The Strolling Astronomer

Feature Story: Concentric

By Howard Eskildsen, [email protected] Online Readers Left-click your mouse on the e-mail address in blue text to contact the author of this article, and selected references also in blue text at the end of this paper for more information there. This paper by ALPO member and astrophotographer Howard Eskidsen is only one of many that ratios were calculated using Lunar averaged 0.065, much shallower than were presented at ALCon 2013, Reconnaissance Orbiter data. Crater the T/D ratio of 0.20 that is typical for held in Atlanta, Georgia. coordinates were reproducible to within non-concentric craters. Mean crater rim 0.02°. Outer rim diameters (D) ranged elevations were below the mean lunar Abstract from 2.3km to 24.2 km with the mean radius of 1737.4 km with the mean 1.5 8.2 km with error of ± 0.2 km. Inner km lower than the mean lunar radius. Fifty-five concentric caters were toroid rim diameters (T) averaged 4.3 identified and measured for diameter, km, and calculated toroid to diameter depth, toroid crest diameter, ratios (T/D ratio) averaged 0.51. The d/ coordinates, and depth/diameter (d/D) D ratios for the concentric craters

Table 1: Eastern Hemisphere Diameter Data

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Table 1A: Eastern Hemisphere Elevation/Depth Data

Concentric Craters pure highland areas. None are found in While the most notable concentrics have A small percentage of craters that would the central maria (Wood 1978). Their rounded, doughnut-like toroids, others normally fall in the classification of ages range from Pre-Imbrian (>3.85 Ga) have flattened inner mounds, and a few simple craters show a curious inner ring to Eratosthenian (1.1-3.2 Ga), with most have sharp inner rims. The space or (torus or toroid) that averages about 50% of the craters being of Imbrian age (3.2- moat between the inner and outer rims of the diameter of the outer ring (Wood, 3.85 Ga). Notably, however, no varies in appearance, and a few have 1978). The crater sizes range from 2-20 Copernican age (<1.1 Ga) craters are confluent lobes of rubble that may give km outer diameter with an average outer known to exist on the (Trang et al., the appearance of another ring between diameter around 8 km, though most fall 2011). inner and out rings when viewed at low within the 2-12 km diameter size. (Note resolution. sub-kilometer “bench” craters and multi- Most, but not all, of the toroid rims are ringed basins are not being considered in concentric with the outer crater rims and Chuck Wood in his 1978 paper describes this paper). They also tend to be the ratio of the toroid diameter (T) to the several variations of morphology. Most shallower in depth than normal craters of outer crater rim diameter (D) range from common are typified by Hesiodius A with similar size which would be expected to 0.2 to 0.9 (T/D ratio). Most of the T/D the usual characteristics described above. have a depth (d) to diameter (D) ratio ratios range from 0.3 to 0.6 and average Marth was described as appearing like a around 0.2 (Trang et al., 2011). 0.5. While the outer rim margins cratered dome. Some craters have craters this size are normally slightly elliptical inner and outer rings as typified Concentrics have a non-uniform concave, the outer margins of the toroid by the crater in Struve, while others have distribution over the moon that is similar tends to be slightly convex and the area a round outer ring and elliptical toroid to the distribution floor-fractured craters. inside the torus is usually concave (Wood, such as H, which is also off Seventy percent of them are found on 1979). center from outer ring. Craters such as the margins of maria, 20% in the smooth Gruithuisen K have raised, rubbly moat floors of -flooded crater, and 10% in area that resembles a third ring. A few

Volume 56, No. 1, Winter 2014 Page 37 The Strolling Astronomer craters are fractured and cracked, highly concentric craters. Exogenic hypotheses Endogenic formation hypotheses include worn such as the concentric craters near include a fortuitous double impact either successive eruptions from same vent, Mons Jura, and have been described as nearly simultaneously by tidally spilt symmetrical collapse of the outer rim, or having “bread crust” appearing interior. object, a second smaller impact cratering into extrusive domes. Another Garbart J is shown to have an inner rim sometime later than the initial impact, or endogenic hypothesis involves volcanic modification of existing craters by that is low and inconspicuous while an impact into a layered target. distortion from intrusion of laccoliths Chamberlain was described as having a Exogenic origins seem unlikely due to the below the surface or by extrusion of lava high concentric “collar”, but on LROC non-uniform distribution of the craters, above the surface (Wöhler and Lena, images looks as if it could possibly be a due to the presence of non-concentric 2009) due to separate impacts. craters in proximity to concentrics, and also due the lack of Copernican-age Any hypothesis for concentric crater Various mechanisms have been proposed concentric craters (Trang, 2010). formation must account for the to explain the formation of the following:

