Nature of a hook-like shadow observed by Wilkins and Moore on Plato’s floor

Nature of the hook-like shadow observed by Wilkins and Moore on Plato’s floor in 1952

(paper submitted to ALPO)

by Giancarlo Favero^(a), Raffaello Lena (^b), Giorgio Mengoli (^b), Alessandro Cipolat(b) and Piermario Gualdoni(b)

During the 1998 ALPO meeting held in Atlanta, Harry Jamieson read a paper by Bill O’Connell entitled "Plato’s Hook. Clementine and CCD images shed light on the shadowy mystery of a 45 year old drawing". The author commented the drawing of Plato made by H. P. Wilkins during the night of April the 3^rd, 1952 (fig.1), observing the Moon with the 83 cm refractor of Meudon Observatory. O’Connell pointed out a curved shadow, the so-called Plato’s hook, projected on the south-east portion of Plato’s floor with eastern illumination. The drawing is reported on p. 234 of the second edition of "The Moon" by Wilkins and Moore, Faber and Faber Ltd, London, 1961.

O’Connell discarded the hypothesis that Plato’s floor could be responsible of the feature, on the basis of Wilkins’s and Moore’s opinion that it is "remarkably smooth and level". In his CCD archives O’Connell found one image which – after a crude stretching – revealed a shadow with a curved tip. He concluded that Wilkins’s feature is real, but it doesn’t appear at each sunrise on Plato.

Fig. 1

H. P. Wilkins portrait of Plato drawn on April the 3^rd, 1952, at 21:30 UT, observing the Moon with the Meudon grande lunette of 83 cm (altitude of the Sun over Plato, H = 5.32°; azimuth of the Sun, A = 94.95°; co-longitude of the Sun, C = 16.48°). The hook-like shadow near the south-east wall is evident, as is the smooth general contour of the shadow on the floor.

After examination of Lunar Orbiter and Clementine images, O’Connell discarded also the possibility that a lobate flow front may be responsible of the curved shadow. As Wilkins drawing and O’Connell CCD image differ both in libration and in solar altitude, but on his opinion the hook appears on both, O’Connell concluded that the event was proven but its visibility rules were not yet understood.

Wilkins’s drawing (fig. 1) is remarkable in reporting the hook shadow, but it is not unique. A similar drawing (fig. 2), traced at the same time by P. Moore that observed with the same instrument, appeared on the booklet "Our Moon" by H. P. Wilkins, Frederick Muller Ltd, London, 1958.

Portrait of Plato drawn at the same time than fig. 1 by P. Moore, observing with the same instrument (same data as fig. 1). Features on the floor are similar, in particular the "hook", while those outside are crudely different, revealing that the authors were concerned on the floor.

Comparing the two drawings shows similarities and differences. Similar are: the elliptical shape of the walled plain (1.32:1 major to minor axis ratio); the general profile of the shadows, in particular of the hook-like one under examination; the position of four craterlets on Plato’s floor; the absence of a fifth craterlet, which was searched for, by the observers, but was not seen; the position of about twenty white spots on Plato’s floor.

The remainder of the two drawings, i.e. the features outside Plato, shows differences going from evident to crude. One can conclude, according to Wilkins’s words ("The Moon", p. 235, row 20: "Wilkins has observed the interior …") that on 3 April 1952 the observers were concerned with Plato’s floor, and completed the rest of their drawings by heart in later times.

The features similarly reported by the two expert observers on Plato’s floor show small differences, typical of the visual observations. For instance, the craterlet near the centre is placed by Wilkins at 0.45 unites of the major axis starting from east, while Moore placed it at 0.47 unites. The difference of 5% can be taken as a typical limit to the precision (standard deviation) of a visual estimate. Also the position of the hook and the general profile of the shadow on Plato’s floor appear slightly different.

