Past research-          (current research)      (bibliography)

 (1) Shapes of shadows in impact craters I

       I began this project in 2001 because of a need for a simple way to accurately determine the depths of simple impact craters from single-image planetary photography. The dead simple existing shadow method required the shadow to cross the crater center while other, much more sophisticated methods ( stereogrammetry, photoclinometry, altimetry) are quite involved and have their own limitations.

       I realized that the shape of a crater uniquely fixes the shape of the shadow cast within it by the Sun. The reverse is NOT generally true, however I was able to prove mathematically that if the crater is assumed to be radially symmetric (ie. it’s profile is the same along any radius) that the shape of the shadow would then uniquely fix the shape of the crater. This led me to look for a mathematical relationship between the shadow dimensions (ie. the length, which can be measured directly from imagery) to the depth of the crater (which cannot). My findings included:

[1] A circular-arc shadow-front indicates that a crater is parabolic in cross-section (below left).

[2] A crater containing an elliptical-arc shadow front is roughly conical in cross-section (below right).

 I used [1], [2] and a little algebra to derive simple equations for calculating the depths of common crater shapes (parabolic, conical), independent of how long the shadows are. This work was published in the April 2002 issue of Meteoritics and Planetary Science.


Here's a neat 'reality check':

The big dish on top of the GI (above) is, of course, parabolic. It displays perfectly the shape of the shadow in a parabola. Compare my calculation of what a shadow advancing across a parabolic depression should look like (below, left) to the reality in another dish antenna:
I have a couple of really cool ideas for practical uses for all this, if/when people ever colonize the Moon.....

(2) Terra Meridiani, Mars - "the Hematite Region"
I also worked with MS student Sharon Hansen on a project to investigate the geologic history of Terra Meridiani, Mars (here is a good background read on TM). Instruments on the Mars Global Surveyor and Mars Odyssey spacecraft had both detected the presence of gray hematite in TM, an iron oxide mineral usually formed (on Earth) in association with liquid water. Hence TM became a prime candidate for landing a Mars Rover, and an area of intense interest to the planetary science community.
      To investigate, we analysed image m0704322 taken by MOC (left). We found the imaged area consists of 2 different surface units; one darker in color and characterized by ubiquitous dunes and  very few small impact craters (Unit 2), the other lighter, with few dunes and plenty of small craters (Unit1). From 'crater counting'(!) we found that Unit 1 is older than Unit 2. We concluded that Unit 2 represents a darker sandy material (which would contain the hematite) being wind-blown over the top and across a lighter solid underlying surface, which outcrops as Unit 1. These conclusions were later proven essentially correct by Mars Rover Opportunity, which landed near here in Jan 2004. We presented this work as a poster at LPSC 2002. This was Sharon's thesis work.

(3) Obliquity-driven climate and atmospheric change on Mars

     In summer 2002 I also got involved in a study of the effects of  Mars' changing rotational and orbital motions on its atmosphere and polar caps, with REU summer student Christina Williams. Mars has seasons like the Earth, because it too is 'tilted' on its rotation axis. But because Mars does not have a large Moon to stabilize its obliquity (its tilt), Mars is subject to large (10s of degrees) and rapid (tens to hundreds of thousands of years) chaotic variations in its obliquity. When Mars’ obliquity is small, its poles get very little solar energy and much of its atmosphere of CO2 "freezes out” into polar caps; when it is large they get much more sunlight, and the CO2 icecaps evaporate into an atmosphere.

       In our study we looked at the effects of Mars' changing obliquity on the icecaps and atmosphere of Mars by modelling the energy balance at various latitudes over several martian years, for different values of obliquity. We found that the changing obliquity may rapidly switch Mars' climate between an icecap-dominated state (when obliquity < 20o) and an atmosphere-dominated state (when obliquity > 25o). Mars' obliquity is believed to change rapidly enough that it may take Mars as little as a few tens of thousands of years to switch climates like this. Currently Mars' obliquity is ~25o so it is right on the edge between the atmosphere-dominated state and the transition region between 20o and 25o. So we may be seeing Mars at a time when its climate is rapidly changing! This was Christina's REU summer student project. And though we used a pretty simple thermal-radiative model, its results agree quite closely with those of other, more sophisticated, later studies. 

(4) Atmospheric effects on impact cratering and meteoritics on Mars

    In 2004-06, partly motivated by (3) above, I conducted a detailed study of the effects that the martian atmosphere and its density variations have on impact cratering and meteorite production rates on Mars. I found that even today's thin, 6 millibar atmosphere has significant effects (below, left). Most incoming meteoroids (iron ones in the below example) penetrate straight through the atmosphere and are destroyed in crater-forming hypervelocity impacts  (the hatched area in the graphs below); but a small percentage of the smallest objects I studied are instead slowed enough to land as meteorites (the white areas). This should result in "turndowns" (deficits) in martian crater populations for craters less than a few 10s of meters in diameter (hint to the MRO team). Cratering rates are important because they are the only way we have of estimating the ages of planetary surfaces, so this deficit may therefore represent a real complication for "crater-counting" methods of surface dating at these sizes, making crater counts underestimate surface ages. In addition, these effects vary in time due to obliquity related atmospheric changes (see (3) above) and from place to place (due to altitude differences) and even seasonally (as icecaps and atmosphere expand and contract seasonally).

  Meteorites:       As noted, I found that atmospheric deceleration should also result in a scattering of small meteorites on Mars, especially irons. These irons would be especially interesting because they should be disproportionately numerous (because of their resistance to fragmentation in the air and on impact) and easy to detect, compared to other (stony) types, and may even represent a useful resource if/when humans ever go there. In addition, their rate-response to atmospheric variations should make them a useful proxy (indicator) of past martian climate conditions. Surprisingly, a few of these predicted irons could be fairly large - up to 200-300 kg according to my 2006 results.

