Current & recent research-      (past research)   (bibliography)

(1) Shapes of shadows in impact craters II

        My earlier work on shadows in craters, though useful (and which I and others have used), considered only three special cases of impact crater shape: parabolic, conical, and flat-floored. While many craters can be well-approximated by these shapes, I realized that parabolas and cones constitute only special cases in a continuum of  geometric shapes, the conic sections, which are more generally represented by hyperbolas and ellipses.  Substituting the more general expression for a conic section for the parabolic and conical assumptions I had made before would lead to a much more general relationship between shadow and crater, if I could work out the math connecting the two...

       And it turned out I could. Though the math was quite difficult, eventually terms cancelled out or merged together (I love when that happens!) and left some surprisingly simple equations defining how the full shapes of impact craters could be calculated from measurements of the shadows they cast. It turns out that if a crater is conic-section-shaped (elliptical, parabolic, hyperbolic, or conical), then the boundary of any shadow cast within it must be an arc of an ellipse. This 'free shadowfront ellipse' (left) can be measured, and the crater shape obtained, much easier than using other existing methods (ie. stereogrammetry, photoclinometry, altimetry).


At left are cartoons of the shadows cast in elliptical craters (a and b), a parabolic one (c), and a hyperbolic one (d).


       I have implemented the required shadow measurement and crater-shape calculation procedure into a computer program I call CRATERZ. On the left, below, are the numerical results of applying it to a well-known impact crater on the Moon, along with a plot of the shadowfront ellipse (SFE). On the right is this same result compared to results obtained by stereogrammetry using Lunar Reconnaissance Orbiter Narrow Angle Camera (LRO_NAC) imagery, and measured with the Lunar Orbiter Laser Altimeter (LOLA). All 3 results are a very close match - they differ only at the small flat crater bottom, something that is actually very easy to account for anyways.  The major difference? The CRATERZ cross section was much easier to obtain, and it comes in the form of just 3 simple numbers...


       So who cares about the shapes of  holes in the ground? Well we can tell many things about the impact processes that originally formed them, the surface processes that subsequently modify them, the properties and ages of the planetary surfaces they form on, and even the thermal environments within them (for example, whether they may contain water ice!). Here are a few of the applications of this 'free shadowfront method' (FSM) I plan to pursue:

1. Secondary vs. primary craters - Because impact crater population densities are currently our only way of estimating the ages of planetary surfaces, how many of them are primary vs. secondary (formed by impacts of secondary ejecta) has been an important and much-debated question in planetary science. One of the major problems is that we currently have no convincing way of identifying and counting all of the secondaries. I plan to compare the shapes of many primaries to those of a bunch of obvious secondaries to see if, and how, their shapes differ. This may well lead to a quantitative way of telling them apart, or at least another tool for doing so.

2. Shapes of brand new craters on Mars - By comparing imagery from a few years ago to fresh imagery, over the last few years numerous (>250) BRAND NEW (less than a few years old) impact craters have been detected forming on Mars. Obviously these are the absolute youngest, most pristine small (meters to tens of meters) impact craters we know of. They therefore represent a starting point or baseline for what the shapes of small craters are immediately after impact. But how do their shapes change with time? What processes modify them, and how, on Mars? On other worlds? Here, by measuring these fresh craters and comparing them to others on Mars, and elsewhere, I plan to address these questions.

3. Determination of a better paradigm for simple impact crater shapes -  Currently the idea that simple craters are generally close to parabolic and about 20% as deep (d) as they are in diameter (D) is deeply embedded in Planetary Science. Even the few textbooks available for Planetary Science stress these assumptions....assumptions which I have found to be rather inaccurate. In fact almost all that I have studied/measured so far on the Moon and Mercury are hyperbolic - between parabolic and cone-shaped. And their d/D values are sometimes near 0.20, but usually not. Since these assumptions are used for several important purposes in Planetary Science, a new model is called for! And I am just the man for the job.

4. A survey of mercurian and lunar simple crater shapes - Crater depth vs. diameter surveys have been used for almost 50 years in planetary science, for a variety of purposes. Currently the FSM is the only good way of determining not only the shapes of large enough populations of small, simple craters to conduct statistical surveys, but also the best way of obtaining their depths and diameters at the same time. Compiling shape and dimensions databases of these craters will in itself be useful to planetary science. But the much more interesting part will be analyzing the results for systematic variations in depth and shape versus other variables, such as surface properties, location, surface age, and many other possibilities.

5. A new, quantitative crater "degradation state" scale for estimating the relative ages of craters - Estimating the ages of things (like surfaces, craters etc...) is often central to Planetary Science, but the current way of doing this for simple craters is a totally subjective scale based on a set of "degradation state" criteria. The "sharpness" of the rim, "brightness" of ejecta, "blockiness" of the crater (in terms of boulders and rocks) are some of them. Because it is so qualitative, the criteria are so subjective, and people even use totally different ones, different researchers rarely agree with each other. If I can couple some numerical crater shape characteristics to crater age I might be able to construct a quantitative, objective means of classifying relative crater ages . . . . and I already have a good start on this!

I have more ideas, but this is already a long list . . . . .

(2) Climate coupled meteoritics on Mars

       Because it lacks a large moon to stabilize its axis of rotation, the planet Mars undergoes large, complex variations in its obliquity angle ("tilt" relative to the Sun) (first figure, below). This greatly affects how much sunlight the poles get over the course of a year (2nd figure) - the larger the obliquity, the more sun the poles get. And this in turn affects the balance between Mars' atmosphere vs. its polar caps of water and CO2 ices (see item #3, here); the greater the obliquity, the less CO2 is in the polar caps and the denser the atmosphere is, and vice versa.


