different shadow lengths
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Fig. 1 - The shadow indicated (a) appears significantly longer than the other astronaut's shadow. (NASA: 16mm DAC frame from Apollo 11)

One astronaut, Fig. 1(a), casts a significantly longer shadow than the other. This could happen if they were being lit by different light sources. Since the sun is the only significant source of light on the lunar surface, their shadows should be equally long. [Mary Bennett David Percy]

We can reject the multiple light source theory without too much difficulty. Notice that the astronauts are closely in line with each other with respect to the light source. A light set to illuminate one could hardly avoid also illuminating the other. This would cause each astronaut to cast two shadows, one from each light source.

Many of Bennett's and Percy's arguments are based on apparent lengths and directions of shadows cast in photographs. Their argument in this case and many others presumes a flat level surface upon which to cast shadows. The foreground of the image is darker than the background, indicating that the terrain is not at all level. The ground slopes downhill away from the camera to roughly the center of the image, then begins to slope upward again and receives more direct sunlight.

Fig. 2 - Computer-generated images of objects of identical height casting shadows of different length on an uneven surface.
With 3D graphics we can see the behavior of objects casting shadows onto variously sloping surfaces. In Fig. 2 the two cylinders are exactly the same height, but are on different sides of a shallow depression. The light source shines at a low angle from a great distance away.

The view in Fig. 2 (right) is from directly overhead and shows clearly that the shadow cast by the cylinder on the "downhill" side is distinctly longer than the other shadow. Note also that the ground exhibits exactly the same kind of variable lighting that we see in the photograph, helping confirm that this (not some mysterious extra light source) is the phenomenon at work, although we note that the variation might also be caused by the astronauts churning up darker subsurface soil.

Fig. 3 -A crude apparatus to demonstrate the theoretical principle in Fig. 2, seen here edge-on to show its construction.
Fig. 4 -The apparatus in Fig. 3 seen from approximately the same angle as the astronauts photographed from the LM in Fig. 1.
Fig. 5 -The apparatus in Fig. 3 seen from overhead.
Figs. 3-5 show a crude apparatus to test the basic optical principles described above and shown synthetically in Fig. 2. The pasteboard sheet is bent to simulate a fluctuation in terrain. This fluctuation is exaggerated compared to what is likely the case near the flag pole at the Apollo 11 landing site. In Fig. 3 the apparatus is seen edge-on to show its curvature and the lengths of the dowel pins.

It is propped up to simulate a sun elevation of approximately 10° at a time of day where the sun elevation was some 60°.

In Fig. 4 the line of sight is approximately that of Fig. 1. It can be clearly seen that the shadows are of different lengths. The dowel pin nearest the sun casts a lengthier shadow, just as the up-sun astronaut in Fig. 1 casts a lengthier shadow.

Fig. 5 is the same setup as seen from "above" -- i.e., from what would be overhead were this arranged horizontally. Here all trace of shadow distortion due to curvature vanishes, and the difference in shadow length is most apparent.

Other frames from the same film show the astronauts casting shadows of equal length as they move about. They are obviously moving toward and away from a large light source. [Mary Bennett and David Percy]

Fig. 6 - The Apollo 11 astronauts standing apart from each other. (NASA: Apollo 11 16mm DAC still frame)
Again Bennett and Percy rely heavily on their presumption that the ground is essentially flat. The shadow of someone walking around on rough terrain would also lengthen or shorten. A low sun elevation would greatly amplify such differences in shadow length.

In this case, we consider that the astronaut on the right in Fig. 1 is standing atop a small rise and the astronaut on the left is at a lower elevation, casting his shadow on mostly level ground.

We further consider that one astronaut in Fig. 6 has stepped back away from the flag while the other one has gone some distance away, probably to take photographs. He is no longer on the small rise and is now also casting a shadow onto relatively level ground.

Bennett's and Percy's argument that the shadow lengths are caused by variations in illumination angles due to a nearby (versus infinitely distant) light source would also require the shadows to diverge slightly in the second photograph. But we observe the shadows to be virtually parallel, converging slightly due to the perspective we would expect from such a camera angle. But if Bennett and Percy are correct, the distant astronaut's shadow should point farther away; the shadows should appear to diverge.

Fig. 7 - Astronauts illuminated by a nearby light. The astronaut farthest from the light will cast the longer shadow, and the shadows will diverge slightly if the astronauts are laterally displaced from the axis of illumination.
Fig. 7 shows what would happen if David Percy's hypothesis were attempted. The astronaut closer to the light would cast a short shadow compared to the one cast by the one farther away from the light. But in Fig. 1 the astronaut closer to the hypothetical light is casting the longer shadow. Clearly this cannot be caused by the divergence characteristic to a nearby light.

