Due and Scope
Due: [insert date]. Submit calculations, evidence tables, and concise interpretations.
Learning objectives: interpret craters, rays, regolith, and density on airless worlds; use lunar samples as chronology anchors; evaluate geomorphic and mineral evidence for water on Mars without overclaiming life.
Instructions: Carry units through calculations, distinguish past from present water, and identify observation versus inference. Revisions may be resubmitted with a change note.
Problems
1. Airless-World Crater Chronology 25 points
Two lunar image tiles each cover \(2.0\times10^4\,\mathrm{km^2}\). Tile H in the highlands contains 260 craters larger than 1 km. Tile M in a mare basalt plain contains 52 craters larger than 1 km, plus bright rays from a nearby young crater crossing the tile.
- Compute crater density for each tile in craters per \(10^4\,\mathrm{km^2}\).
- Compute the density ratio \(H/M\).
- Rank the highland surface, mare basalt, and bright rays from oldest to youngest.
- Explain why lunar sample ages are needed to turn relative crater density into an absolute chronology.
Deliverables: density table, age sequence, and chronology explanation.
2. Moon-Mercury Density Comparison 25 points
Use \(\rho=M/(4\pi R^3/3)\). The Moon has \(M=7.35\times10^{22}\) kg and \(R=1737\) km. Mercury has \(M=3.30\times10^{23}\) kg and \(R=2440\) km.
- Compute both mean densities in g cm\(^{-3}\).
- Which object is more metal-rich by inference? Defend the answer.
- Explain how a giant impact can plausibly help explain both the Moon's low iron fraction and Mercury's high metal fraction.
Deliverables: density calculations and a 150-200 word interpretation.
3. Mars Water Evidence Ranking 25 points
Rank the following observations for the claim "Mars had sustained liquid water at the surface in the past": valley networks, hydrated clay minerals, polar ice, recurring slope lineae, and a delta deposit in an ancient crater lake basin.
- Create a ranking from strongest to weakest for the stated claim.
- For each observation, mark whether it best supports past liquid water, present ice, present brines, or general volatile inventory.
- State one ambiguity or alternative explanation for each observation.
- Explain why evidence for water is not automatically evidence for life.
Deliverables: ranked evidence table and interpretation paragraph.
4. Delta Volume and Minimum Water Transport 25 points
A fan-shaped deposit in a martian crater covers \(45\,\mathrm{km^2}\) and has average exposed thickness \(20\) m. Assume the deposit is sediment with porosity 0.35 and grain density \(3000\,\mathrm{kg\ m^{-3}}\).
- Compute the bulk volume of the deposit in m\(^3\).
- Compute the solid-grain volume and sediment mass.
- If only 2% of suspended sediment carried by water is finally preserved in this deposit, estimate the minimum transported sediment mass.
- Explain why this supports sustained transport better than a single isolated channel image.
Deliverables: volume and mass calculations with units and geologic interpretation.
OpenStax Companion Practice
Recommended for additional practice: OpenStax Astronomy 2e, Chapter 9, Review Questions 10, 11, 13, 16, and 20; Thought Questions 21, 27, and 31; Figuring for Yourself 32-35; Chapter 10, Review Questions 4, 6, and 12; Thought Questions 19, 23, and 27; Figuring for Yourself 28 and 32. Verify numbering against the adopted PDF before LMS release.