 One of the arguments of the moon hoaxers against Apollo is that the earth looks too small on the photos: The moon looks bigger seen from the earth, and the earth is almost four times larger than the moon. The Apollo believers counter-argument that the moon looks smaller when taken in photo (which is true), and that the photo would be taken with a wide angle which would explain the small size of the earth. |
 In the documentation of the command module, they say that the astronauts had a Hasselblad camera with a focal distance of 80mm, for a film which was 2.8 inch large (an inch=25.4 mm); this gives angle of view of 48°. They also said that the astronauts could adapt on it a lens with a focal distance of 250°, which was reducing the angle of view to 16°, but was allowing to magnify 3 times distant objects. They could also adapt a lens with a focal distance of 500°, which was reducing the angle of view to 8°, but was allowing to magnify 6 times distant objects.  But, to take photos on the lunar surface, the astronauts also would have had a Hasselblad equipped with a 60mm biogon lens. I was first skeptic about that, for they don't talk about it in the documentation of the command module, but it is in fact confirmed in the mission report of Apollo 11, in which you can find this: "Photographic procedures planned for the lunar geologic experiment for use with the 70-mm Hasselblad with 60-mm lens were the panorama survey..." So, yes, a 60mm lens with a 70mm film was used to take photos on the lunar surface. And, with these data, it gives a view angle of 60°.  In particular, the sequence of the earth rise in Apollo 11 would have been taken with the 250mm lens, which explains that the earth appears bigger on them than on the other photos of the missions. |
 Knowing the size of the photosensitive sensor and the focal distance of the lens, it is possible to determine the angle of view of the camera: If we call H the height of the sensor, F the focal distance, and A the angle of view, then the angle of view may be determined by the following formula: A=2*atan((H/2)/F). For instance, with the film of 70mm and a focal length of 60mm, we obtain the following angle of view with this formula: View angle=2*atan((70/2)/60)=60.5°.  In order to make comparisons with the camera of Apollo, I needed to use a camera of which the angle of view was known. I used an old FinePix A101 camera, because the specification was giving information about its focal distance. The specification of my camera says that the focal distance of my camera is equivalent to a 36mm focal on a 35mm camera; this allows me to determine the angle of view of my camera with the following formula: Angle of view=2*atan(35/(2*36))=52° My camera has an angle of view of 52° (a moderate large angle of view). |
But, does the relative large angle of view of the Hasselblad camera account for the small size of the earth we see on the photos of the missions? Some people think that it is possible to directly determine the size of an object on the photo knowing its real size and its distance to the camera, but it is far from being that simple. It's true up to some distance, but the more the distance becomes important, and less it is true.  This is a photo taken from the Sacré-Coeur, with an angle of view of 92.6°; I could calculate it for the one who took this photos gave the properties of his camera (focal distance of 17mm, Film 14 inches). The photo has a width of 270mm on my screen, and the Eiffel tower a height of 12mm, which corresponds to an angle of 4.115° for the Eiffel tower (the whole picture covering an angle of 92.6°). The Eiffel tower has a height of 320m and is at a distance of 4690m of the sacré-coeur, from which the photo is taken, with the view angle of 4.115°, it would give a height of 337 meters for the Eiffel tower, so a little more than the real height. The difference is not big, but, for much greater distances, the difference between the real angle and the theoretical angle becomes much more consistent. And, for the earth seen from the moon or the moon seen from the earth, the distance is so huge that the difference between the real angle and the theoretical angle becomes much greater. So, if the earth appears under its theoretical angle on the photos of Apollo, it much to the contrary proves that it appears too small, for it should appear bigger. |
 The moon is at an average distance of 380,000 kilometers from the earth; its diameter is 3474km; so its angle of view from the earth is theoretically equal to atan(3474/380000)=0.52°.  I have taken a photo of the moon by a clear night; the moon was not quite full, so its width does not exactly represent its diameter, but its height does.  If my camera was really seeing the moon under its theoretical angle of view of 0.5°, then what my camera would see is not the white spot on the left (the real moon on my photo), but the small dot I have added on the right, which is almost three times smaller (in diameter). |
 The sun is at an average distance of 150 millions kilometers from the earth, its diameter is 1,391,000 km. So it is seen from the earth under a theoretical angle of view equal to atan(1,391,000/150,000,000)=0.53°, so an angle of view very close to the one of the moon.  If we were really seeing the sun under this angle of view, then, when I take a photo with the sun on it, what we would see on the photo is not this...  ...But this, a very small sun! |
