Other
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufm.p31a1386c&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #P31A-1386
Other
6022 Impact Phenomena (5420, 8136), 8136 Impact Phenomena (5420, 6022)
Scientific paper
At the last LPSC meeting I presented the outline of a method for determining simple impact crater shapes from shadows. In theory the shadow cast within a simple crater provides enough information to derive its cross-sectional shape from shadow measurements, at least to the maximum depth to which the shadow extends. Under certain simple assumptions, this can be done analytically. If the crater is conic-section - shaped, then it can be shown that the down-sun bound of any shadow cast within it is elliptical, with one axis along the direction of illumination and the other (perpendicular to it) of semi-length D/2 (where D is diameter). The properties of this shadow-ellipse can be related to the parameters of the crater shape conic-section, thus measurements of the shadow-ellipse yield not only crater depth and diameter but also the approximate crater shape, in terms of conic sections. The method also does not depend upon the shadow crossing near the crater center, which avoids a pitfall of older shadow measurement methods. The technique is also amenable to computer implementation, which has already been largely completed. Once computerized, crater measurements can be made rapidly and repeatably. The program reads in an image, its resolution, and the solar elevation and azimuth. The user then defines the crater rim by 'clicking' on three points, and the shadow ellipse by clicking on two more. The program calculates and outputs the diameter, the depth, and parameters describing the crater's approximating conic-section. It is highly applicable to situations where only single-image photography is available, for example MESSENGER flybys of Mercury. At the meeting I will present the finished math for this method and give some examples of its use.
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