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# 6.26 Incidence of Craters

The longer a surface has existed in the Solar System, the more often it has been hit by interplanetary debris. By looking at different worlds, or different parts of the same world, we learn whether the surface is ancient or young, and thus whether the world is geologically dead (ancient surfaces) or geologically active (young surfaces). For example, counts of impact craters show us that Earth has the youngest surface features and greatest degree of activity, Venus has the next youngest surface, Mars is intermediate, and Mercury and our moon have ancient, dormant surfaces. Remember that we are not talking about the age of the planet in general, but the characteristic age of its visible surface features. All the planets formed 4.6 billion years ago.

Size and visual comparison of the four terrestrial planets Mercury, Venus, Earth and Mars and the terrestrial dwarf planet Ceres. Click here for original source URL

The source of craters is debris in the Solar System. Some of this material is left over from the formation process, where a large cloud of gas and dust collapsed into a disk and large rocky bodies grew by accretion to a wide range of sizes. The impact rate or cratering rate was hundreds of time higher in the first hundred million years after formation than it is now. The nature of the debris is that the size distribution is a power law, which means a logarithmic distribution in terms of sizes and numbers. Specifically, if there was one object a kilometer in diameter, there are ten objects 100 meters in diameter, a hundred objects 10 meters in diameter, a thousand objects in diameter, and so on. These are just illustrative sizes and numbers; in practice there is a smooth distribution where all sizes are represented. Now that the material of formation has been mostly "mopped up," debris is sparse, the space between planets and moons is mostly empty, and cratering rates are low. The biggest source of craters is impacts from asteroids that migrate or wander away from the asteroid belt. The gravity of the Sun means that most of them will migrate towards the inner Solar System. The second biggest source of craters is impacts with comets. Given their high speeds and potential for devastation, we can be thankful that large impacts are rare!

Counting craters leads us to revisit the idea of uncertainty in measurement. We believe that cratering is caused by an essentially random process: impacts caused by interplanetary debris. Cratering is random in time — the epoch of impact cannot be predicted. It is also random in space — the pattern of craters on a planetary surface has no pattern. In a counting experiment, the error depends on the square root of the number of events. To get an idea how counting statistics work, take a well-shuffled deck of cards and deal out thirteen cards. Consider a face card to be one type of "event" and a numbered card (including aces) to be another type of "event." You know that on average the thirteen cards should include three face cards and ten numbered cards. But what are the actual numbers in the hand you dealt? Reshuffle the deck and deal thirteen cards a number of times, each time noting the number of face cards and numbered cards. The distribution of the numbers of face cards and numbered cards is an illustration of random counting statistics.

Collage of Jupiter's moons. Click here for original source URL.

Scale model of the diameter of the planets. Click here for original source URL.