 28,97 g/mol
= 1,760441836×10²⁰ mol

V = nRT/P = 4,157289337×10¹⁸ m³
T at 1014 hPa = 14,85° C or 288 K

Nasa Earth Fact Sheet : nssdc.gsfc.nasa.gov/planetary/fact…

Current atmosphere
101400×4,157289337×10¹⁸ ÷(1,7604×10²⁰×8,3144598)
= 288 K

100% CO₂ atmosphere (Faint young Sun paradox)

101400×4,157289337×10¹⁸ ÷(1,1590×10²⁰×8,3144598)
= 437 K

100% CH₄ atmosphere

101400×4,157289337×10¹⁸ ÷(3,1875×10²⁰×8,3144598)
= 159 K

As we can see the first animals used CO₂ and replaced it with CH₄ which explains the rapid decline in temperature and drop in CO₂. Not because the sun energy is trapped due to the chemical but due to the molecular mass.

source picture :news.cnrs.fr/articles/when-…

We also see in the graph that due to the death of the anaerobic bacteria by rising O₂ the production of CH₄ declines, survival of the fittest the aerobic organism takes and shapes his world like his predecessors did.

"That is not to say that a hard snowball never happened. Extensive glaciation took place around 2.2 billion years ago, in the Paleoproterozoic era, and it seems plausible that global ice cover occurred then, Sohl says."
giss.nasa.gov/research/featu…

Although climate politics want us to believe CO₂ and CH₄ are gasses that trap sun's energy, an atmosphere with only CO₂ and CH₄ does not prevent loss of atmospheric warmth. CH₄ a stronger GHG then CO₂ should trap the heat even more, but it doesn't it drops.

Following the graph we can calculate the approximate molar mass an approximate composition by the ideal gas law, because we know the temperature around 3,5 billion ya to be ~ 80° C and 60° C around circa 2,5 billion ya.

n= PV/TR
101400 J m⁻³ 4,157289337×10¹⁸ m³/
(353,15 K 8,3144598 J K⁻¹ mol⁻¹ )
= 1,435671099×10²⁰ mol
M = m/n
5,1×10²¹ g ÷ 1,435671099×10²⁰ mol
= 35,52 g mol⁻¹

n= PV/TR
101400 J m⁻³ 4,157289337×10¹⁸ m³/
(333,15 K 8,3144598 J K⁻¹ mol⁻¹ )
= 1,521858768×10²⁰ mol
M = m/n
5,1×10²¹ g ÷ 1,435671099×10²⁰ mol
= 33,51 g mol⁻¹

Molar mass CO₂ = 44,01 g mol⁻¹
Molar mass CH₄ = 16,04 g mol⁻¹

An atmosphere with 70% CO₂ and 30% CH₄
(44,01g mol⁻¹×0,7)+(16,04 g mol⁻¹×0,3)= 35,619 g mol⁻¹
An atmosphere with 60% CO₂ and 40% CH₄
(44,01g mol⁻¹×0,6)+(16,04 g mol⁻¹×0,4)= 32,82 g mol⁻¹

Temperature drop from 40°C to 0° C at start of the great oxidation event to 2,2 billion ya.
n= PV/TR
101400 J m⁻³ 4,157289337×10¹⁸ m³/
(273,15 K 8,3144598 J K⁻¹ mol⁻¹ )
= 1,856149547×10²⁰
M = m/n
5,1×10²¹ g ÷ 1,856149547×10²⁰ mol
= 27,47 g mol⁻¹

Molar mass CO₂ = 44,01 g mol⁻¹
Molar mass CH₄ = 16,04 g mol⁻¹
Molar mass O₂ = 32 g mol⁻¹

An atmosphere with 20% CO₂ and 50% CH₄ and 30% O₂
(44,01g mol⁻¹×0,2)+(16,04 g mol⁻¹×0,5)+ (32 g mol⁻¹×0,3)
= 26,422 g mol⁻¹

The death of anaerobic bacteria and the rising oxygen started a new cycle, the nitrogen cycle, by two different groups of microorganisms: the ammonia-oxidizing bacteria or archaea and the nitrite-oxidizing bacteria.
sciencedirect.com/science/articl…

Molar mass CO₂ = 44,01 g mol⁻¹
Molar mass CH₄ = 16,04 g mol⁻¹
Molar mass O₂ = 32 g mol⁻¹
Molar mass N₂ = 28,01 g mol⁻¹

10% CO₂ and 10% CH₄ and 30% O₂ and 50% N₂
(44,01g mol⁻¹×0,1)+(16,04 g mol⁻¹×0,1)+ (32 g mol⁻¹×0,3)+(28,01 g mol⁻¹×0,5)
= 29,61 g mol⁻¹

So we see why it takes a billion year for the first widespread multi cellular organism to appear around 600 million years ago, the already suggest hypothesis of the frozen earth, had to wait till the molar mass was raised by N₂ cycle and the oceans melted again.

This triggers the Cambrian explosion.

A big temperature drop kills 85% of life,
The Ordovician Mass Extinction, 440 million years ago.

