111 Astronomy Lab Manual
Fall 2004
Scaling of Splash Craters and Ejecta Trajectories
Introduction
The surface of many bodies in our solar system exhibit evidence for impact craters. Some surfaces, like portions of the Moon appear saturated with craters, that is the craters are so closely packed that some craters lie on top of areas previously covered by craters. Other bodies, like Io and Europa have few if any craters. The variations must be caused by differences in the cratering rate and by processes which remove craters (such as erosion, plate tectonics or lava flows) or prevent the formation of some craters (such as an atmosphere). On most bodies, there are fewer large craters than small craters. This can be quantified with a size frequency distribution which measures the number of craters as a function of crater diameter. The easiest thing to measure from an image of a distant crater is its diameter. However, the relation between the diameter of a crater and the size of the meteor that made it is not necessarily simple. The diameter of a crater could also depend on the impact velocity, v, and mass, m, of the impactor. We might expect the diameter to depend primarily on the kinetic energy, E=mv2, of the meteor. It could also depend on the inclination of the trajectory. Crater morphology also is expected to depend on the geological composition and structure of the substrate and a host of other factors. Phoebe, moon of Saturn, delivers on its promise to reveal new wonders to the Cassini spacecraft by showing probable evidence of an ice-rich body overlain with a thin layer of dark material. The sharply-defined crater at above center exhibits two or more layers of alternating bright and dark material. Imaging scientists on the Cassini mission have hypothesized that the layering might occur during the crater formation, when ejecta thrown out from the crater buries the pre-existing surface that was itself covered by a relatively thin, dark deposit over an icy mantle. The lower thin dark layer on the crater wall appears to define the base of the ejecta blanket. The ejecta blanket itself appears to be mantled by a more recent dark surface lag. The image also shows streaks, which would have been formed as loose fragments from impact ejecta slipped down the slope of the crater. This image was obtained on June, 11 2004 at a phase, or Sun-Phoebe-spacecraft, angle of 79 degrees, and from a distance of 13,377 kilometers. Photo and caption credit NASA and the CassiniHuygens mission.
Astronomy 111 Lab Manual
Fall 2004
1. Scaling laws
On the moon and other bodies, scaling laws have been derived relating the diameter of a crater to the energy, radius and angle of the impacting meteoroid. These scaling laws are often based on experiments on earth mimicking the formation of craters. The advantage of using an experiment is that you can know in advance the properties of the impactor (velocity, angle, mass) and you can control the properties of your substrate. 1. By dropping a heavy object into the tub of salt, measure a crater diameter and depth. What is the approximate shape of the crater? Does it have a raised edge? Can you see any evidence for ejected material? Estimate about how much larger the crater diameter is than your impactor. On the moon and Earth, crater diameters are about 10 times larger than the meteors that formed them. Compare your value to that estimated for the Moon and Earth. Drop your heavy object from different heights. How does crater diameter and depth depend on the height that you dropped the heavy object? How does the crater diameter depend on impactor kinetic energy? Does the crater shape depend on the angle of the impactor trajectory?
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The trajectories of ejected material
The ejecta of craters differ in its morphology on different planetary objects. For example, on the moon, the ejecta is made of pieces of rock and so can show rays. On Mars, sometimes the ejecta behave like a fluid, possibly due to volatile chemicals in the ground. This slightly oblique Hasselblad photograph, taken from Apollo 17, of the moon, is an excellent of view a small, very young impact crater. Slightly less than 3 km in diameter, it is located on the west flank of the large crater Gagarin on the lunar far side. The youthfulness of this small crater is illustrated by its sharply defined rim crest; by its bright continuous blanket of ejecta extending outward for 1 to 2 crater diameters; and, most particularly, by its exceptionally welldeveloped radial pattern of bright rays. The rays consist of narrow, diffuse streaks and shorter bright spots. They are formed when ejected material from the impact site is redeposited as projectiles in the form of discrete blocks and clusters of disaggregated debris. The brightening is probably caused by the shock effects on the rock that was excavated from the impact site and deposited onto the older, darker surface materials. Material ejected at earlier times may be traveling at different speeds and angles compared to material ejected at later times. Material ejected at different times could originate from different geological depths in the rock. For example, the figure below shows a manmade impact crater at different times after impact, showing that the angle of the ejecta is a function of time since impact.
Astronomy 111 Lab Manual
Fall 2004
Procedure for Freeze frame filming:
By lighting the tub of salt very brightly, we can force the camcorder to take very short exposure images. The camcorder (in movie mode) will take an image every 1/30th of a second. If the exposure of each individual image in the movie short then the camcorder behaves like a strobe camera, taking a freeze frame image very 1/30th of a second. The exposure time of each image for our camcorder can be a minimum of 1/8000th of a second long. This is so short that objects will appear to be frozen even though they are actually still moving. Connect the fire-wire to the computer and turn on the camcorder. The computer should detect the camcorder as new hardware. Using the software windows movie-maker. Under record or video settings, change the setting to Digital Device Format DV-AVI for highest quality video. To make the camera freeze frame or strobe, you need to have the tub well lit and you need to force the camera to take very short exposures. Follow instructions on page 37 of the camcorder manual. Set the [AUTO/MANUAL/FOCUS] switch on the Camcorder to MANUAL. The [MNL] indication appears. Press the [ENTER] button until the shutter speed indication appears (press twice). Us...