Aki Roberge
April 21, 1998
Second Year Seminar Paper
Johns Hopkins University
The Planets After Formation
Cratering:
Up till now, I have discussed only endogenic processes that affect planetary surfaces, those that arise "within" the planet. I will now discuss the last important process (except weathering, which is important for the Earth, but not really for other planets), an exogenic one, acting on the planet from "outside". Not until this century were impact craters firmly identified on the Earth, though they are almost visible to the naked eye on the Moon. Craters are formed by the impact of meteorites, small, extraterrestrial solid bodies which strike the surface of the Earth. (Before striking, it is called a meteor.) They are less than 1 km in diameter; larger objects are called comets or asteroids.
A) Crater Terminology and Morphology
Primary craters are formed by the impact of the original meteorite, while secondary craters are formed by material that is thrown out from the primary crater. A primary crater has a rim of debris, grading outward into a thinner layer. All material deposited outside the primary crater is called ejecta. Powedered and melted material may be thrown out at very high speed, leaving long bright deposits called rays. The floor of a crater typically has a lens-shaped mass of breccia, rubble, and small ammounts of lava. Breccia is a rock composed of fragments of other rocks that were violently broken up, then re-consolidated. Below the lens is highly fractured bedrock; the fractures may penetrate to about 3 times the depth of the crater.
Two Types of Craters
Simple craters:
These are small and have bowl-shaped floors with raised rims. The ejecta show inverted layering, as if the material inside the crater was folded back and out, like flower petals. For these types of craters, the crater characteristics conform to a few simple formulae.
crater diameter: D
crater depth: d = 0.2*D
rim height: h = 0.04*D
crater volume: V = (PI*d/6)*[0.75*D^2 + d^2]
Complex craters:
These are larger than simple craters and have more flattened floors. Their final shape is affected by gravity; the rims may slump inward. They also may have central peaks, which are formed by material rebounding. In photos of a drop of milk falling into a cup, one may see that the milk forms into a circular rim with a splash rising up in the center. The formation of central peaks is a similar effect, only fantastically more massive.
An example of a simple crater on Earth is Barringer Meteor Crater, in Arizona. It has a diameter of 1 km, is 50,000 years old. The impactor was about 30 meters in diameter and struck with a speed of about 20 km/s. A picture of this crater is shown below.
An example of a complex crater is Yuty Crater, on Mars, shown below.
The transition between simple and complex craters scales as roughly 1/g, where g is the acceleration of gravity at the planet's surface. Thus, the transition from simple to complex craters occurs at smaller crater sizes on larger worlds.
The very largest impact structures are called basins. These are huge systems of concentric rings; the inner rings are roughly defined circles of hills, the outer rings are well-defined and may represent the true crater rim. The rings are often spaced at intervals of square root of two times the inner ring radius. (don't know the reason) An example of a basin was shown earlier, the Orientale Basin on the Moon.
Crater Scaling
The size of a crater depends on the kinetic energy of the impactor,W, the target density,p, and the material strength of both the impactor and target. For terrestrial planets, the crater diameter D is proportional to the cube root of W, and the crater depth d is proportional to (W/g)^(1/4).
B) Determining Surface Ages
Impact craters give several types of information about planets. They may expose underlying material and/or tell about the material strength of the surface. But most importantly, astronomers use their numbers to date planetary surfaces.
1) Relative dating
Planetary surfaces are bombarded by metorites over their lifetimes, slowly accumulating more and more craters. If the surface is re-made, that wipes out the craters. Thus, an old surface will have lots of craters and a young one, few craters. So, one may simply count crater densities in different areas of a world to determine the relative ages of the areas. Also, one may relatively date surface structures using the principle that younger formations overlie older ones. If N = number of craters larger than D, then ...
N = C*D^(-1.8)
The negative exponent is due to the fact there's more small craters than large ones. One counts N, then solves for C, which is proportional to the age of the surface.
2) Absolute dating
For absolute dating, one wishes to find the ages of surfaces in years, rather than just being able to say which are older than others. This requires an estimate of the flux of impactors over time, ie. how many meteorites per unit area strike per unit time. This is not well known. Also, eventualy a very old surface will reach a point when the craters are so closely spaced that new ones simply obliterate old ones. This is referred to as saturation cratering. All one can say is that the age of a surface that is saturated is greater than or equal to 4 billion years. When using craters for dating, it is also important not to count secondary craters or volcanic craters. It's not always easy to tell them apart from a distance, so one can see that using craters to date surfaces is a tricky business. But without actual surface samples, it is the only way.