Table 2: Western Hemisphere Diameter Data

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• The non-uniform distribution of the • Spectroscopic studies showing the described by Wohler and Lena (2011): concentric craters interior composition to be very simi- “At the bottom of the transient cavity, lar to the surrounding terrain. however, the flexural rigidity of the • The lack of Copernican age craters. overburden and the overburden weight Of the various hypotheses, volcanic per unit area were reduced to 30% and • Presence of normal non-concentric modification of the crater appears to be 61% of their original values, respectively, craters of younger age in close prox- most likely candidate, and spectral according to the relations given in [4,10]. imity to some of the concentric cra- studies support the intrusive model. If the impact occurred during the magma ters. Trang (2011) describes the process: “The intrusion phase, the thinned part of the idea suggests that dikes have propagated overburden was probably unable to resist • Presence of ejecta blanket remnants into impact-induced fractures producing the pressurized magma, which in turn around several of the concentric cra- a laccolith. The laccolith grows, uplifting may have lifted up the crater floor, thus ters. the crater floor. The inner torus is leading to the shallow crater depth. In created either because impact melt in the this line of thought, the inner depression • 5. Shallow depth compared to simi- center of the crater is inhibiting uplift or of the concentric crater is a remnant of lar non-concentric craters the floor relative to the sides, or inflation the original bowl-shaped crater floor.” is followed by a large deflation or collapse.” The process is further

Table 2A: Western Hemisphere Elevation/Depth Data

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Purpose of current study described earlier by Chuck Wood, but was subject to cylindrical distortion.) was not in his original paper. Elevation plots were obtained from query The current study was undertaken to use paths drawn across the center of the LROC data to obtain high resolution Methods crater (one from west to east and the images, to determine coordinates of the other from north to south) that extended crater centers, measure the diameters of The craters were located on the LROC well beyond the outer crater rim, and the outer rim crests (D) and toroid rim ACT-REACT QuickMap, the coordinates elevation profiles were obtained from the crests (T), and the crater depths (d). The of the apparent center of the craters Query Results box. Four rim elevation toroid/crater diameter (T/D) ratio and recorded and the diameters and depths data points were obtained and two the dept (d)/diameter (D) ratios were measured and recorded. The diameter central crater elevation points were calculated from the measured data. measurements were made by placing the obtained. The deepest central crater QuickMap cursor over one rim crest and elevation was subtracted from the mean Craters studied included the concentrics tracing a line (query path) through the of the rim elevation to determine the listed by Chuck Wood in 1978, most of center of the crater to the crest of the crater depth. the other craters listed in the http://the- opposite side of the rim and reading the moon.wikispaces.com/ geodetic distance from the Path Query Eastern hemisphere diameter Concentric+Crater website (Wood et al., box. In some cases, where parts of the measurements and calculations are listed 2007), and a few other concentric rim were obliterated in the desired area in Table 1 and elevation measurements craters discovered by internet search. of measurement, the diameters were and crater depth calculations are One concentric, E, was measured from northwest to southeast presented in Table 1A. Corresponding accidently “discovered” while measuring and from northeast to southwest and the western hemisphere measurements are another concentric; the “discovered” averages taken. (Note: Geodetic distance listed in Table 2 and Table 2A. Depth/ concentric, as usual, had already been was used since the cartographic distance diameter ratio and toroid diameter/crater

Table 3: Eastern Hemisphere Depth/Diameter and Toroid Ratio Calculations

Page 40 Volume 56, No. 1, Winter 2014 The Strolling Astronomer diameter ratios are listed in Table 3 for measured a third and fourth time, and touch up of brightness and contrast was the eastern hemisphere and Table 3A for corrections were made as needed. The done as well, and then the photo the western hemisphere. coordinates were also cross-checked with cropped to desired size. In order to cross Chuck Wood’s measurement and any check the coordinates, all of the craters All measurements were entered into discrepancies were again measured. were located on the Image Map by Excel spreadsheet and calculations done entering the coordinates from the using the spreadsheet formulas. Once all Images were obtained from LROC WMS spreadsheet into the latitude and the data had been assembled and Image Map set at the highest possible longitude boxes in the Map Options box. calculations done, each measurement resolution of the orthographic projection, Only one was found to be in error which was repeated. Any positional error and a final image was assembled from was exactly one degree, and that was greater than 0.02 degrees and any four frames centered on the concentric corrected. (See tables 1, 1A, 2, 2A, 3 diameter error greater than 0.2km was using Photoshop Elements 6. Some and 3A.)

