Instructor Notes
Accept reasonable evidence rankings when students defend past versus present water carefully. Require units for density, volume, and mass.
Problem 1. Airless-World Crater Chronology
Worked solution: Tile H density is \(260/(2.0\times10^4)=130\) craters per \(10^4\,\mathrm{km^2}\). Tile M density is \(52/(2.0\times10^4)=26\) craters per \(10^4\,\mathrm{km^2}\). Ratio \(H/M=130/26=5\). The highlands are oldest, mare basalt is younger, and bright rays crossing the mare are youngest. Crater counts provide relative ages because older exposed surfaces accumulate more impacts, but sample ages from returned rocks calibrate crater density to absolute time and reveal changes in impact flux.
| Criterion | Points | Notes |
|---|
| Crater densities | 8 | Correct area normalization. |
| Density ratio | 4 | Expected ratio 5. |
| Age sequence | 6 | Highlands, mare, rays. |
| Sample calibration explanation | 7 | Must mention absolute chronology. |
Common errors: treating crater density as absolute age without calibration or ignoring rays as a cross-cutting young feature.
Problem 2. Moon-Mercury Density Comparison
Worked solution: Moon: \(R=1.737\times10^6\) m, \(V=2.20\times10^{19}\,\mathrm{m^3}\), \(\rho=7.35\times10^{22}/2.20\times10^{19}=3340\,\mathrm{kg\ m^{-3}}=3.34\,\mathrm{g\ cm^{-3}}\). Mercury: \(R=2.440\times10^6\) m, \(V=6.08\times10^{19}\,\mathrm{m^3}\), \(\rho=3.30\times10^{23}/6.08\times10^{19}=5430\,\mathrm{kg\ m^{-3}}=5.43\,\mathrm{g\ cm^{-3}}\). Mercury is inferred to be more metal-rich. A giant impact can strip silicate mantle from Mercury, raising the metal fraction, while the Moon can form mostly from silicate-rich impact debris orbiting Earth, leaving it iron-poor relative to Earth.
| Criterion | Points | Notes |
|---|
| Moon density | 6 | About 3.34 g/cm3. |
| Mercury density | 6 | About 5.43 g/cm3. |
| Metal-rich inference | 5 | Recognize density as inference. |
| Giant-impact comparison | 8 | Must explain opposite outcomes. |
Common errors: using radius in km with SI mass, or claiming the impact scenario is directly proven by density alone.
Problem 3. Mars Water Evidence Ranking
Worked solution: A strong ranking for past sustained liquid water is: delta deposit, valley networks, hydrated clay minerals, polar ice, recurring slope lineae. Delta deposits require sediment transport into standing water over time; valley networks support flowing liquid; clays support water-rock alteration; polar ice is present water inventory but not surface liquid in the past; recurring slope lineae are debated and may involve dry granular flows or salts. Evidence for water is not evidence for life because habitability also needs chemical energy, stability, nutrients, protection from radiation, and direct biosignature evidence.
| Criterion | Points | Notes |
|---|
| Ranking | 7 | Reasonable alternatives allowed if defended. |
| Past/present classification | 6 | Must separate liquid/ice/brines. |
| Ambiguities | 6 | One per evidence type. |
| Water versus life reasoning | 6 | No overclaiming. |
Common errors: treating polar ice as proof of ancient lakes or treating possible brines as confirmed present habitability.
Problem 4. Delta Volume and Minimum Water Transport
Worked solution: Area \(45\,\mathrm{km^2}=4.5\times10^7\,\mathrm{m^2}\). Volume \(V=4.5\times10^7\times20=9.0\times10^8\,\mathrm{m^3}\). Solid-grain volume is \((1-0.35)V=0.65\times9.0\times10^8=5.85\times10^8\,\mathrm{m^3}\). Sediment mass is \(5.85\times10^8\times3000=1.76\times10^{12}\) kg. If this is 2% of transported suspended sediment, minimum transported mass is \(1.76\times10^{12}/0.02=8.8\times10^{13}\) kg. A deposit of this scale requires repeated or sustained transport, accommodation space, and standing or slowing water, making it stronger evidence than one channel that might record a shorter event.
| Criterion | Points | Notes |
|---|
| Volume | 6 | Unit conversion required. |
| Solid volume and mass | 7 | Porosity applied correctly. |
| Transported mass | 5 | Divide by 0.02. |
| Geologic interpretation | 7 | Sustained transport argument. |
Common errors: multiplying by porosity instead of solid fraction, or equating all channels with deltas.
OpenStax Companion Practice Notes
Chapter 9 entries reinforce lunar/Mercury surfaces and densities; Chapter 10 entries reinforce Mars water and climate evidence. Verify PDF numbering before release.