Questions: Impact Crater Scaling Laws and Morphological Transitions

Question 1

Planetary scientists observe that on Moon-like body X the simple-to-complex crater transition occurs at ~18 km diameter, while on body Y it occurs at ~4 km. What does this imply about the two bodies?

• A. Body Y has stronger surface gravity than body X, because its craters collapse into complex forms at smaller sizes
• B. Body X has stronger surface gravity than body Y, because lower gravity allows larger simple craters to remain stable
• C. Body X has weaker crustal rock than body Y, causing earlier structural collapse
• D. Both bodies have the same gravity; the difference reflects different impactor populations

Answer: (A)

The simple-to-complex transition threshold scales inversely with surface gravity — stronger gravity means a smaller critical diameter because gravity drives the isostatically unstable crater floor to rebound at smaller scales. Body Y's transition at 4 km indicates stronger surface gravity (similar to Earth's ~2–4 km threshold), while body X's transition at 18 km indicates weaker gravity (similar to the Moon's ~15–20 km threshold). Option B reverses the logic: it is higher gravity, not lower, that causes collapse at smaller sizes.

Question 2

What physically causes the formation of a central peak in a complex impact crater?

• A. The impactor itself remains embedded in the crust and pushes upward after the initial impact
• B. The excavated cavity is gravitationally unstable — the crater floor rebounds isostatically upward, driven by the pressure differential created by the excavated mass, forming a central uplift
• C. Ejecta falling back into the crater piles up in the center, mimicking a peak
• D. Central peaks form only in craters with unusually high impactor velocities that inject energy deep into the crust

Answer: (B)

Central peaks form from dynamic rebound of the crater floor — not from the impactor, ejecta fallback, or unusually energetic impacts per se. When a large crater is excavated, the rock beneath is left under enormous pressure from the surrounding material, and the cavity is too deep to be gravitationally stable. The floor surges upward in a process analogous to a trampoline bouncing back after being pushed down (or the crown splash in a liquid drop impact). This rebound is fast — it occurs in seconds to minutes for large craters. The same process produces the terraced walls from inward slumping and reduces the depth-to-diameter ratio compared to simple craters.

Question 3

Complex craters have a greater depth-to-diameter ratio than simple craters because central peaks indicate deeper excavation.

• T. True
• F. False

Answer: False

The opposite is true. Simple craters have a depth-to-diameter ratio of roughly 1:5. Complex craters, by contrast, have smaller depth-to-diameter ratios — the crater floor has rebounded upward (forming the central peak) and the walls have slumped inward (forming terraces), both of which reduce the net depth relative to width. A common misconception is that the dramatic central peak indicates a deeper hole; in fact, it is evidence that the initial deep cavity has partially collapsed, making the final crater shallower relative to its diameter.

Question 4

Measuring where the simple-to-complex crater transition occurs on a planetary body's surface can provide information about that body's surface gravity even without sending a lander.

• T. True
• F. False

Answer: True

The transition diameter depends on surface gravity (and to a lesser extent crustal strength) because gravity drives the isostatically unstable floor rebound. On high-gravity Earth, the transition occurs at 2–4 km; on low-gravity Moon, at 15–20 km. By mapping crater populations in orbital imagery, identifying where the morphological transition falls, and applying scaling relations, planetary scientists can estimate surface gravity — and by extension bulk density and internal structure — purely from remote sensing. This is a powerful example of crater morphology as a diagnostic tool.

Question 5

Explain why the simple-to-complex crater transition occurs at smaller diameters on planets with stronger surface gravity, using the physics of crater floor rebound.

Model answer: When an impact excavates a crater, it removes a large mass of rock, leaving the material beneath the crater floor under reduced confining pressure. Gravity then drives the floor upward to re-equilibrate — a process called isostatic rebound. For a crater to undergo this rebound (forming a complex crater), the depth of excavation must be large enough that gravitational instability exceeds the material's rock strength. On a high-gravity planet, gravitational stresses scale up with g, so even a shallower (smaller) crater reaches the instability threshold. On a low-gravity body, rock strength can stabilize deeper (larger) simple craters before gravitational collapse becomes dominant. The transition diameter therefore scales roughly as D_transition ∝ 1/g, meaning stronger gravity → smaller transition diameter.

This gravity dependence is why the same sized crater can be simple on the Moon but complex on Earth. It also explains why the transition diameter varies across a single planetary body — regions with weaker crust (e.g., old, fractured highlands versus young, intact volcanic plains) can show different transition sizes because the strength term in the scaling law changes even while gravity is constant.