Instructor Notes

Reward careful comparison rather than memorized planet facts. Ocean evidence is indirect; students should identify ambiguity in each measurement.

Problem 1. Giant-Planet Density and Composition

Worked solution: Jupiter: \(318/11.2^3=0.226\rho_E=1.25\,\mathrm{g\ cm^{-3}}\). Saturn: \(95/9.45^3=0.113\rho_E=0.62\,\mathrm{g\ cm^{-3}}\), less dense than water. Uranus: \(14.5/4.01^3=0.225\rho_E=1.24\,\mathrm{g\ cm^{-3}}\). Neptune: \(17.1/3.88^3=0.293\rho_E=1.61\,\mathrm{g\ cm^{-3}}\). Low density means large volume relative to mass, not small mass. Uranus and Neptune are denser than Saturn and comparable/higher than Jupiter despite much lower mass, consistent with larger fractions of ice/rock and smaller H/He envelopes.

Criterion	Points	Notes
Density calculations	12	Four planets.
Less-than-water identification	3	Saturn only.
Density concept	4	Mass versus volume.
Composition interpretation	6	H/He versus ice/rock enrichment.

Common errors: assuming low density means low gravity or low mass, or forgetting the radius cubed term.

Problem 2. Sunlight and Internal Heat

Worked solution: Relative sunlight is \(1/r^2\). Jupiter: \(1/5.2^2=0.037\). Saturn: \(1/9.5^2=0.011\). Uranus: \(1/19.2^2=0.0027\). Neptune: \(1/30^2=0.0011\). Neptune emitting 2.6 times absorbed sunlight implies a substantial internal heat source; Uranus emitting roughly absorbed sunlight implies much weaker internal heat escape or different interior structure. Thermal infrared measurements, energy-balance comparisons, cloud-top temperatures, and atmospheric dynamics help distinguish absorbed solar energy from internal heat.

Criterion	Points	Notes
Relative flux table	10	Use inverse square.
Neptune/Uranus comparison	7	Internal heat interpretation.
Observation	5	Thermal IR or energy balance.
Units/clarity	3	Dimensionless relative flux accepted.

Common errors: using \(1/r\), or saying Neptune receives more sunlight because it has active weather.

Problem 3. Europa Ocean Evidence Chain

Worked solution: Induced magnetic signal is most direct: a conducting salty layer can respond to Jupiter's changing magnetic environment; ambiguity includes plasma interaction or ionosphere assumptions. Young fractured surface suggests resurfacing and mobile ice over a warmer interior; ambiguity includes impact gardening or solid-state convection without a global ocean. Plumes would sample subsurface material if confirmed; ambiguity includes detection limits, viewing geometry, or surface sputtering. Tidal heating from eccentricity maintained by resonance supplies energy that can keep subsurface water liquid despite weak sunlight.

Criterion	Points	Notes
Evidence chain table	9	Measurement plus interpretation.
Ambiguities	6	One per observation.
Ranking	4	Magnetic signal usually strongest.
Tidal/resonance reasoning	6	Connect eccentricity to heating.

Common errors: treating a plume claim as automatically confirmed ocean material or omitting magnetic-system uncertainties.

Problem 4. Ring-Particle Orbital Periods

Worked solution: \(P_{outer}/P_{inner}=(137000/75000)^{3/2}=1.827^{1.5}=2.47\). If the inner period is 5.0 h, the outer period is \(12.3\) h. Different orbital periods create shear because inner particles lap outer particles. Collisions, spreading, and resonances can alter ring structure; narrow rings therefore need confinement by shepherd moons, resonant forcing, or replenishment from source material.

Criterion	Points	Notes
Period ratio	8	Expected about 2.47.
Outer period	5	About 12.3 h.
Shear explanation	5	Different orbital speeds.
Confinement/replenishment	7	Specific mechanisms.

Common errors: using linear radius ratio as period ratio, or treating rings as rigid disks.

OpenStax Companion Practice Notes

Chapter 11 entries support giant-planet comparison; Chapter 12 entries support Galilean moons, rings, and Enceladus. Verify numbering against the adopted PDF before release.