Left: Note that Mars oscillates with double-amplitudes of up to about 20 degrees on timescales of ~100,000 years. Note also that until about 5 Mya its obliquity oscillated about a mean value of about 36 degrees then switched to its present state, oscillating about ~26 deg. Thus until ~5 My ago most if not all of Mars' CO2 should have been in the atmosphere, and after that it cycled numerous times between atmosphere and icecaps. At a current obliquity of ~25 deg, Mars has only small ice caps - mostly of water ice. During  recent obliquity excursions as low as ~18 degrees, Mars should have had much larger icecaps, and much less atmosphere.



Left: When Mars' obliquity switched from about an average of 36 deg to an average of about 26 deg, about 5 Mya ago, the annual solar energy incident on the poles fell by almost one third (375 ->250 Watts/m^2.








In previous work I studied the connection between Mars' atmospheric density and its meteoritic processes (see #4, 5 and 7, here). I showed that even the current martian atmosphere can easily aerobrake and land kg-sized iron meteorites on Mars, and even land ones up to a few hundred kg in mass. I also found that denser martian atmospheric conditions - ones almost sure to have often existed even within just the last few million years - should be even more effective, landing many more, and even larger iron meteorites (figure below). The next step in this project will be to couple my Mars meteoritics computer program to models of atmospheric density and estimate past meteorite production rates.  If there is enough CO2 on Mars to generate a surface pressure as much as ten times the current value, Mars may  literally be littered with iron meteorites - to the point where meteoritic iron may constitute a significant resource if/when human beings ever get there.... 


Left: Martian meteorite production (white bars) increases greatly for atmospheres 3x (20mB) and 10x (60mB) denser than today's. The numbers given are the pressure at Mars' surface, which is just a convenient way of expressing the atmospheric density in terms which are intuitively comprehensible.

     At my 5 April 2014 update of this page the rover Curiosity is approaching Mt Sharp on Mars. Mt Sharp is a 5 km tall eroding structure composed of flat layers of ancient sedimentary rock, apparently deposited by water when Mars atmosphere was much denser, and layered as they were laid down by differing processes as the climate varied. Because these rocks were laid down under a much denser atmosphere, I suspect that they are rich in iron meteorites, and because it is eroding and because iron meteorites erode much slower than rock, as the rock erodes away it should leave any irons behind on the surface. So I expect Curiosity to start encountering numbers of irons lying around when it reaches the mountain or maybe even before. I expect it will encounter further irons as it begins to ascend the mountain as well. The numbers of irons it finds might even vary, if the atmosphere was varying significantly when the rocks were formed. Of course much depends on how long any such meteorites were exposed to water after they arrived. If they were exposed to water for too long they would have been oxidized away into various iron oxides. (As of 9/2014 Curiosity HAS found at least one iron!)

And some projects I plan to do soon:

(3) Modelling the thermal/radiative environment within permanently semi-shadowed craters

     There is now ubiquitous evidence that many permanently semi-shaded craters near the poles of Mercury and the Moon contain water ice on or near their surfaces - water which represents a key resource for any future human activities on these planets. The cold-trapping and continued existence of this water depends critically on the thermal and radiative environments within these craters. In the vacuum of space, water ice has to be kept very very cold or it sublimates away. This environment can be 'modelled' by taking into account shadows and incident solar radiation, its absorption/reflection from, conduction into/out of , and re-radiation/re-absorption from - the surface. The shape of the crater plays an important role in all this, yet all the models I have seen assume an idealized parabolic or even spherical crater shape - none use actual realistic crater shapes. The parabolic model in particular has become essentially embedded in the field of Planetary Science and needs to be updated. I want to construct a model using the actual shapes of these craters, or at least a much more accurate model (obtained using the FSM - see above) and see how a more realistic crater shape favors (or doesn't favor) trapping and retention of water ice on these two planetary bodies.

(4) Impact azimuth determination from crater shape

     Another problem in cratering studies is determining the impact azimuth (the horizontal direction from which the impactor approached before impact) of an oblique (non-vertical) impacting object, especially for impact angles greater than about 15 degrees. Asymmetries in the crater shape (such as gross elongation in the direction of impact) can be used, if present, but for impact at angles greater than ~15 deg, craters are very circular, and any other asymmetries may be quite small, and dominated by the overall symmetric shape of the crater. But there are ways to get rid of the symmetric part of the crater and look only at the asymmetric part! You start by representing it's shape in the form of some set of orthogonal functions - then just drop the symmetric parts! I will try both Bessel functions and Empirical Orthogonal Functions and see what happens. I think the EOFs will have the advantage that they will be more physically meaningful. Anyways, I look forward to this particular project because it will give me a chance to do some real math again . .

(5) A Meteor Camera Network

      I also want to set up a meteor camera network. I do this already, but so far mostly as a "hobby" as I only have one camera. The idea is that there would be several meteor-activated, high-speed wide-angle, video cameras set up around the Interior Alaska area, all covering the same large area of the night sky. When a meteor triggers the cameras they would each save a video clip of the event, including the background star field. The videos could then be used to triangulate the meteor's flight path through the atmosphere, and calculations would give its orbit before encountering Earth, and predict where any pieces may have landed (if any). I have put together a single prototype of this system but would need more cameras and people to maintain them if I want to form a network. There are several such networks already operating, however interior Alaska has a number of advantages for this. including long, clear winter nights.

Anyway, here's an integrated video of a specially brilliant meteor I captured at about 0330-09nov2014:

 Note the explosive fragmentation events. They are as bright as the Moon!