... but the training photo
S69-31060 shows it peeking out from the thermal blanket at no more Armstrong's mid-chest height. ...
Now I see the similarity of your picture of the MESA – thank you for the hint. It is obviously well representative for the real LM. I realised this when I saw the following picture, which gives a greater overview (
www.hq.nasa.gov/office/pao/History/alsj/a11/ap11-S69-31585.jpg), and also lunar pictures with Armstrong working on the MESA (
www.history.nasa.gov/alsj/a11/AS11-40-5886.jpg).
Therefore the constellation of the camera with respect to the ladder is quite well known: the distance from the camera to Aldrin on the ladder can be estimated to 2-3m (I will calculate with 3m in the following) and the camera is approximately on the height of Armstrongs chest, i.e. about at 1.3m.
...No, that's not what I was asking... But what I was asking was how you estimated the length of the actual shadow in the photograph...
I never estimated directly a length of a shadow. Initially I estimated the sun inclination angle according to the photo with the Solar Wind Collector where the perspective contractions were expected to be small: I measured the height and the length of the shadow on the picture and calculated the sun inclination angle as arctan(height/shadow_length)=21°. With this I calculated the length of the shadow of the LM as 6.5m(=height of the LM)/tan(21°)=17m. To this result I added a margin (see my paper). Finally I looked for the sun inclination at the time and location of the landing (15°) and recalculated the length of the shadow to 6.5m/tan(15°) = 24m. This new result was well covered with the applied margin.
I made all calculations for a flat terrain. If the terrain were sloping up in the direction of the critical border of the ridge (the worse case for the “looking down to the sky”-effect) then the shadow would be shorter, so I had not to add extra margin.
This analysis is now complemented by the detailed analysis of the live video, see below.
...Check this high res jpeg topo map (file is 32MB in size) of the Apollo 11 landing site terrain: ...
Thank you for the map. It is effectively the same map as I have referenced already in (#73). The indicated view angle is heading east, i.e. to the direction of the sun, which has never been addressed here.
...Again, please will you tell us
how upright the astronaut is? ALL the astronauts were leaning forward to a significant degree because of the need to balance with a large backpack on. The top of the helmet would come into view from considerably below the height you describe. ...
My estimation of the camera height (mathematical horizon) is indeed not totally justified and can therefore be challenged.
So I have applied a second way of determining the camera height:
On the attached picture there is besides Aldrin also Armstrong. Both are almost 1.8m. Armstrongs head is visible. The position of his feet is vertically below his head and in the extension of his shadow, which I have indicated with a blue line. It is not clearly known whether Armstrong is fully upright. If not his head could be a bit higher, i.e. his head could be on the same height as the head of Aldrin. This would fit with my initial assumption of a high horizon.
Therefore let us assume that also Armstrong is upright (as Aldrin). Since his head is visible below Aldrins head the camera must be on a lower height. The sketch on the right in the attached picture shows the constellation and how the height of the camera can be reconstructed with the theorem on intersecting lines. There are vertical yellow bars on the sketch; 2.4 short bars are needed to reach the camera height from the top and 2.4 long bars to reach it from the bottom. The full bars are shown, the two 40%-bars have to be imagined in the middle. The full bars are also shown on the picture. The resulting height is finally indicated with the yellow dashed line with the label Horizon_low. I have neglected perspective contractions. This method gives the lower end of the possible horizon because a fully upright Armstrong has been assumed. The resulting horizon is on the height of the chest of Aldrin at about 1.4m. This fits well with the height according to the training picture (1.3m).
There are now two constellations for further investigations:
(1) mathematical horizon or camera height at approximate 1.8m (head) or
(2) at 1.4m (chest).
The tilt of the picture (roll angle) is well adjusted. This is visible a bit later in the video when Armstrong passes by, always facing to the camera. Here the vertical direction looks perfect; it is not influenced by his bearing, i.e. whether he is leaning forward or not. Therefore the horizontal direction, which is perpendicular to the vertical one, is also good – in the sense that an observer does not notice any anomaly.
Let us have a closer look to the two constellations:
(1) Horizon high (at the height of Aldrins head, at approx. 1.8m):
Here the border of the ridge fits well to a flat area (soccer field). It would also fit if both the border line and the platform were slightly inclined in either direction. The whole area is below the horizon.
Both lines, the border and the horizon, meet in the vanishing point.
The “Looking down to the sky”-effect is extraordinary large.
(2) Horizon low (at the height of Aldrins chest, at approx. 1.4m)
Here the left part of the terrain is higher and the right part lower than the horizon. This would fit to a significantly inclining terrain, which has neither been observed on the colour photos nor on the video, specifically not on the sequence around the flag. But more important is that the “Looking down to the sky”-effect is still obvious on the right side.
How big is the down-slope of the line-of-sight?
Since the constellation is known the picture can be scaled: a 1:10 angle (= 100mrad or 5.7°) corresponds to a length of 30cm at Aldrin, calculating with a distance of 3 m from the camera to Aldrin (see above). Such a 30cm-ruler is indicated as a red line at Aldrin and also as a vertical line to demonstrate the down-sloping of the line of sight. The vertical line is labelled with “100 mrad” and has the same length as the 30cm-ruler.
For both cases a 1:10 down slope of the line of sight to the sky or even larger can be observed. This would still be the case even if the camera or horizon were set to 1.3m, i.e. to the estimated height of the camera according to the training picture, or if the horizon were rotated by a few degrees to compensate for the approximate approach.
Even if the distance from Aldrin to the camera were doubled to 6m, the down slope would still be unrealistically large.
It may be astonishing that the down-slope of the line of sight is even larger than 1:10. One possible reason is the margin which has been applied in the previous cases.
My subjective estimation of the horizon is case (1), i.e. the high horizon. I may be right for one of the following two reasons:
1. The MESA and therefore the camera on the “real” LM, i.e. the one which has been used for the video, are higher compared to the one on the training picture.
2. For the video just another camera position has been used, i.e. a position above the nominal camera location.
ConclusionAfter this detailed analysis of the video picture with Aldrin at the ladder a “Looking down to the sky”-effect of more than 1:10 is present for all possible camera heights. This clearly demonstrates that this video must have been shot in a studio.
Just as a reminder: a “Looking down to the sky” of 1:10 is huge. It would only be possible on a 8600m high platform – with no visible mountains in the neighbourhood of 170 km. This result is even clearer than the previous one (see
www.apollophotos.ch – English Version – Paper) which additionally took the colour photos into consideration and where ample margin was applied. The result was there a down-slope of 1.5:30, which led to a 2100 m high mountain with no visible neighbours in the next 87km.
To exclude such a “Looking down to the sky”-effects from being reality on the Moon, the used maps with equidistance of 600m and the LRO images are more than sufficient.
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