I also found that meteorite production would be dramatically greater for plausible, denser  Mars atmospheres (<--middle and right figures). As little as 3x denser atmosphere results in large increases in iron meteorite rates (middle), and Mars should be literally strewn with them if its atmosphere has 'geologically recently' been as much as 10x denser (right).

       This work appeared in the November 2005 and October 2006 issues of the Planetary Science journal IcarusAs of 2013, the Mars Rovers have now found several iron meteorites in the 10s - 100s of kilograms range, confirming their existence and sizes, if not yet their numbers.

(5) Heat Shield Rock

       Just as I was starting to write up the publications for (4) above (2005), guess what Mars Rover Opportunity found, lying quietly next to the rover's discarded heat shield??  No, not Jimmy Hoffa...  It was actually this "basketball-sized", 50-60 kg nickel-iron meteorite!!! (left)HeatShiieldRock.jpg which someone showed off their originality by naming "Heat Shield Rock". So I whipped out the math and programming I did in (4) and showed that HSR (today officially named "Terra Meridiani"...again, very original) would be difficult, but not impossible, to explain without a denser martian atmosphere. At the time a number of planetary people had sounded off that HSR must require an ancient, denser martian atmosphere to land intact. But...  WRONG!!  I found that, while improbable and rather rare, such events could occur even today, given certain entry angle and speed conditions. Such conditions would also lead to a very shallow impact angle, which would make HSR ricochet, bounce, and roll across the martian surface. This would explain the absence of any impact pit near the meteorite, which some have also used to claim that HSR "must" be very ancient. Such a pit could be hundreds of meters away, even if HSR has just landed recently.  HSR therefore represents only strong evidence, not proof, that Mars once had a denser atmosphere, (much as I wished it did).  This work was published in 3October2006 issue of Geophysical Research Letters.

(6) A third moon of Mars??

    The double, elliptical impact feature shown below provides a lot of information about the impact event that formed it. The sizes of the craters can be used to estimate the energies of the impacts, their ellipticity and the shapes of their ejecta blankets indicate the impacts occurred at angles of less than 10 degrees above horizontal, and their orientations show that the impactors were travelling almost due west-to-east before impact. Thus the smaller object impacted about 12.5 km directly "uprange" of the smaller one, relative positioning which means that the objects were probably parts of a single object which fragmented at or near atmospheric entry, and the small fragment fell behind the large one due to differential atmospheric drag before impact.

         All of this information strongly constrains the formative impact event. I used my computer model of atmospheric entry and passage of meteoroids to try to reproduce (in a virtual sense) this event. I found that it was not even close to possible to do this if the impactor had been just a single asteroid that broke in two, even if I set various parameters all to be as favorable as possible. A double asteroid could work, but turns out to be quite unlikely since it would have to 'coincidentally' hit the surface at a very sharp angle, AND with the two asteroids oriented uprange-downrange as observed.
         But when I put in a "moonlet" in a tidally-decaying orbit the results fit the observations like a glove. The positioning of the craters and the very shallow impact angles fell right out of the simulation! Thus my conclusion to all this was that only a double asteroid or an impacting moonlet can account for this feature. Further, the impact angles and crater positions, and the prograde (west->east) direction of the impactors' trajectory, all favor a former third moon of Mars over a double asteroid as the explanation - especially since Mars does have another moon, Phobos, which is tidally decaying in just the same way and will impact in a few million years. I found that this 3rd moon would have been 1-2 km in diameter, which is quite a bit smaller than either of Mars' existing moons. Given the estimated age (from crater counts again!) of the surface it impacted, this event would have taken place less than one billion years ago (the solar system is ~4.5 billion years old). Finally, if the moonlet was in a circular, equatorial orbit - like Phobos and Deimos - when it came down (and there's reason to assume it was), then the location and direction of travel at impact require that some 40 degrees of true polar wander of Mars rotational pole must have occurred since the impact.

        Anyways, I have named this ex-moon "Lowermos", from a science fiction story I read long ago but can no longer find.....       This work appeared in the October 2008 issue of ICARUS, and inspired a poster at a Geophysical Institute April Fools day poster session....)

(7) More heavy metal on Mars . . .

      Starting in August 2009 the Mars Opportunity rover found three more iron meteorites lying on Terra Meridiani within a few hundred meters of each other (below left). The largest (and first) of these was nicknamed "Block Island". As soon as I had enough information about BI, I launched into studying it in much the same way as I previously did for HSR. As BI is considerably larger than HSR (~240 kg; or ~530lb), I expected that there would be no way Mars' current atmosphere could slow it down enough for it to survive impact. After all, Mars atmosphere today is roughly equivalent to that of the Earth...AT AND ABOVE 30km (20 mi) ALTITUDE! -- and I had shown it could barely slow even  HSR down enough.

       But once again, that is not what my calculations showed. Though it would take very special entry angle and velocity conditions, I found that Mars' modern atmosphere could in fact land even BI! It would have to enter Mars' atmosphere so shallowly that it would almost, but not quite, simply pass right through the top of it and back out into space (below). The atmosphere would then slow it down just enough to capture it, and it would then follow a very long trajectory which curves around almost parallel to Mars' surface, until finally slowed enough to fall to the ground as a meteorite. Interestingly, such a flight path means that HSR, BI, and the other two Meridiani meteorites could all be fragments of a larger object that broke up in flight - ie. a 'strewn field' of meteorites. Anyways, BI, like HSR, still does not provide definitive proof of a once-denser martian atmosphere - only the very high probability that it did once exist - though a mountain of other evidence makes it pretty certain at this point.   This work was published in  Journal of Geophysical Research-Planets, July 2010 (issue E7)