Lecture 06: Impact Cratering and Surface Age Dating

Learning Objectives

1. Derive the crater-scaling relation connecting impactor energy, size, and velocity to final crater diameter.
2. Explain crater-count chronology and how it is calibrated using radiometrically dated, sample-returned lunar surfaces.
3. Apply crater-count dating to estimate the relative and absolute ages of planetary surfaces.
4. Distinguish primary impact craters from secondary craters and evaluate the limitations of the method.

Impact Cratering Basics

• An impact crater forms when a projectile's kinetic energy is deposited into a target surface far faster than the material can respond elastically, producing shock compression, excavation, and often melting.
• Crater diameter is typically 10-20 times the impactor's diameter for typical solar-system impact velocities (10-70 km/s), because the excavated volume greatly exceeds the impactor's own volume.
• Complex craters (with central peaks or peak rings) form above a size threshold (∼2-4 km on the Moon, larger on more massive bodies where gravity more strongly resists collapse) as the initial transient crater collapses under gravity.

Crater Scaling Relations

• Pi-group scaling (dimensional analysis) relates final crater diameter D to impactor diameter d, impact velocity v, and the ratio of impactor to target density, typically as D ∝ d⁴⁄⁵ v²⁄⁵ g⁻¹⁄⁵ for gravity-dominated craters.
• This scaling means crater diameter grows sub-linearly with impact energy (D ∝ E²⁄⁵ roughly, since E ∝ d³v²), so a 100-times more energetic impact produces roughly a 4-6 times larger crater, not a 100-times larger one.
• Scaling laws are calibrated using nuclear-test and laboratory hypervelocity-impact experiments as well as well-characterized natural craters (e.g., Meteor Crater, Arizona, whose ∼50 m iron impactor and ∼12-13 km/s impact velocity produced a 1.2 km diameter crater).

Crater-Count Chronology: The Basic Idea

• If the impact flux (impacts per unit area per unit time) has been roughly known and roughly constant (at least over the last ∼3 Gyr) for a given region of the solar system, then a surface's crater density (craters per unit area, typically above some reference diameter) increases monotonically with the surface's age.
• A surface with more craters per unit area is therefore older (has existed longer without being resurfaced) than one with fewer craters per unit area, all else being equal.
• This relative dating method requires no direct sample of the surface in question, making it broadly applicable across the solar system wherever high-resolution imaging exists.

Calibrating Absolute Ages: The Lunar Chronology Function

• Apollo and Luna sample-return missions dated specific lunar mare and highland surfaces radiometrically (via isotopic techniques such as ⁴⁴Ar/³⁹Ar dating), giving absolute ages for surfaces whose crater densities were also measured.
• Combining radiometric ages with measured crater densities at several calibration points produces the lunar chronology function, an empirical curve relating crater density to absolute surface age for the Moon.
• This function shows the impact flux was substantially higher (by roughly an order of magnitude) before ∼3.8-3.9 Gyr ago than it has been since, a period sometimes called the Late Heavy Bombardment, though its exact character remains debated.

Extending Chronology Beyond the Moon

• Extrapolating the lunar chronology function to other bodies requires correcting for differences in impactor population (main-belt asteroids dominate the inner solar system; comets and Kuiper Belt objects dominate the outer solar system) and in gravitational focusing (a more massive target attracts impactors more strongly, increasing the effective impact flux).
• Mars's crater chronology is considered reasonably well calibrated (via meteorite dating of Martian samples and modeling of the asteroid belt's dynamical evolution), while chronologies for the giant-planet satellites remain more uncertain because their impactor populations (comets, other satellites' ejecta) are less well characterized.
• This uncertainty is explicitly disclosed whenever this course cites an outer-solar-system crater-count age (e.g., for Europa in Lecture 05 and Lecture 13).

Primary vs. Secondary Craters

• Primary craters form directly from an interplanetary impactor; secondary craters form from debris ejected by a nearby (sometimes very distant) primary impact, re-impacting the surface at lower velocity.
• Secondary craters can be numerous and can bias small-crater counts if not properly identified and excluded (they often cluster in chains or clusters radiating from a primary crater).
• This complication means crater-count ages are most robust when based on larger craters (which are almost always primary) and when secondary contamination is explicitly assessed.

