Know all the Angles

Any Sun angles displaying virtually double what should have been recorded at a specific location on a specific date are totally impossible, so we are left with no other alternative than to conclude that here are more examples of a Whistle Blower's subtle manipulation of shadow length in order to encode the data that reveals the hoax.

Dark Moon, p. 23

Contrary to what David Percy says, there are other ways to alter a shadow besides blowing on it.

As we shall see, it's extremely rare for a photograph--terrestrial or lunar--to show a shadow of the proper length. For example, during the Apollo 11 EVA, the sun's angle was between 13 and 15 degrees, which means the astronauts cast shadows with lengths four times their height. Yet this annotated picture from Dark Moon has a shadow that seemingly shows a sun angle of 26 degrees:

Annotated version of NASA AS11-40-5872 (DM, ch. 1, ill. 23)

Since Aldrin's shadow goes off the picture, it's tempting to suspect that David Percy ended his line a little too soon. He didn't. If you look at a higher-resolution version of AS11-40-5872, you will see that all the shadows show nearly the same steep sun angle.

Neil Armstrong waiting for Buzz Aldrin, Apollo 11 MET 109:38 (DM ch. 1, ill. 24) Because short shadows are the rule and not the exception, Percy had no problem finding more examples. This TV image (right) does show an astronaut's full shadow, and it is clearly not four times longer than Neil Armstrong is tall. (I could not find a link to this clip on the ALSJ, but I'm pretty sure it shows Neil Armstrong at Mission Elapsed Time at 109:38, shortly after he collected the contingency sample and was waiting for Buzz Aldrin to emerge from the LM.)

David Percy drew the diagonal correctly, but he made one small mistake: he assumed it meant something.

Drawing a line from top of head to tip of shadow will give you a true sun angle if, and only if, the shadow was photographed broadside-on. View it from any other angle and the shadow will be foreshortened (that perspective thing again), and the results will be utterly meaningless.

Demo of varying sun angles within a picture

The posts' shadows in the above scene were pointing in the same direction and had the same length, but that was not how the camera saw them. If we're going to find the sun's height from the apparent shadow length, we first need to find out where the shadow is pointing, and by how much.

So let's do it. Let's see if the angle at which Neil Armstrong took AS11-40-5872 really will give the kind of shadow we saw on Buzz Aldrin. And let's see if that foreshortened shadow length really will match a 14° sun angle.

This partial map (which you can find over here or on page 35 of Dark Moon) shows the relative positions of Armstrong, Aldrin, and their cameras. The shadows were pointing nearly due west (give or take a couple of degrees). But the cameras were aimed either southeast or northeast.

Annotated map of the Apollo 11 landing site

When Neil Armstrong snapped AS11-40-5872, he was at the position marked "5872" in the top centre of the map, while Aldrin was at the Solar Wind Collector (SWC). For the TV image, the camera was positioned on the MESA lid midway between the LM's +Y and +Z pads, while Armstrong was standing near the +Z pad just outside the LM's shadow.

The astronauts' shadows were viewed at angles between 35° and 40°, enough to make them look nearly 50% shorter.

A shadow can be compared to a triangle, with its height representing the object making the shadow, its length being the shadow itself, and the hypotenuse formed by the angle of the sun.

This triangle represents the angle of the sun at Tranquillity Base on 20 July 1969. Imagine Buzz Aldrin is standing up against the triangle's left side. The 14° sun is shining down along the hypotenuse to cast a long shadow represented by the triangle's base, which is 4 times as long as the triangle is high. This triangle models how long Buzz Aldrin's shadow should have looked if Neil Armstrong had photographed him from a 90° angle.

Now let's turn our triangle to the 35° angle at which Armstrong had actually photographed Aldrin, like so:

Triangle turned to a 35° angle from camera

It's still the same triangle, but now perspective makes its length appear only 2½ times its height, while its angle measured against the horizon (the far edge of the table) is nearly 30° (which corresponds closely with the angle of the lens flares).

And then we place the tilted triangle over Percy's annotated image:

It's a pretty good match, but not perfect. (Nothing is perfect in the real world.) My rough math suggest that a 35° viewing angle of a 14° sun angle should give an apparent angle of 23.5°. These extra few degrees could be caused by Neil Armstrong taking this picture on higher ground--a likelihood further borne out by the fact that the far horizon appears above Aldrin's helmet. Finally, there are my own errors in cutting and turning that triangle. (As for the ragged point, that resulted from an over-reliance on Photoshop's Magic Wand.)

So with these caveats in mind, let's turn to Percy's second picture.

In the TV image, Neil's shadow was pointing away from the camera at an angle of 40°. Here's how our triangle looked when we turned it away at a 40° angle and pasted it between Percy's line and Armstrong's shadow:

Once again the triangle's hypotenuse represents the sunbeam travelling from the astronaut's head to the end of his shadow. And once again a 14° angle can be raised to an "impossible" steepness by viewing it off-kilter (and perhaps with a little bit of help from slightly unflat ground).