The large northern maximum of the shadow reported in both drawings is nearly opposite to the hook as far as the major axis of the ellipse is concerned. This shadow displays also a peculiar orientation, its symmetry axis being directed nearly north-south. Given the light direction, nearly parallel to Plato’s major axis, that shadow should be projected by a sort of "shelf", a peak protruding horizontally toward the south from a point on the north-east wall. Therefore we have not only one, but two peculiar shadows (the "hook" and the "shelf").

Fig. 3 shows the heavily stretched CCD image by O’Connell. The shadow general profile is dissimilar from those sketched by Wilkins and Moore, because of different Sun height (5° calculated for the 1952 drawings against 3° for the CCD image) and lunar libration (Plato is less elliptical in the CCD image, 1.24:1 axis ratio).

CCD image by O’Connell showing the shadows on Plato’s floor, with peaks and valleys which create a contour considerably different from those in the previous drawings. Image taken with 8" SCT at f/20, on February 16, 1997, 1:01 UT (H = 2.97°, A = 92.37°, C = 13.00°). Following O’Connell, the tip of the southern, most elongated shadow, is bent toward south, creating the appearance of Wilkins and Moore hook-like shadows.

O’Connell proposed the identification of the 1952 hook-shaped shadow with his longer southern shadow, slightly bent on the top, even if he recognised that the position of this feature is definitely western and northern than that of Wilkins and Moore. For these same reasons we were doubtful of the O’Connell claim and extended the analysis of the problem on our archives.

In our CCD archives we found the images reported in fig. 4 to 8. In fig. 4, 5 and 6, taken with low Sun’s altitude, shadows similar to those of O’Connell are evident. The southern longest peak shows a curved northern profile, but not so much – in our opinion - to reproduce the hook. Moreover, the overall shadow profile appearing in the three images is incompatible with that of the 1952 drawings.

CCD image of Plato taken by G. Favero on 25 January 1999 at 18:21 UT (H = 2.96°, A = 92.96°, C =13.46°) with a PXL 211 camera (TC-211 sensor) fitted to a Newton of diameter 355 mm and an equivalent focal length of 16.8. The elaboration shows the profile of the shadow on Plato’s floor, which looks very similar to that one recorded by O’Connell. Just north of the tip of the southern and longest peak, the shadow of a craterlet is visible which could bent the shadow tip as in the O’Connell image. Fig. 4b shows the labelling of the shadows tip (numbers 1-9) and the position (white dot) of the relevant peak on the wall rim.

CCD image of Plato taken by G. Mengoli on 14 March 2000 at 17:56 UT (H = 5.15°, A = 98.50°, C = 19.16°) with an HX516 camera fitted to a Meade 152 mm refractor equipped with a Barlow lens 1.83X. Given the data of the Sun, the shadows should be similar to those in fig. 1 and 2. On the contrary, the shadows on Plato’s floor are similar to those of fig. 3 and 4.

CCD image of Plato taken by G. Favero on 14 March 2000 at 21:43 UT (H = 6.33°, A = 100.03°, C = 21.08°) with the same instrumentation of fig. 6. On the north-north-east part of the floor the "shelf" shadow is indicated (named "Mensola" in the frame), which is originated by the merging of the east wall shadow with a curved one cast westerly by a round hill on the Plato floor.

Fig. 6 shows also the northern peculiar shadow found in the Wilkins and Moore drawings, described by us as being attributable to a "shelf". Our image reveals that this feature comes from the fusion of the east wall shadow with the shadow of a hill located on the Plato floor, at the foot of the northern wall.

Fig. 7 displays a shadow contour different from those of the last three images, but similar to those appearing in the drawings by Wilkins and Moore. Fig. 8 shows an even closer similarity with the 1952 drawings. The solar height in fig. 7 is nearly 11° and in fig. 8 is nearly 9° over Plato’s floor, so the east shadow has lost peaks and valleys and now shows a more regular contour, probably originated from the inner wall terraces. At the foot of the southern terraces now appears an elongated and complex hill (ch in the following) whose curved shadow combines with the east wall shadow to create the hook-like feature.