 So, since it is difficult to determine the size of an object on a photo knowing its distance to the camera, how can we have an idea of the size that the earth should have on the photos of the lunar missions?  In fact, it is possible to do it if we have a reference at the same distance from the camera. Indeed, the ratio of the sizes of objects which are at the same distance from the camera is respected, whatever this common distance to the camera. Indeed, if we can't see the earth from the moon, on the other hand, we can see the moon from the earth! And the moon is at the same distance from the earth as the earth is from the moon (who does not understand that?). Therefore, it becomes fairly simple to know the size the earth would have on a photo taken with my camera: I take the moon with my camera.  I first scale the earth in order to perfectly superpose it on the moon of my photo (I took a bigger definition for the photo than what is shown here).  Then I finally magnify the earth by the ratio of the sizes of the earth and the moon, so 3.67 (ratio of the diameters). There I obtain the size the earth would have on the photo if I was taking it from the moon. In fact, I made the earth slightly smaller than it should exactly be, rather than bigger, so to be sure that I would not be suspected of oversizing the earth on the photo; that means that the earth would even be slightly bigger than what I represent on the photo. |
 The earth is seen from the moon under a theoretical angle of view of 1.9°; if it was really seen under this angle, then it would appear like the little earth I have represented on the right of the actual earth, and which is about three times smaller thnt the actual size of the earth as seen from the moon.  Relatively to my camera, the earth would have (60*35)/(70*36)=0.83 the size of the earth taken with my camera if taken by the Hasselblad with the biogon lens; it would look like this. /b> |
 So, now that we have a valid reference, we can have the size that the earth would have on the photos of the missions, if effectively taken with the 60mm biogon lens. If we take the photo AS17-134-20384 of Apollo 17, for instance, instead of appearing with the size of the actual photo (left on the double view), the earth would appear with the size I represented on the right of the double view.  Now, I can make the demonstration that the angle of view of the hasselblad used to take photos on the lunar surface was not really 60°, but consistently less instead. In fact, there are possibilities of measuring the angle of view in the missions, by using complete pans that the astronauts made, notably in Apollo 17. I start from a hill, I measure the displacement from a photo to the next by using a common point on two consecutive photos, I add all these displacements all along the whole turn, and I make a rule of three with this sum, the width of a photo and the angle of 360° corresponding to the whole turn; I obtained an angle of 45.6° with this process. I may have made some little errors of measurement, but this angle is much less the one of the 60mm lens (60°).  Now, for those who would insist that the photos might have been taken with a wide angle of view, I can make the clear demonstration that it can't be the case. NASA has built a panoramic with photos made by as an astronaut as he turned on himself to sweep the whole lunar landscape. I must say that it is a neat work, and the result cannot be contested, as it has been made by NASA itself. Link to the panorama of Apollo 17  This panoramic covers a whole angle of 360°. The part which is between the two red bars which have been drawn represents a sixth of the panoramic, so an angle of 60°.  I show this part of the panoramic which represents an angle of 60°.  This is the photo AS17-134-20425 which represents the same view.  Now, if we compare the photo AS17-134-20425 (left part of the double view) with the part extracted from the panoramic which represents an angle of 60° (right part of the double view), it is very clear that the photo AS17-134-20425 covers an angle consistently smaller than the part extracted from the panoramic, certainly not much more than an angle of 40°. So, we have the confirmation that the Hasselblad used to take photos on the lunar surface had an angle of view which was consistently less than 60°, hardly more than 40°.  And, with the real angle of view of the camera, the earth we see on the photos of Apollo would appear still bigger relatively to the one we see on the photos, something like this.  Anyway, not only they could give the size they wanted to the fake earth, but they could also use the angle of view they wanted, in a totally free way, on the fake moonset. These two photos referenced as AS15-82-11057, illustrate that fact. One version covers a smaller part of the landscape than the other one, and it is not because the two photos are taken from difference distances; the close foreground is indeed exactly the same, which doubtlessly proves that they are taken from the same point of view. That means that the zoom has been slightly changed between the two photos, what the astronauts had no possibility to do. Someone has told me that one photo could be cropped, but it can't be the case: If it was, I could superpose the one which covers a smaller part of landscape over a corresponding window of the one covering a bigger part of landscape; but, in fact, I can't: When I try to superpose the left sides, the right sides don't fit, and vice versa. That proves that the zoom has doubtlessly been changed between the two photos, and also proves they can't have been taken on the moon, as it was impossible to do by the astronauts. |
