Problems
1. Estimating the Tunguska Event Energy 15 points
The 1908 Tunguska event is estimated to have involved a stony/icy impactor roughly 60 m in diameter striking at ∼15 km/s (it exploded in the atmosphere before reaching the ground, an airburst rather than a cratering impact, but its kinetic energy can still be estimated the same way). Using an assumed density of 2000 kg/m³, compute the impactor's kinetic energy and express it in megatons of TNT equivalent (1 MT = 4.184 × 10¹⁵ J). Compare your result to the commonly cited estimate of 3-15 megatons for the Tunguska event.
2. Olympus Mons and the Hawaiian Hotspot Track 15 points
The Pacific Plate moves at roughly 7.0 cm/yr over the fixed Hawaiian hotspot, and the resulting Hawaiian-Emperor seamount chain is roughly 2400.0 km long. Estimate the total time this chain took to form, in millions of years, and compare it to the estimated multi-hundred-million-year construction time of Mars's single, stationary Olympus Mons (22.0 km tall, 600.0 km diameter). Explain, referencing Lecture 05's plate-tectonic argument, why Mars produced one enormous volcano rather than a long chain of smaller ones.
3. Crater Density and Venus’s Resurfacing Event 15 points
Venus's crater population is far below saturation and shows a narrow range of degradation states across its entire surface, despite Venus being 4.5 Gyr old. Using the concepts from Lectures 05-06, explain in a short paragraph why this observation supports a discrete, relatively recent (∼300-700 Myr ago) global resurfacing event rather than either (a) a surface that has simply never been struck by many impactors, or (b) a surface that formed recently at the same time as the planet itself.
4. Simple versus Complex Crater Transition 15 points
The simple-to-complex crater transition diameter is expected to be smaller on more massive bodies (because stronger gravity more effectively collapses the initial transient cavity). Mars (g = 3.71 m/s²) has stronger surface gravity than the Moon (g = 1.62 m/s²), so gravity alone predicts Mars should have a smaller transition diameter than the Moon. Yet published values give the Moon a transition diameter of roughly 2-4 km, while Mars's is roughly 5-10 km -- larger, the opposite of the gravity-only prediction. Explain, in a short paragraph, why this is not actually a contradiction of the underlying physics.
5. Mercury’s Crater-Count Volcanic History 15 points
MESSENGER-based crater counts indicate Mercury's youngest volcanic plains are roughly 3.7-3.9 Gyr old. Using the surface-to-volume cooling argument from Lecture 04 and Mercury's small size relative to Earth and Mars, explain in a short paragraph why an early cessation of volcanism on Mercury is consistent with theoretical expectation, and state one specific piece of independent evidence (from Lecture 03 or 05) that supports the same conclusion.