CCD image of Plato taken by A. Cipolat and P. Gualdoni on 14 February 2000 at 20:30 UT (H = 10.70°, A = 104.75°, C = 27.45°) with an HX516 camera fitted to a Mewlon Takahashi of diameter 250 mm at f/12. The east wall shadow is considerably shorter than in the previous images, and its contour looks much like those reported in Wilkins’s and Moore’s drawings. A curved shadow is evident near the south-east wall, in the correct position for the Plato’s hook.

CCD image of Plato taken by G. Favero on 16 February 1997 at 20:00 UT (H = 8.90°, A = 99.99°, C = 22.62°) with the same instrumentation of fig. 4 and 6. The shadow on Plato’s floor is slightly more extended than in the previous image and its contour is similar to that one recorded by Wilkins and Moore. It is marked out a curved shadow coincident in position and shape with the Plato’s hook of fig. 1 and 2. It is created by the merging of the east wall shadow with the shadow of an elongated and complex hill on the Plato floor. Fig. 8b reports the shadows tip labels and the identification (white dot) of the complex hill (ch) responsible for the curved shadow.

An image of Plato extracted from the plate D2-a of the "Orthographic Atlas of the Moon", by Kuiper, Arthur and Whitaker, was sent us by dr. Harry Jamieson. Plate D2-a is part of plate W121, i.e. the number 121 taken at the Mt. Wilson Observatory on September 15, 1919, at 13:23 UT (H = 9.49, A = 255.53, C = 172.10). Comparing this map with our fig. 4, we estimated, as follow, the co-ordinates of the principal features under discussion.

First of all fig. 4 was rotated until the axes of the shadows on Plato’s floor appeared horizontal. The result can be seen in fig. 4b, where the shadows are labelled from 1 to 9. In this image, the peak on the eastern wall which cast a shadow and the tip of that shadow lie both on the same horizontal line.

Comparing our fig. 4, taken at the sunrise (H = 2.96°, A = 92.96°), with the Orthographic Plato image, taken at the sunset (H = 9.49°, A = 255.53°) - both under a grazing illumination - we obtained the rim profile of the eastern wall. This profile is the line separating the shadow from the light on the crater rim. The rim profile line has the same shape in the two images, because of the opposite grazing illumination. It is highly probable that the top of the peaks casting the pointed shadows recorded in fig. 4 lie on this line. The intersections between the profile line of the east wall rim and the horizontal lines defined from the shadows (as previously described) identify the most probable positions of the peaks casting the shadows.

In fig. 4b each white point indicates where a peak probably lie on the east crater wall rim. The peak top is located at the left of the white point, on the line separating the lighted surface from shadowed one.

The longest shadow, labelled 3 in fig. 4b, is the shadow that O’Connell defined "the hook" (compare with fig. 3). It is cast by the peak (which we also label 3) at the head of the mountains chain directed initially to the south-east then abruptly turning nearly 90° to the south-west.

The co-ordinates of peak 3 and those of the other eight peaks are reported in Table 1.

Co-ordinates of the complex hill (ch, vide infra) and of the nine peaks on the eastern Plato’s wall which cast the shadows 1-9 (fig. 4b) at sunrise.

Peak	eta	xi	lat. (°)	long. (°)

ch	0.7693	-0.0875	50.29	-7.87
1	0.7700	-0.0822	50.35	-7.40
2	0.7715	-0.0800	50.49	-7.22
3	0.7724	-0.0759	50.57	-6.86
4	0.7800	-0.0727	51.26	-6.67
5	0.7830	-0.0719	51.54	-6.64
6	0.7859	-0.0716	51.80	-6.65
7	0.7905	-0.0729	52.23	-6.84
8	0.7941	-0.0748	52.57	-7.07
9	0.7968	-0.0769	52.84	-7.31

Fig. 5 (H = 5.15°, A = 98.50°, C = 19.16°) shows the shadows on Plato’s floor under nearly the same lighting conditions declared for the 1952 drawings (H = 5.32°, A = 94.95°, C = 16.48). Comparing fig. 5 with figures 1- 4 ascertain that: i) in fig. 5 the shadow displays a profile similar to that of fig. 3 and 4, but is obviously less extended; ii) this shadow profile is different from those of fig. 1 and 2. It seems unlikely that shadow 3 may be the "hook" lacking any curvature.