 Now, you don't even have to trust my photo of the moon (though you can make yourself the same test as I made), I can demonstrate you that the size of the earth is abnormal, incoherent, without taking the size of the moon as seen from the earth as a reference, simply by comparing the size of the earth on photos of different missions. I have had a close look to the earth of a photo of Apollo 17, the famous photo of Schmitt holding the flag, taken by Cernan kneeling (AS17-134-20384), and the one of a photo of Apollo 11, taken by an astronaut raising his camera to the sky (AS11-40-5923), using the high resolution photos.  I have taken a window containing the earth of exactly the same size of the two high definition photos (200x200 pixels); the earth should logically have the same size on the two photos, and yet, you can see that it is not the case; the earth of Apollo 17 is slightly bigger than the one of Apollo 11; on my screen, I have measured 2.8cm for the diameter of the earth of Apollo 17 (in paint, on the high resolution photo), and 2.5cm for the earth of Apollo 11; that makes a ratio of 1.12 between the earth of Apollo 17 and the one of Apollo 11 (that could even be a little more, for the high resolution photo of Apollo 11 is slightly greater than the one of Apollo 17). So, for an equal distance of the earth, the earth of Apollo 17 is 1.12 times too big relatively to the one of Apollo 11.  Of course, there is a question of a difference of the distance of the earth between Apollo 17 and Apollo 11, but, even the maximal ratio of distances of the moon (perigee and apogee) does not explain this difference, for this ratio is only 1.123; of course, if the earth of Apollo 17 had been taken as the moon was at its perigee, while the one of Apollo 11 had been taken as the moon was at its apogee, it could explain this difference of size. But, it is far from being the case, as you are going to see: The landing of Apollo 11 happened on July 20th 1969; the previous apogee happened on July 13th, so 7 days before, and the next perigee happened on July 28th, so 8 days later; the landing of Apollo 17 happened on December 11th 1972; the previous apogee happened on December 4th so also 7 days before, and the next perigee happened on December 19th, so also 8 days later. If means that the landings of Apollo 11 and Apollo 17 happened in exactly the same conditions relatively to the apogee and the perigee, and so the distances of the earth are comparable in these two missions, and the difference of distance much less than the difference between the apogee and the perigee, which means that there is no rational explanation for the difference of size of the earth between Apollo 17 and Apollo 11. The conclusion is that there definitively is a problem of abnormal variation of size of the earth on the photos of Apollo! |
 The size is not the only problem with the earth of the photos of Apollo, there also is a problem with the orientation of the crescent of the earth as I am going to show. The moon landings of Apollo happened near the first quarter of the moon. At that moment, when someone would have been on the center of the visible side of the moon, he would have seen the crescent of the earth as I represent it on this illustration, that is vertical.  When an observer is on the extreme east of the visible side of the moon, he would have an orientation which is perpendicular to the one he has when he is at the center of the moon.  So, we are going to turn the whole scene so that the observer becomes vertical.  And, when he appears vertical, this is the way he sees the crescent of the earth, that is horizontal, with the lit part above.  Besides, you'll notice that this is precisely the way that the crescent of the earth appears when the earth starts to appear on a photo of Apollo 11 (taken with the 250mm lens), as the command module reaches the extreme east of the visible side of the moon.  When an observer is on the extreme west of the visible side of the moon, he would also have an orientation which is perpendicular to the one he has when he is on the center of the moon, but inverted relatively to the one he has when he is on the extreme east of the moon.  So, we are going to turn the whole scene, so that the observer becomes vertical.  And, when he appears vertical, this is the way he sees the crescent of the earth, that is horizontal too, but with the lit part underneath instead of above.  When an observer is at mid way between the center of the moon and the extreme east of the moon, he appears bent at 45° on the left relatively to the one he has when he is on the center of the moon.  So, we are going to turn the whole scene, so that the observer becomes vertical.  