Table 3A: Western Hemisphere Depth/Diameter and Toroid Ratio Calculations

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Graph A: Diameter Distribution

Graph B: Toroid/Diameter Ratios

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Graph C: Depth/Diameter (d/D) Ratio Distribution

Graph D: Mean Lunar Elevation of Crater Rims

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Discussion (Crozier H) while the lowest rim elevation References was recorded in the South Pole-Aitkins Of 57 concentric craters listed on various Basin at a depth of -6.3 km (near Albers, S., 2005. Jens Meyer Moon articles and websites, 55 were measured Minkowski). The elevation distribution is Map, URL: http://www.lpod.org/ ?m=20060827 http://laps.noaa.gov/ for rim elevation and diameter, toroid consistent with the distribution of the albers/sos/sos.html ( diameter, and depth. Depth/diameter majority of the craters along the margins last date accessed: 11 July 2013). calculations from those data were of maria which are mostly on the near accurate to two significant figures, and side of the moon. (See Graph D.) the coordinates for their location were Eskildsen, H., Lena, R., 2011. Humboldt: Concentric Crater and LPDs. within ±0.02°. Two of the initially listed Selenology Today 25, pp. 1-16. craters (29 and 57) could not be verified Conclusion as concentric craters and were excluded Images of concentric craters from the Eskildsen, Howard, 2013. Archytas G from calculations, while seven others (6, LROC WMS Map and measurements Concentric Crater. Selenology Today 19, 36, 37, 40, 48, and 49) were from the LROC ACT-REACT QuickMap 31, pp. 25-28. URL: http://www.lunar- included in the calculations, but could were used to measure crater coordinates, captures.com//Selenologists/ possibly be something other than a crater rim (D) and toroid (T) diameters, selenologytoday31.pdf concentric crater. and T/D rations crater rim elevation and crater depths (d) were measured, and Trang, D., 2010. The Origin of Lunar The 55 craters measured had an average used to calculate d/D ratios of each of Concentric Craters. 2010 GSA Denver diameter of 8.2 km with nearly half of the selected concentric craters using the Annual Meeting. the craters (27) measuring between 4km latest data available from the Lunar and 8km. All of the craters were greater Reconnaissance Orbiter. Trang, D., Gillis-Davis J., Hawke, B., than 2 km diameter, but only 6 craters Bussey, D., 2011. The Origin of Lunar Concentric Craters. 42nd Lunar and were greater than 12 km. The largest The mean rim diameter of 8.2 km is Planetary Science Conference. concentric measured 24.2km; this within limits of error of Wood’s (1978) skewed the mean to the right. (See mean of 8.3km, while the mean T/D Wöhler, C and Lena, R., 2009. The Graph A.) ratio of 4.3 is slightly lower his ratio Lunar Concentric Crater Archytas G ~0.5. Several of the concentrics had Associated with an Intrusive Dome. The mean toroid diameter was 4.3km indistinct and irregular toroid margins Lunar and Planetary Science and the mean toroid/diameter (T/D) that added uncertainty to their Conference XXXX. Abstract1091, The ratio was 0.51. All were between 0.2 measurements. Woodlands, Texas. URL: http:// and 0.8; only one crater had a ratio www.lpi.usra.edu/meetings/lpsc2009/ smaller than 0.3, and three craters had Measurements of crater rim elevations pdf/1091.pdf T/D ratios greater than 0.7. (See Graph and depth allowed the d/D ratios to be B.) calculated to two significant figures. The Wood, C.A., 1978. Lunar Concentric mean d/D was 0.065 which is Craters. Lunar and Planetary Science Conference IX, pp.1,264-1,266. Depth/Diameter (d/D) ratios were considerably shallower than the d/D ratio considerably shallower than would be of ~0.2 for ordinary craters of similar expected from a typical crater of the size. This suggests that modification of Wood, C., 2004. Concentric Craters LPOD June 23, 2004, URL: http:// same size as the concentric craters. the interiors of the craters occurred after www.lpod.org/archive/archive/2004/06/ Normally a d/D ratio of 0.2 would be formation and is consistent with the LPOD-2004-06-23.htm (last date expected, but the mean d/D of the currently favored hypothesis of igneous accessed: 11 July 2013). concentrics measured was 0.065 with intrusion for the origin of concentric only seven craters with a d/D ratio craters. However, it is possible that not Wood, C., 2006. Concentric Craters, greater than 0.10. The deepest all of the concentric craters formed in URL: http://www.lpod.org/?m=20060827 concentric crater had a d/D of 0.156. that manner. For example, the (last date accessed: 11 July 2013). (See Graph C.) concentric crater near Chamberlin looks very much like a fortuitous second Wood, C., Caes, D., Mosher, J., Moore, Thirty-seven of the 55 craters measured smaller impact within an older crater. J., 2007. Concentric Craters, URL: http:/ had rim elevations between 0.5km and /the-moon.wikispaces.com/ Concentric+Crater 2.5km below the lunar mean radius of There is much more to be learned about , (last date 1737.4 km (per LROC ACT REACT these fascinating craters by more detailed accessed: 11 July 2013). QuickMap), with a distribution peak in study of each individual crater and their the -1.5 to -2.0 km elevation range. The context to further characterize their highest mean crater rim elevation was morphologies and from spectral analysis 0.627km above the mean lunar radius of their interiors and surroundings.

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