The new life that flourished, killed itself, the plants that use CO₂ dropped the levels even lower which also made the production of CH₄ by anaerobic bacteria fall, creating a atmosphere much more like we experience today with 78% N₂ and 21% O₂

CO₂, abundance, used, transforms atmosphere to
CO₂+CH₄ life flourish using CO₂ producing O₂, kills 99% of all life , flourish and transforms atmosphere to
CO₂+CH₄+O₂ and freezes the earth till it tips, life flourish use CO₂ stops CH₄ add O₂, kills 85% of all life.

As we have seen the sun does not keep the earths oceans from freezing only the atmosphere, only the pressure of the parts in the atmosphere on the surface. We use only an theoretical ideal law gas, with fixed pressure and volume, a little change has an enormous effect.

It's a very delicate balance, and because the N₂ cycle (28,01 g mol⁻¹) dependent on the O₂ cycle (32 g mol⁻¹) and the O₂ cycle depends on the CO₂ cycle (44,01 g mol⁻¹) and can freeze the world (27,47 g mol⁻¹) over for a billion year.
It's not so bad to add a bit of CO₂.

The process that keeps enough CO₂ in the mix is the similar process that started billion years ago, release of CO₂ by tectonic activity, the Wilson cycle. Without it all CO₂ would have been used up in 1 million year, our 1% anthropogenic emission wouldn't sustain it.

Anyway that is my two cent (short version)

"At these high altitudes, the residual atmospheric gases sort into strata according to molecular mass. Temperatures increase with altitude due to absorption of highly energetic solar radiation by the small amount of residual oxygen still present."
earthobservatory.nasa.gov/glossary/all

Molar mass H = 1,01 g mol⁻¹
Molar mass He = 4,00 g mol⁻¹

Molar mass CO₂ = 44,01 g mol⁻¹
Molar mass CH₄ = 16,04 g mol⁻¹
Molar mass N₂ = 28,01 g mol⁻¹

Molar mass O = 16 g mol⁻¹
Molar mass O₂ = 32 g mol⁻¹
Molar mass O₃ = 48 g mol⁻¹

"The theoretical top boundary of the exosphere is 190,000 km (half way to the Moon). This is the point at which the solar radiation coming from the Sun overcomes the Earth’s gravitational pull on the atmospheric particles." Like Hydrogen and Helium.
universetoday.com/40451/exospher…

Average molecular speed (v) in m s⁻¹
Gas constant (R) 8,3144598 kg m² s⁻² K⁻¹ mol⁻¹
Mesopause coldest place on earth 173 K (T)
Molar mass H, M= 0,00101 kg mol⁻¹

v = √ (3 RT/M)

v =√(3×8,3144598 kg m² s⁻² K⁻¹ mol⁻¹×173 K÷0,001kg mol⁻¹) = 2077,307063532 m s⁻¹

A hydrogen with an initial velocity (v) of 2077,31 m/s.
The time before the hydrogen stops and start falling down can be calculated by gravitational acceleration
g = 9,81 m s⁻²
t = v ÷ g
= (2077,31 m s⁻¹) / (9,81 m s⁻²)
= 211,97 s

The distance (r) traveled by the hydrogen before it turns and start falling down can be calculated by using (t) as
r = 1/2 gt²
r = 1/2 (9,81 m s⁻²) (211,97 s)²
= 220388,15 m or 220 km
Thermosphere 80km to 600km

Molar mass O, M= 0,016 kg mol⁻¹
v =√(3×8,3144598 kg m² s⁻² K⁻¹ mol⁻¹×173 K÷0,016 kg mol⁻¹) = 519,32 m s⁻¹
t = v ÷ g
= (519,32 m s⁻¹) / (9,81 m s⁻²)
= 52,93 s
r = 1/2 (9,81 m s⁻²) (52,93 s)² = 13746,19 m or 13km

The ozone layer.

Molar mass O₂, M= 0,032 kg mol⁻¹
v =√(3×8,3144598 kg m² s⁻² K⁻¹ mol⁻¹×173 K÷0,032 kg mol⁻¹) = 367,21 m s⁻¹
t = v ÷ g
= (367,21 m s⁻¹) / (9,81 m s⁻²)
= 37,43 s
r = 1/2 (9,81 m s⁻²) (37,43 s)² = 6873,09 m the low pressure atmosphere at Mount Everest.

Molar mass atmosphere , M= 0,029 kg mol⁻¹
v =√(3×8,3144598 kg m² s⁻² K⁻¹ mol⁻¹× 255 K÷0,029 kg mol⁻¹) = 468,33 m s⁻¹
t = v ÷ g
= (468,33 m s⁻¹) / (9,81 m s⁻²)
= 47,74 s
r = 1/2 (9,81 m s⁻²) (47,74 s)² = 11178,88 m the boundary of our atmosphere.

https://twitter.com/nix_bit/status/1186394950495358976

Venus
Molar mass atmosphere , M= 0,044 kg mol⁻¹
v =√(3×8,3144598 kg m² s⁻² K⁻¹ mol⁻¹× 737 K÷0,044 kg mol⁻¹) = 468,33 m s⁻¹
t = v ÷ g
= (646,37 m s⁻¹) / (8,87 m s⁻²)
= 72,85 s
r = 1/2 (8,87 m s⁻²) (72,85 s)² = 26035 m or maximum boundary of the atmosphere of Venus

"The most Earth-like atmosphere in the solar system occurs 30 to 40 miles (50 to 60 kilometers) above the surface of Venus." space.com/18527-venus-at…