Saturation and Resurfacing Signatures

• A surface can become "saturated" (new craters erasing older ones at the same rate they form) once crater density reaches an equilibrium value, at which point crater counting alone can no longer measure further age increases.
• A surface with an anomalously low crater density for its inferred age, or with a sharp population of small young craters overlying a population of larger degraded ones, signals a discrete resurfacing event (as inferred for Venus in Lecture 05).
• Crater degradation state (sharp rims versus eroded, infilled rims) provides an additional, independent age indicator beyond simple crater density.

Impact Flux Through Solar System History

• The impact flux in the inner solar system has declined roughly monotonically since the Late Heavy Bombardment period, with occasional debated spikes from specific dynamical events (e.g., large asteroid family breakups).
• The outer solar system's impactor population (comets, Kuiper Belt objects) is thought to have been strongly reshaped by the giant planets' orbital migration (the Nice model), linking crater chronology directly back to the planet-formation and migration physics of Lecture 02.
• Ongoing impact monitoring (e.g., of Jupiter, via amateur and professional observation of fireball impacts) provides a present-day calibration point for current impact rates.

Applications: Dating Martian and Mercurian Surfaces

• Crater counts on Mars indicate its northern lowlands are systematically younger than its southern highlands, consistent with (though not proof of) either resurfacing by ancient oceans/lava or an ancient giant impact (Lecture 05's hemispheric dichotomy).
• MESSENGER-based crater counts on Mercury indicate its youngest volcanic plains are roughly 3.7-3.9 Gyr old, meaning Mercury's volcanism, unlike Mars's or Venus's, appears to have ceased relatively early in solar system history.
• These applications illustrate crater-count dating's central role in reconstructing the geological histories developed qualitatively in Lecture 05.

Limitations and Honest Uncertainty

• Crater-count ages carry genuine, quantifiable uncertainty from Poisson counting statistics (especially for small survey areas with few craters), secondary-crater contamination, and chronology-function extrapolation beyond the Moon.
• This course requires that any quoted crater-count age be accompanied by an honest statement of which of these uncertainty sources applies, rather than presenting a single number as though it were exact.
• Cross-checking crater-count ages against independent methods (radiometric dating of returned or meteoritic samples, stratigraphic superposition) is the strongest available validation, exactly as this course's Lecture 03 emphasized for interior-structure inference.

Worked Example: Crater Diameter from Impactor Energy: The Chicxulub Impactor

The Chicxulub impactor (associated with the Cretaceous-Paleogene extinction) is estimated at ∼10-15 km diameter, striking at ∼20 km/s; take d = 12 km, v = 20 km/s, target/impactor density ratio ≈ 1 (both roughly chondritic/crustal rock, ρ ≈ 2700-3000 kg/m³).

Impact kinetic energy: E = ½ m v², with m = (4/3)π(d/2)³ρ ≈ (4/3)π(6000 m)³(3000 kg/m³) ≈ 2.71e+15 kg, giving E ≈ 5.43e+23 J.

For reference, this is roughly 1.30e+08 times the energy of a 1-megaton nuclear weapon (4.184 × 10¹⁵ J), consistent with published estimates of the Chicxulub impact energy (∼10⁸-10⁸₀ MT).

The resulting crater (the Chicxulub crater, Yucatán, Mexico) has a final diameter of ∼150-180 km, an excavated-to-impactor diameter ratio of roughly 12-15, consistent with the pi-group scaling relation's expectation for a gravity-dominated crater of this size.

Summary and Next Lecture

• Crater diameter scales sub-linearly with impact energy, so the largest basins in the solar system required disproportionately large impactors.
• Crater-count chronology, anchored by radiometrically dated Apollo/Luna samples, converts crater density into an absolute surface age wherever the local chronology function is well calibrated.
• Applying crater counting honestly requires accounting for secondary-crater contamination, saturation, and chronology-extrapolation uncertainty beyond the Moon.

Next: Lecture 07 leaves the solid surface behind and begins the atmospheres unit by deriving the hydrostatic structure of a planetary atmosphere.