Introduction

    Two papers that recently appeared in this Journal proposed that the hook-like shadow on the floor of the lunar crater Plato drawn by Wilkins and Moore on April 3, 1952, is projected by a complex and elongated hill lying on Plato’s floor (Favero, Lena, et al, 2000; Favero, Lena, et al, 2001). The authors reported that the shadow cast by Plato’s Gamma Peak never displays significant curvature when the solar elevation (H) is between 3° and 8°. In response to this, Braga and Ferri argued in a letter to J.A.L.P.O. that the "hook" is the Gamma Peak’s shadow, which in some instances appears slightly curved at low sun (Braga and Ferri, 2001). They included a fuzzy video image by Sorrentino in which the shadow cast by Plato Gamma shows curvature (image taken with an f/10 SCT of F = 200 mm, on February 13, 2000, at H = 4.14 ° and colongitude (C) = 16.7°). We think that this fuzzy image of Plato is insufficient evidence to prove that the Gamma Peak’s shadow may display any curvature. To show that the curvature is not due to chance (for example, deformation by the seeing), an independent and contemporaneous image by at least one other observer should have been obtained. Recently, Sorrentino proposed two computed dates (March 22, 2002, at 19:46 UT and May 20, 2002, at 20:11 UT) when the solar illumination would reproduce conditions suitable for detecting Plato Gamma’s shadow curvature (Sorrentino, 2002). To study the possible causes of the aspect of the Gamma Peak’s shadow described by Braga and Ferri, we imaged Plato and its surroundings exactly at the two times computed by Sorrentino, using web-cams and CCD cameras fitted to different telescopes.
 

Instruments and Measures

    This report is based on an analysis of a number of visual observations and images taken on the computed dates and sent to us. We strongly encouraged observers to participate in organized, simultaneous observations. This effort by observers significantly reinforces the level of confidence we have in our data for each date. A synchronized time signal was used in order to assure accurate timing of the observations. For each observation, we calculated the solar altitude, azimuth (A), and colongitude as seen from Plato, using the Lunar Observer's Tool Kit software by Harry Jamieson.
    Table 1 lists the 11 observers, their instruments, and the dates and times of the 13 observations they supplied.
Table 1

Contributing observers and instruments for computed dates, where (a) is March 22, 2002 and (b) is May 20, 2002
 

contributing  observers	telescope  D e F/D	type	Number of submitted reports	date and time (UT)
Bares A.	Newton  250 mm f/12	CCD	1 (b)	(b) 19:56-21:00
Basso S.	SC  200 mm f/10	Web-cam	1 (b)	(b) 20:20-20:28
Di Iorio G.	SC 200 mm f/10	CCD	1 (b)	(b) 20:02-21:35
Fattinnanzi C.	Newton  200 mm f/6	Web-cam	1 (b)	(b) 19:31-20:14
Fazzo M.	SC 275 mm f/10	Web-cam	1 (b)	(b) 19:50-21:14
Lena R.	Refractor 100 mm f/15	Visual	2 (a-b)	(a) 19:40-19:50 (b) 19:45-21:20
Martina S. Ferrero G.	SC 200 mm f/10	Web-cam	1 (a)	(a) 19:46
Mengoli G.	SC 250 mm f/10	CCD	1 (a)	(a) 18:10 -18:50
Moroni P.	SC 200 mm f/10	Web-cam	2 (a-b)	(a) 19.38-19:44 (b) 20:10-20:12
Padulosi F.	MK 90 mm f/14	Web-cam	1 (b)	(b) 20:03-20:28
Porta R.	SC 250 mm f/6	Visual	1 (b)	(b) 19:50-20:25

Results

    On both dates, the visual observers found no curvature in the shadow of Gamma Peak.
    We received March 22 images from three observers, and May 20 images from seven observers (Table 1). Because of the plentiful simultaneous observations on the latter date, we analyzed the curvature of the Gamma Peak's shadow on each of the approximately 200 images taken on that date. We report the results in Table 2. In every instance when curvature was detected, as enumerated in Table 2, there was no confirmation of the curvature by a simultaneous observation by an independent observer.
    Examples of images.  Figures 1 through 7 are oriented with north at the top and IAU west at the left. Figures 8 and 9 are oriented with north at the right and west at the top. Seeing is reported using the Antoniadi Scale.
Table 2 Distribution of Gamma Peak shadow’s curvature (%).
 
 
 

linear	curved toward South	curved North
74 %	18% (*)	8 % (*)

(*) The Gamma Peak shadow curvature toward south and toward north was not confirmed by simultaneous and independent records.

Images of March 22, 2002.  Figure 1 displays the Gamma Peak’s shadow slightly curved. This is one of the many images obtained under poor seeing conditions. Figure 2 is a contemporaneous image made in better seeing conditions with nearly identical instrumentation by summing 20 times as many frames. In it, the Gamma Peak’s shadow doesn’t display any significant curvature. Figure 3 was taken about an hour before Figures 1 and 2, and it shows no curvature.
 
 

figure 1
 
 
 

figure 2
 
 
 

figure 3

Images of May 20, 2002.  Figure 4 shows curvature in the shadow of the Gamma Peak. Figure 5 is one of several images taken by several other observers at the same time as Figure 4 but under better seeing conditions, and it shows no curvature. Figure 6 displays slight curvature of the Gamma Peak’s shadow. Figure 7 is one of many images contemporaneous with Figure 6, but obtained under better seeing conditions, that show no curvature.
 