Fig. 8 - Two cylindrical power-tool batteries illuminated by a 75-watt PAR 32 studio lamp from a distance of 18 inches (0.5 meter).
Fig. 9 - The same objects as in Fig. 8, placed the same distance from the light but displaced perpendicular to the lighting axis. Note the extreme divergence of the shadows.
Fig. 10 - The same objects as in Fig. 9 illuminated by sunlight.
Figs. 8 and 9 demonstrate this empirically. Fig. 8 shows that the length of the shadow of the closer object is shorter. It also shows that the shadows diverge in distance. However this effect will be mitigated in a more realistic lighting design.

In Fig. 9 the objects are a similar distance from the light, but are separated laterally as theorized by Bennett and Percy to explain Fig. 6. However we can see that the shadows will appear to diverge, whereas in Fig. 6 the shadows appear to converge slightly.

In Fig. 10 the same objects are illuminated by sunlight. They appear very nearly parallel, but actually converge slightly as perspective dictates. Clearly the objects illuminated in sunlight produce shadows closer to those in Fig. 6 than objects illuminated with artificial studio lighting.

Photos of the area show it to be flat. [Mary Bennett and David Percy]

Fig. 11 - A photograph of the area in the film footage as reproduced on Aulis Publishing's web site, ostensibly to prove that the terrain is flat. (NASA: AS11-40-5905)
The authors present the photograph in Fig. 11. Their argument appears to be, "It's flat because it looks flat to us." The horizon isn't flat, but that's anywhere from a hundred feet to five miles away from the area we're interested in.

The question to ask is whether we'd see any evidence variation if it really were there. What would be sufficient evidence of terrain variation? We might expect to see variations in the lighting. Terrain less directly lit might appear darker, as we noted above. We might also look for hard-edged discontinuities that represent the crests of rises. We might also look for objects that disappear abruptly as if behind rises. We might also look for shadows that behave a bit differently than expected.

Observing some or all of these would suggest a variation in terrain. But would failing to observe them prove that the terrain was flat? No. In logic this is called the fallacy of inverse implication, encapsulated by the maxim, "Absence of evidence is not evidence of absence." Just because Bennett and Percy fail to observe any expected indicators of slope doesn't mean no such slope exists. There are cases in which the slope exists without exhibiting the most common indicators.

For this specific photo, we note little color variation, no hard-edged discontinuities. It's unclear whether the flag pole disappears behind a rise or simply into the soil.

Fig. 12 - The solar wind experiment. Its top is square and it is oriented facing the sun. (NASA: AS11-40-5873)
The shadow in the foreground is cast by the solar wind collector. As shown in Fig. 12, the collector is simply a rectangular sheet of material hung on a pole to collect particles from the solar wind. The shadow shows it was correctly deployed facing the sun as directly as possible.

Correctly aligned, the square top should cast a nearly-perfect rectangular shadow. But in the authors' proof photo we see the tip of the collector's shadow become gradually thinner, as if it were falling on a patch of ground sloping away from the camera.

The strongest evidence, however, of irregular terrain is the shadow of the flag and flagpole. They are mostly invisible in Fig. 11 (the authors' version of the photo), but we can examine it more closely in a larger image (Fig. 13).

Fig. 13 - An enlargement of the flagpole shadow area of Fig. 11. The periodic white line represents the theoretical straight line. The shadow itself is not straight, indicating a variation in terrain. (NASA: AS11-40-5873, annotation by Clavius)
The white line represents a theoretical straight line that would be the shadow cast by a perfectly straight flagpole. But it is plain that the shadow is not perfectly straight. Since Bennett and Percy cannot argue that the object casting the shadow is curved, nor can this effect be produced by artificial light sources, we have no choice but to conclude that the surface onto which this shadow is being cast is not planar.

The evidence Bennett and Percy present to establish a planar surface is ironically the best evidence of a non-planar surface. A significant and abrupt change in the angle of the lunar surface can be found in the area onto which the shadows in question are being cast. In fact, the flagpole shadow very closely resembles the simplified computer model in Fig. 2 and the empirical model in Fig. 4. When viewed from a high angle (Fig. 1) shadows cast onto non-planar terrain vary in length, but not necessarily in shape. Linear objects cast apparently linear shadows. But when viewed from a low angle (Fig. 13), such shadows display a change in shape or direction, such as we see in the proof photo. Linear objects cannot cast curved or bent shadows onto a planar surface.

The irregularity in the terrain corresponds exactly to the location in which the variations in shadow length are observed. We further note that the flagpole shadow cannot be produced by any of the hoax methods Percy has suggested, and in fact can only be produced by a lunar surface irregularity. This obvious irregularity has the shape and orientation that would produce the shadows observed in Fig. 1.

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