Lab 03: Crater-Count Chronology Using Real Lunar Calibration Data

Apparatus and Setup

This lab uses real, radiometrically anchored lunar chronology calibration points from Apollo sample-return sites, following the lunar chronology function methodology introduced in Lecture 06. Representative published crater densities (craters per km² above 1 km diameter) are provided for three radiometrically dated regions.

Materials and Data

Procedure

1. Plot (by hand or with a simple script) crater density versus radiometric age for the three calibration points, and note that the relationship is strongly nonlinear (crater density rises much more steeply for the oldest surfaces), consistent with the higher impact flux before ∼3.8-3.9 Gyr ago described in Lecture 06.
2. Using a simple local linear interpolation between the two youngest points (Tranquillitatis and Imbrium) as an approximation, estimate the local slope of crater density versus age in this age range, and use it to estimate the age of a hypothetical fourth surface with crater density 3.1 × 10⁻³ craters/km².
3. Explain, in one paragraph, why this same local linear interpolation would give a badly wrong age estimate if applied to a much older surface (e.g., one with crater density comparable to the highlands value), and connect your answer to the nonlinearity noted in step 1.
4. Using the pi-group crater-scaling relation from Lecture 06 (D ∝ E²⁄⁵), estimate by what factor the final crater diameter increases if an impactor's kinetic energy increases by a factor of 100.
5. List two specific sources of systematic uncertainty (from Lecture 06's discussion) that would affect a crater-count age estimate for a surface that had never been sampled by any lander, and explain briefly how each one could bias the estimated age.

Analysis and Uncertainty

The local linear interpolation used in step 2 is explicitly an approximation, valid only over a narrow age range where the true crater-density-versus-age curve is not changing its slope too rapidly; extending it far beyond the calibration points it was fit to (as the highlands comparison in step 3 illustrates) is a common and serious methodological error in real crater-count studies.

Deliverables

• A plot or table of crater density versus age for the three calibration points.
• A computed local slope and an age estimate for the hypothetical fourth surface.
• A written explanation of why linear interpolation fails when extrapolated to much older surfaces.
• The crater-scaling factor computed from the pi-group relation.
• Two specific, correctly explained sources of systematic uncertainty.

Assessment Criteria

• Correct slope and interpolated-age calculation.
• Correct qualitative and quantitative explanation of chronology-function nonlinearity.
• Correct application of the D ∝ E²⁄⁵ scaling relation.
• Two distinct, correctly explained uncertainty sources (not the same source restated twice).

References and Provenance

• OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Section 9.5 (cratering) and Section 9.6 (the Moon).
• Crater density values are representative published estimates consistent with the lunar chronology function (Neukum et al. 2001; Stoffler & Ryder 2001), not independently re-verified by live fetch this session; radiometric ages are standard published Apollo sample-return results; see materials/ASTR320/reference-log.md.
• Generated by materials/ASTR320/src/generate_astr320_labs_psets.py.