Apparatus and Setup
This lab combines the Jeans-escape formalism (Lecture 09) with the magnetopause pressure-balance model (Lecture 10), using real measured planetary magnetic-field strengths, to compare Earth's and Jupiter's magnetospheric standoff distances quantitatively.
Materials and Data
| Planet | Equatorial surface field B₀ (T) | Radius (km) |
|---|---|---|
| Earth | 3.1 × 10⁻⁵ | 6371.0 |
| Jupiter | 4.28e-04 | 69911.0 |
Assume typical solar-wind conditions at 1 AU (ρ_sw ≈ 8.4e-21 kg/m³, v_sw ≈ 400 km/s) for Earth; for Jupiter, note that the solar wind is roughly 27 times less dense at 5.2 AU than at 1 AU (inverse-square dilution), a correction you must apply.
Procedure
- Using the magnetopause pressure-balance formula from Lecture 10, compute Earth's magnetopause standoff distance in Earth radii, using the solar-wind density and speed given above.
- Correct the solar-wind density for Jupiter's greater distance (5.2 AU versus 1 AU) using the inverse-square dilution law, then compute Jupiter's magnetopause standoff distance in Jupiter radii.
- Compare your computed standoff distances (in units of each planet's own radius) to the observed values (∼10 R_E for Earth; ∼50-100 R_J for Jupiter, which varies substantially with solar-wind pressure) and discuss whether the order of magnitude matches.
- Using the Jeans-escape parameter formula from Lecture 09, compute λ for atomic hydrogen at Jupiter's cloud-top temperature (∼165 K) using Jupiter's escape velocity (59.5 km/s, from Lecture 01's table), and compare it to Earth's value from Lecture 09's worked example. Explain why Jupiter, despite its much colder cloud tops, retains hydrogen far more effectively than Earth does.
- In one paragraph, explain how a much larger magnetopause standoff distance (relative to the planet's own radius) might, in principle, provide additional protection against non-thermal atmospheric escape, and state why this is a plausible but not fully quantified effect (per Lecture 10's discussion).
Analysis and Uncertainty
Solar-wind density and speed both vary substantially with solar activity (by roughly a factor of a few), so the specific standoff-distance values computed here should be understood as representative, not exact, and should be reported with this caveat.
Deliverables
- Computed Earth and Jupiter magnetopause standoff distances, with the solar-wind density correction shown explicitly for Jupiter.
- A comparison to observed standoff distances.
- A computed Jeans parameter for hydrogen at Jupiter, compared to Earth's.
- A written paragraph on magnetic shielding and atmospheric escape.
Assessment Criteria
- Correct pressure-balance calculation for both planets, including the inverse-square solar-wind density correction for Jupiter.
- Correct comparison to observed standoff distances with appropriate uncertainty caveats.
- Correct Jeans-parameter calculation and correct qualitative explanation (large escape velocity, not just cold temperature, is the dominant factor for Jupiter).
- Written paragraph correctly hedges the magnetic-shielding claim as plausible but not fully quantified.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Section 10.3 and Section 11.2.
- Jupiter's and Earth's equatorial magnetic field strengths: standard published values (Connerney et al. 2018, Geophysical Research Letters, for Jupiter's Juno-derived field), 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.