The Origins and Composition of the Atmosphere and Hydrosphere

Atmospheric Layers by Altitude: * Troposphere: Extends from the surface up to approximately $10\,km$ . * Stratosphere: Ranges from approximately $20\,km$ to $50\,km$ . * Mesosphere: Ranges from approximately $50\,km$ to $85\,km$ . * Thermosphere: Extends significantly above the Mesosphere, with markers noted at $100\,km$ , $110\,km$ , $120\,km$ , $130\,km$ , $140\,km$ , $150\,km$ , $160\,km$ , and $170\,km$ . * Exosphere: The outermost layer, with markers ranging from $490\,km$ to $520\,km$ .
Temperature Gradients: * Temperature displays distinct fluctuations across different layers, measured in degrees Celsius ( $^{\circ}C$ ). * Scale markers provided: $-100$ , $-50$ , $0$ , $50$ , $100$ , $150$ , and $200$ . * Special temperature indices noted: $500/1500$ in relation to altitude.

Major Gases: * Nitrogen (N): $78.08\%$ * Oxygen (O2): $20.95\%$ * Argon (Ar): $0.93\%$
Trace Gases: * Carbon Dioxide (CO2): $0.038\%$ * Neon (Ne): $0.0018\%$ * Helium (He): $0.0005\%$ * Methane (CH4): $0.0001\%$ * Krypton (Kr): $0.0001\%$ * Hydrogen (H): $0.00005\%$

Outgassing Mechanism: The atmosphere and hydrosphere are products of the Earth outgassing over geological time, driven primarily by volcanic activity.
Volcanic Volatiles: Typical volcanic emissions do not match the current atmospheric composition. Volcanic volatiles are dominated by: * Water vapour. * Carbon dioxide ( $CO_2$ ). * Sulfur dioxide ( $SO_2$ ). * Smaller amounts of nitrogen, halogens, hydrides, and other volatile compounds.
Inorganic Oxygen Production: In the first billion years of Earth's history, oxygen was only present in trace amounts. This was produced by the inorganic mechanism of UV radiation breaking down water vapour, which releases only tiny amounts of free oxygen.
Biological Oxygen Production: The shift to an oxygen-rich atmosphere was necessitated by the evolution of higher forms of life. The primary source is oxygen-producing photosynthesis. * Cyanobacteria: The first organisms to evolve this process. * Timeline: Archaean era, ranging from $3.8\,Ga$ to $2.5\,Ga$ ago. * Key Conclusion: The breathable atmosphere is a biological byproduct, not merely a primary feature of the geosphere.

Thermal Constraints: The existence of the hydrosphere is intimately linked to the atmosphere. Water, being a volatile compound, can only remain on the Earth's surface because the surface temperature is maintained below $100\,^{\circ}C$ .
Scientific Focus: To study the origins of these systems, researchers focus on atmospheric components with limited interaction with the modern biosphere, specifically nitrogen and inert (noble) gases.

Gravitational Influence: A Solar System object's ability to retain an atmosphere depends on the strength of its surface gravitational field. Stronger fields exert stronger gravitational forces on gas molecules, preventing them from being lost to space.
Escape Velocity ( $V_{esc}$ ): This is the minimum velocity required for a body (or molecule) to have sufficient kinetic energy to overcome a planet's gravitational field. * Formula: $V_{esc} = \left(\frac{2GM}{r}\right)^{0.5}$ * Where $M$ is the mass and $r$ is the radius of the body.
Temperature and Velocity: The average velocity of a molecule is proportional to its temperature. * A fraction of molecules will always possess enough speed to overcome gravity. * At low temperatures, this escape fraction is negligible. * At high temperatures, the proportion of molecules exceeding escape velocity increases until most molecules are lost.
The Exobase: Escape occurs in the upper atmosphere where the air is so thin that an outward-moving molecule has a negligible chance of colliding with another.

Molecular Mass Factor: Different gases have different molecular masses; therefore, their average velocities differ at a given temperature.
Retention Rule: For a planet to retain a gas over a duration similar to the age of the Solar System, the average velocity of the gas molecules should be less than approximately one-sixth ( $1/6$ ) of the escape velocity ( $V_{esc}$ ).
Comparison of Planetary Bodies: * Giant Planets: Plot well above the retention lines, allowing them to retain any of the gases. * The Moon: Plots below all lines, meaning it cannot retain any gases.

Atmospheric Abundance: * Nitrogen: $\approx 78.1\%$ * Argon: $\approx 0.93\%$ * Trace Inert Gases: Neon ( $Ne$ ), Krypton ( $Kr$ ), and Xenon ( $Xe$ ).
Chemical Inertness: Nitrogen's massive presence is due to its inorganic chemical inertness, despite bacterial "fixing" processes.
Isotopic Significance: The isotopic composition of inert gases in the atmosphere and mantle provides insight into the Earth's volatile element sources and planetary degassing timescales. * Argon Isotopes: Dominantly $^{40}Ar$ , which is the daughter product of the radioactive decay of $^{40}K$ . * Half-life of $^{40}K$ : $1.28\,Ga$ . * Information: Reflects the history of planetary outgassing over the entire age of the Earth. * Xenon Isotopes: $^{129}Xe$ is the daughter product of the radioactive decay of $^{129}I$ . * Half-life of $^{129}I$ : $15.7\,Ma$ . * Information: Provides data on the timescales of outgassing during the very early phases of Earth evolution (analogous to $Hf-W$ or $Mg-Al$ systems in meteorites).