Learning Objectives
- Calculate greenhouse offset from effective and observed surface temperatures.
- Estimate thermal molecular speeds and compare them with escape velocity.
- Evaluate why pressure, composition, albedo, and gravity must be interpreted together.
Preparation
Review Lecture 6 on radiative balance, greenhouse warming, atmospheric pressure, and atmospheric escape.
Materials and Data
../data/lab-04-atmospheres-climate.csv, containing solar flux, albedo, effective temperature, surface temperature, pressure, escape velocity, and atmospheric composition.- Spreadsheet or calculator with square-root function.
- NASA Planetary Fact Sheet values and Titan satellite fact-sheet values; see
../data/lab-data-provenance.md.
Apparatus and Setup
- Open the CSV and create columns for greenhouse offset, molecular thermal speed, and escape-speed ratio.
- For mean molecular mass, convert atomic mass units to kg using 1 amu = 1.6605 x 10-27 kg.
- Use surface temperature for molecular-speed estimates and mark Mercury as exosphere-only rather than a stable lower atmosphere.
Procedure
- Calculate greenhouse offset as \(T_{surface} - T_{effective}\) for every body with both temperatures listed.
- Estimate root-mean-square molecular speed using \(v_{rms}=\sqrt{3kT/m}\), where \(k=1.380649\times10^{-23}\) J K-1.
- Compute \(v_{escape}/v_{rms}\) for Venus, Earth, Mars, and Titan. Exclude Mercury from the ratio table if you cannot assign a single atmospheric molecular mass.
- Make a two-axis comparison table: greenhouse offset and escape-speed ratio.
- Classify each world as greenhouse-dominated, escape-limited, pressure-limited, or exosphere-only, and defend the classification with measurements.
Measurement Record
| Body | Greenhouse offset (K) | vrms (km/s) | vesc/vrms | Climate/escape classification |
|---|---|---|---|---|
| Venus | ||||
| Earth | ||||
| Mars | ||||
| Titan |
Analysis and Uncertainty
Use +/-3 K for effective and surface temperatures unless your instructor supplies more precise values. Propagate greenhouse-offset uncertainty by adding temperature uncertainties in quadrature. For molecular speed, evaluate sensitivity by recalculating with mean molecular mass +/-1 amu; for mixed atmospheres this is a model uncertainty, not an instrumental measurement error.
Deliverables
- Completed calculation table for greenhouse offset and escape-speed ratio.
- Scatter plot of surface pressure versus greenhouse offset, with labels for all five bodies.
- Short classification paragraph comparing Venus, Mars, and Titan.
- Provenance note citing NASA Planetary Fact Sheet and
lab-04-atmospheres-climate.csv.
Assessment Criteria
- Correct greenhouse and molecular-speed calculations: 30%.
- Classification uses multiple measured quantities: 25%.
- Uncertainty and model sensitivity are explicitly treated: 20%.
- Plot has units, labels, and readable scaling: 15%.
- Complete provenance note: 10%.
References, Software, and Data Provenance
Data file: materials/ASTR120/data/lab-04-atmospheres-climate.csv. Sources: NASA Planetary Fact Sheet and Saturnian satellite fact-sheet entries for Titan. Processing state: real public reference values selected and rounded for instruction. Software: spreadsheet or calculator.