We measured a "fractional latitude" of the "hook" on the 1952 drawings along the meridian passing through its base and intersecting the northern rim near the eastern valley filled of shadow. Assigning the zero value to the point where this meridian intersects the southern crater rim, and the 1.00 value to the point where it crosses the northern rim, the base of the hooked shadow appears centred at a "fractional latitude" 0.12 in both drawings. From fig. 5, the base of shadow 3 results located at 0.21: accounting for the precision of the visual estimates, this value is incompatible with the 1952 values. Moreover, in fig. 5 the shadow 3 don’t displays any curvature.

Inspection of fig. 7 and 8 reveals a shadow profile on the Plato’s floor much similar to that of fig. 1 and 2, the only difference is the relevance of the shadow 3 in our images. In the fig. 7 and 8, taken at H values of 10.7° and 8.9° respectively, a "hooked shadow" is evident near the foot of the Plato southern wall. In fact, this is the shadow of an ovoidal (major axis from north-east to south-west) complex hill (ch in fig. 8b, where other shadows are labelled) whose co-ordinates are reported in Table 1. The "fractional latitude" of the eastern base of the hill’s hooked shadow, measured along its meridian in fig. 8, is 0.10, comparable with the values estimated in the 1952 drawings (0.12). In the same figure the shadow 3 is well recognised, it has "fractional latitude" 0.22 and don’t show any curvature.

The hook-like shadow reported by Wilkins and Moore on their 3 April 1952 drawings is a real feature visible with an 8-11° altitude of the Sun on Plato’s floor. It is not the shadow proposed by O’Connell, which is cast by the tallest peak (3 in this paper) present on the east Plato’s wall, which don’t shows any curvature at different solar heights and is always located very far from the 1952 hook.

The hook-like shadow we suggest is originated by an elongated hill present on the Plato floor, at the foot of the south wall, which became visible when the Sun rises 8-11° over Plato’s floor. This elongated and complex hill, oriented from north-east to south-west, is well visible on fig. 9, reporting an image from Lunar Orbiter IV.

Image IV-127-H3 of the Lunar Orbiter IV taken on 20 may 1967 at 6:26 UT (H = 20,79°, A = 117.47°, C = 43.25°). It has been marked out the elongated and complex hill near the south-east wall of Plato, whose shadow is involved in the formation of the Plato’s "hook" with a Sun’s altitude of about 8-11°.

A final remark is worth to be made. The Sun altitude over Plato calculated for April the 3^rd, 1952 observation (5.32°) is incongruous with the height of the Sun producing the hook-like combined shadow observed by us (8-11°). Also the shadow extension measured on the 1952 drawings (21-22%) is incongruous with the value observed on our CCD frames (10-12%). We can only suggest that the 1952 observations were not made on April the 3^rd at 21:30 UT, but slightly later, when the altitude of the Sun over Plato was higher than 5.32°. This opinion is shared by Patrick Moore (private communication).

If we are correct, we can also explain why the hook-like shadow escaped 48 years of observations scheduled for Sun’s elevations about 5°, too early for this peculiar feature to be observable.

The authors acknowledge the contribution to the observations by Paolo Morini and Piergiovanni Salimbeni. We acknowledge H. D. Jamieson of the Association of Lunar and Planetary Observers for the software tools which allowed the calculation of the solar altitude over the Moon features to be done, for furnishing the orthographic map of Plato and for many stimulating discussions. The fundamental contribution to the paper and the encouragement of dr. Patrick Moore are gratefully acknowledged.