Apply Jeans escape and magnetopause pressure-balance reasoning from Lectures 09-10 to oxygen and helium retention, ion pickup, and the ice giants’ magnetic fields.
Compute the Jeans escape parameter λ for molecular oxygen (m = 32 amu) at Earth (assume exospheric T = 1000 K) and at Mars (assume exospheric T = 300 K, since Mars's thinner atmosphere and weaker greenhouse give it a cooler exosphere than Earth's). Compare both values to the hydrogen values computed in Lecture 09 (Earth λ_H2, Mars λ_H2) and state which species (H₂ or O₂) is retained more effectively on each planet, and why.
NASA's MAVEN mission has directly measured Mars's present-day ion-pickup atmospheric loss rate. Explain, in a short paragraph referencing Lecture 09 and Lecture 10, why this present-day measured loss rate, even if precisely known, cannot alone establish how much atmosphere Mars has lost over its entire 4.5 Gyr history, and what additional information or assumption would be required to make that extrapolation.
Uranus's equatorial surface field is roughly 2.28e-05 T and Neptune's is roughly 1.42e-05 T. Compute the ratio of their magnetic pressures (B²) and state what this implies about their relative magnetopause standoff distances (in planetary radii), holding solar-wind conditions and planetary radius ratio approximately fixed for this estimate.
Venus has no measurable intrinsic magnetic field, yet it does have a weak, induced magnetosphere formed by the interaction between the solar wind and Venus's ionosphere. Explain, in a short paragraph, why this induced magnetosphere is expected to provide much less protection against atmospheric erosion than Earth's intrinsic, dynamo-generated magnetosphere, referencing the dynamo requirements from Lecture 10.
Helium (m = 4 amu) is lighter than most atmospheric gases but heavier than atomic hydrogen. Using Earth's escape velocity (11.2 km/s) and an assumed exospheric temperature of 1000 K, compute the Jeans escape parameter for helium and compare it to the hydrogen value from Lecture 09. State whether Earth's atmosphere should retain helium more or less effectively than hydrogen, and explain why Earth's atmosphere nonetheless contains only trace helium today (a fact not fully explained by Jeans escape alone).
Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.
OpenStax Astronomy 2e, Sections 10.3 and 10.5.
materials/ASTR320/src/generate_astr320_content.py where referenced above.