Instructor Notes

Reward explicit assumptions. Surface-age answers should use both crater density and cross-cutting evidence; climate answers must separate absorbed sunlight from greenhouse-warmed surface temperature.

Problem 1. Crater Counts and Resurfacing

Worked solution: Because each tile is \(1.0\times10^5\,\mathrm{km^2}\), Tile A has 84 craters per \(10^5\,\mathrm{km^2}\), and Tile B has 12 craters per \(10^5\,\mathrm{km^2}\). The ratio is \(84/12=7\). Tile A is older by crater density if impact flux and preservation are comparable. Tile B is younger or resurfaced because it has fewer craters and lava crossing older crater rims. Assumptions include equal detection threshold, comparable impact rate, no saturation, no different target strength, similar erosion/preservation, and correct identification of lava.

Criterion	Points	Notes
Density calculations	8	Units required.
Density ratio	4	Expected ratio 7.
Relative age reasoning	7	Use crater counts and lava evidence.
Assumptions	6	Specific reliability limits.

Common errors: equating fewer craters with younger age without mentioning resurfacing or preservation.

Problem 2. Cross-Cutting Sequence

Worked solution: Oldest to youngest: highland terrain; large crater impact; lava flow filling crater floor; wrinkle ridge crossing the lava; small fresh crater on the ridge; wind streaks from the fresh crater. The rules are superposition and cross-cutting: the crater cuts highlands, lava fills the already existing crater, the ridge deforms or crosses the lava, the fresh crater cuts the ridge, and wind streaks sourced from the fresh crater are youngest surface markings. Low Sun angle can exaggerate relief; high Sun angle can hide subtle ridges; coarse image scale can merge small craters or misidentify flows.

Criterion	Points	Notes
Correct sequence	10	One-point deductions for local swaps.
Rules/evidence	8	Must cite cross-cutting/superposition.
Imaging caveat	5	Illumination or scale accepted.
Clarity	2	Readable ordered list.

Common errors: placing wind streaks before the fresh crater or treating all craters as the same age.

Problem 3. Escape Speed and Atmospheric Retention

Worked solution: Mars: \(v=11.2\sqrt{0.107/0.532}=11.2\sqrt{0.201}=5.0\,\mathrm{km\ s^{-1}}\). Venus: \(v=11.2\sqrt{0.815/0.949}=11.2\sqrt{0.859}=10.4\,\mathrm{km\ s^{-1}}\). Earth is 11.2 km s\(^{-1}\), so the ranking is Earth, Venus, Mars. Escape speed is important but incomplete: temperature, molecular mass, solar EUV, magnetic shielding, outgassing, impact erosion, chemistry, and geological recycling also matter. Venus retained a massive atmosphere despite slightly lower escape speed than Earth because volatile history and greenhouse evolution matter.

Criterion	Points	Notes
Mars calculation	6	Expected about 5.0 km/s.
Venus calculation	6	Expected about 10.4 km/s.
Ranking	4	Earth > Venus > Mars.
Retention interpretation	9	At least two additional variables.

Common errors: saying Mars has no atmosphere because escape speed is low, or ignoring molecular mass and temperature.

Problem 4. Albedo, Solar Flux, and Greenhouse Interpretation

Worked solution: Planet C: \(S=1361/0.72^2=2625\,\mathrm{W\ m^{-2}}\). \(F_{abs}=2625(1-0.75)/4=164\,\mathrm{W\ m^{-2}}\). Planet D: \(S=1361/1.52^2=589\,\mathrm{W\ m^{-2}}\). \(F_{abs}=589(1-0.25)/4=110\,\mathrm{W\ m^{-2}}\). C absorbs more sunlight per square meter despite high albedo. However, surface temperature also depends on greenhouse opacity, atmospheric pressure, heat capacity, circulation, and infrared cooling level, so a lower absorbed flux world could have a warmer surface if greenhouse trapping is much stronger.

Criterion	Points	Notes
Solar flux scaling	8	Use inverse square.
Absorbed flux	8	Divide by 4 and include albedo.
Comparison	3	C absorbs more.
Greenhouse interpretation	6	Separate sunlight from surface temperature.

Common errors: forgetting the factor of 4, reversing albedo's sign, or treating absorbed sunlight as the whole climate.

OpenStax Companion Practice Notes

Chapter 8 entries support greenhouse, impacts, and crater preservation; Chapter 10 entries support Venus/Mars atmospheric and surface comparison. Use as companion practice and verify PDF numbering.