 

Figure 4 and 5
 
 
 

Figure 6 and 7

 Two excellent sequences were taken on May 20 with a CCD camera, and are presented here as Figures 8 and 9. Most of the images in these sequences show no curvature, but in a few of the images a slight curvature is seen. The concavity was sometimes toward the south (Figure 8, image at 19:57:07) and sometimes toward the north (Figure 8, image at 19:57:41). Figure 9 shows one image per second. The shadow of the Gamma Peak can be seen to vary slightly in form from image to image. In particular, images with crisper detail show a straighter shadow.
 
 
 

Figure 8

Figure 9

Discussion

    Observing Plato at the times when a curved appearance should have been detectable (Sorrentino, 2002), we were unable to demonstrate any curvature in the Gamma Peak’s shadow. All our results confirm that any curvature detectable in our images lasts only small intervals of time and is related to seeing-induced defocusing and deformations. Because of these fluctuations, curvature in any of the images must be considered to be spurious.
    This interpretation of the shadow's curvature should be applied to any images obtained at comparable H and A, such as the Gamma Peak’s shadow's curvature seen in the fuzzy image included in the article by Braga and Ferri.
    It is significant that visual observations carried out on the two dates by two observers (Table 1) confirmed that brief seeing-related curvature of the shadow as seen in the images does not produce the subjective visual impression of curvature. This suggests that there is no relation of the hook as seen by Wilkins and Moore to any curvature that shows up on images taken during moments of poor seeing. These two expert visual observers could have easily taken into account the effects of seeing during their observation, and would have reported this information in their drawings or comments. They recorded no such caveat.  By implication, then, the shadow of the Gamma Peak is not the hook.
    Our results show that imaging techniques are more susceptible to the recording of seeing-related artefacts than is visual observing. This has broad implications for amateur astronomers in an age when imaging is considered to yield definitive data.

Acknowledgement

The authors are grateful to the eleven observers whose interest, cooperation, and skill made this study possible.

Figures enclosed
Figure 1) Image taken by S. Martina and G. Ferrero on 22  March 2002 at 19:46 UT (H = 3.46°, A = 96.82°, C = 16.80°) with a webcam Philips ToUcam fitted to a Schmidt-Cassegrain 200 mm f/10. It is the sum of 20 frames (Astrostack ) taken from 2 records of 15 seconds. Seeing IV-V Antoniadi scale.

Figure 2) Image taken by P. Moroni on 22  March 2002 at 19: 38-19:44 UT (H = 3.45°, A = 96.81°, C = 16.78°). with a webcam Vesta Pro Philips fitted to a Schmidt-Cassegrain 200 mm f/10 equipped with a Barlow lens 2X and IR-blocking filter. It is the sum of 400 frames (Iris 3.6). Seeing III Antoniadi Scale. Given the data of the Sun, the shadows should be similar to those in fig. 1. On the contrary, the shadow of the Gamma peak is similar to the shadow of fig. 3.

Figure 3) CCD image of Plato taken by G. Mengoli on 22  March 2002 at 18:40 UT (H = 3.12°, A = 96.38°, C = 16.24°) with an HX516 camera fitted to a Schmidt-Cassegrain 250 mm f/10 equipped with a Barlow lens 1.83X. The shadow of the Gamma peak is similar of the shadow reported in fig. 2.

Figure 4) CCD images  of Plato taken by A. Bares on 20  May   2002 at 20:11 UT UT  (H = 4.24°, A = 96.21°, C = 16.79°)  with an HX516 camera fitted to a Mewlon Takahashi of diameter 250 mm at f/12.  Seeing IV Antoniadi scale.

Figure 5) CCD images  of Plato taken by C. Fattinnanzi on 20  May   2002 at 20:11 UT  (H = 4.24°, A = 96.21°, C = 16.79°) with a Vesta Pro webcam fitted to a Newton  of diameter 200 mm at f/6.  Seeing III Antoniadi scale.

Figure 6) Image taken by  M. Fazzo  on 20  May  2002 at 20:09  UT (H = 4.23°, A = 96.19°, C = 16.78°) with a webcam Vesta Pro  fitted to a Schmidt-Cassegrain 275  mm f/10. Seeing III Antoniadi scale.

Figure 7) CCD images  of Plato taken by A. Bares on 20  May   2002 at 20:09 UT (H = 4.23°, A = 96.19°, C = 16.78°)  with an HX516 camera fitted to a Mewlon Takahashi of diameter 250 mm at f/12.  Seeing III Antoniadi scale.

Figure 8) CCD images  of Plato taken by A. Bares on 20  May   2002 at 19:57,00- 19:57,41 UT  (H = 4.17°, A = 96.12°, C = 16.68°) with an HX516 camera fitted to a Mewlon Takahashi of diameter 250 mm at f/12.  Seeing II-IV Antoniadi scale. The effect of the seeing is well evident.

Figure 9) CCD images  of Plato taken by A. Bares on 20  May   2002 at 19:58- 20:13 UT  (H = 4.17°-4.25°, A = 96.12°-96.22°, C = 16.68°-16.81°) with an HX516 camera fitted to a Mewlon Takahashi of diameter 250 mm at f/12.  Seeing II-IV Antoniadi scale. The effect of the seeing is well evident.
 
 
 
 

References

Braga R., Ferri F. (2001) "Plato's Hook: still an open problem." J.A.L.P.O., 44(1): 12-14.

Favero G., Lena R., Lottero F., Fiaschi M. (2001) "The nature of the hook-like shadow on Plato's floor observed by Wilkins and Moore in 1952 - Part II. Simulations with a computer and a plasticine model." J.A.L.P.O., 43(3): 24-29.

Favero G., Lena R., Mengoli G., Cipolat A., Gualdoni P. (2000) "The nature of the hook-like shadow observed by Wilkins and Moore on Plato's floor in 1952." J.A.L.P.O., 42(3): 126-132.