And, when he appears vertical, this is the way he sees the crescent of the earth, turned at 45° counter-clockwise relatively to the horizontal position.  Finally, last example, when an observer is at mid way between the center of the moon and the extreme west of the moon, he appears bent at 45° on the right relatively to the one he has when he is on the center of the moon,  So, we are going to turn the whole scene, so that the observer becomes vertical.  And, when he appears vertical, this is the way he sees the crescent of the earth, turned at 45° clockwise relatively to the horizontal position.  From what I have explained, it appears that the way that the crescent of the earth appears on a landing site is perfectly predictable, knowing its coordinates. And the way that the crescent of the earth appears on the photos of Apollo 17 and Apollo 11 does not correspond with the location of these sites on the moon. On these photos, the crescent of the earth has an orientation which is close to horizontal, while it should be closer to vertical. |
 We are again going to use the panoramic of Apollo 17 made by NASA. The sun is visible on this panorama, but the earth is not. |
 However, we can see the earth on some photos, and, in particular on this photo, AS17-134-20387, we can see that it is over South massif, in fact a little on the left of this one. |
 This allows us to locate the earth on this panorama. But why did I want to locate the earth on this panorama? You are soon going to understand why. |
 I have found a table giving the apogees et perigees of the moon, year by year. It is relatively to Apollo 17 that this table interests me, so I choose the year 1972 to calculate the perigees and apogees of the moon. |
 This table tells us that there was an apogee of the moon on the 4th of december 1972 at 10h16, and a perigee on the 19th of december at 12h46. The landing of Apollo 17 occurred on december 11th at 19h54. It means that, when Apollo 17 landed, the moon was going from it apogee to its perigee, and was not far from its mid-course between the two extremities of its orbit. |
 On this schema, I represent the orbit of the moon, which looks like a circle, but is in fact an ellipse, with a small eccentricity which makes it close to a circle. The earth is close to the orbit's center, but not exactly on it, a little on the left of it. I have largely oversized the earth on my schema; it is in reality much smaller relatively to the moon's orbit (and so is the moon). The time of Apollo 17's landing would position the moon on its orbit approximately like I show on my schema, i.e. not far from the mid-course between the apogee and the perigee, but a little before. The astronauts see the earth on the right of the sun, and have to turn clockwise of an angle of a little more than 90° to see the earth relatively to the sun. |
 All along the three days of their stay on the moon, the moon continues to progress on its orbit toward the perigee, which means that the angle between the earth and the sun decreases. When they left the moon to return to the CM, the moon was approximately on its orbit like I show on this schema. |
 Now, this is where it is interesting to know where the earth and the sun are on the panorama. The panorama corresponds to an angle of 360°, so the total length of the panorama corresponds to 360°. So, if I want to know which is the angle between the earth and the sun on the panorama, I measure the distance between the earth and the sun on the panorama, I multiply it by 360°, and I divide this product by the total length of the panorama. This gives me an angle over 120°. |
 But this angle of more than 120° corresponds with a position of the moon on its orbit which is much before the position that the moon had when Apollo 17 landed. |
This means that the earth and the sun are too distant from each other on the photos of the mission; their distance does not correspond with the time that Apollo 17 landed on the moon. |
 So, in fact, the normal distance between the sun and the earth on the panorama, corresponding to the time that Apollo 17 landed on the moon, would make that the earth would not be over South massif, but a little before, approximately like I represent it on this modified panorama. I moved the earth, but I could also have left the earth at its position over South Massif, and moved the sun right instead; it would even be more logical, for it is the sun which moves relatively to the moon (as the moon always shows the same side to the earth). |
 And there is something more. Because the moon always shows the same face to the earth, the earth moves very little in the moon's sky. It moves a little because of the moon's libration, but not importantly. On this photo (AS17-134-20387), the astronauts see the earth over the left of South massif. If, at a given moment, they see the earth over the left of South Massif, they should always see it over the left of South Massif, throughout the whole mission. |
 Yet, on this photo (AS17-134-20461), the astronauts now see the earth over the right of South massif. |
 There is an evidence that this is the right of South Massif, for we can see the descending slope of the right of South Massif. |
 It means that the earth abnormally importantly moved in the mission. That might explain why it is too distant from the sun, if it keeps moving right! |
