Apparatus and Setup
This lab applies the hydrostatic scale-height formula (Lecture 07) and the radiative-equilibrium-temperature formula (Lecture 08) to Titan, using real Cassini-Huygens-measured parameters, and compares the results to Earth, Venus, and Mars (recomputed here rather than simply copied from the lecture table).
Materials and Data
| Body | Mass (kg) | Radius (km) | Semimajor axis (AU) | Surface/effective temperature (K) | Bond albedo |
|---|---|---|---|---|---|
| Titan | 1.3452e+23 | 2574.7 | 9.5826 | 93.7 | 0.22 |
| Earth | 5.9724e+24 | 6371.0 | 1.0 | 288.0 | 0.306 |
Procedure
- Compute Titan's surface gravity from its measured mass and radius, using the identical formula from Lecture 01.
- Compute Titan's atmospheric scale height, assuming a nitrogen-dominated atmosphere (mean molecular mass ≈ 28 amu, close to N₂'s 28.014 amu) at its measured ∼93.7 K surface temperature, using the identical scale-height formula from Lecture 07.
- Compare Titan's scale height to Earth's (recompute Earth's using the same formula and Earth's measured temperature and gravity) and explain, referencing the scale-height formula's dependence on T and g, why Titan's scale height is comparable to or even larger than Earth's despite being much colder.
- Compute Titan's zero-greenhouse equilibrium temperature using its measured Bond albedo, semimajor axis (same as Saturn's, since Titan orbits Saturn), and the Sun's luminosity, using the identical equilibrium-temperature formula from Lecture 08.
- Compute the greenhouse temperature excess for Titan (observed surface temperature minus computed equilibrium temperature) and compare it, as a fraction of the total observed temperature, to Earth's and Venus's greenhouse excess fractions from Lecture 08's table.
Analysis and Uncertainty
Titan's actual atmosphere also contains a few percent methane and trace hydrocarbons, which slightly changes its true mean molecular mass from pure N₂'s 28.014 amu; students should state this simplification explicitly and note that it introduces a small (a few percent) systematic uncertainty in the computed scale height.
Deliverables
- Computed surface gravity and scale height for Titan, with all steps shown.
- A comparison to Earth's independently recomputed scale height.
- Computed equilibrium temperature and greenhouse excess for Titan.
- A comparison of Titan's, Earth's, and Venus's greenhouse-excess fractions.
Assessment Criteria
- Correct surface-gravity and scale-height calculations with correct units.
- Correct qualitative explanation of why Titan's scale height is large despite low temperature (weak gravity compensating).
- Correct equilibrium-temperature and greenhouse-excess calculations.
- Correct, properly labeled comparison of greenhouse-excess fractions across three bodies.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Section 10.1-10.4.
- Titan's mass, radius, and surface temperature: standard published Cassini-Huygens values (Niemann et al. 2005, Nature; Fulchignoni et al. 2005, Nature), not independently re-verified by live fetch this session; see
materials/ASTR320/reference-log.md. - Generated by
materials/ASTR320/src/generate_astr320_labs_psets.py.