Expert: Robi Bhattacharjee - 9/5/2008

Question
Hello Robi,
  This article appeared in National Geographic.  Could you please tell me how the trig calculation was performed or somehow make some sense of this for me?
Our final and most conclusive examination was of the photographs taken by Peary near Camp Jesup. Since an inadequate attempt by merchant captain Thomas Hall in Has The North Pole Been Discovered? (1917), there seems to have been no real analysis of Peary’s photographs; accordingly our efforts represent new evidence. Techniques of photographic analysis that were pioneered during World War II developed into a fine craft during the Cold War years of satellite observation. One technique, called photogrammetric rectification, can produce the angle of the elevation of the sun from the shadows in pictures. This angle can be compared with the sun angle calculated from the Nautical Almanac to confirm a specific location and time.

Certain prerequisites must be met. There must be shadows that begin and end within the frame of an uncropped negative; there must be a horizon to determine the orientation of the camera; and the focal length of the camera must be known. Thus not every photograph can be so analyzed.

Establishing the focal length posed an initial problem because the only Peary camera we found was the 1906 camera at the National Geographic Society. With the help of the International Museum of Photography in Rochester, New York, however, we determined the focal length of the type of camera Peary was using in 1909.

The technique is one based on simple perspective. Imaginary lines drawn through each object and the end of its shadow would be, in the real world, parallel to the sun’s rays. Such lines drawn on a two-dimensional picture coverage at a vanishing point (often outside the picture). This vanishing point is also the point at which a ray of sunlight through the camera would cast a shadow of the camera. Thus the vanishing point defines the angle of the sun’s rays relative to the optical axis of the camera--which may be pointing up or down, as shown by the location of the horizon. The mathematical method used to fix these relationships is spherical trigonometry, much like that used in the reduction of a navigation sight. The Nautical Almanac gives the declination of the sun at the Pole or the date, and the time (taken from Peary’s account or other sources) tells which meridian the sun is on. The altitude of the sun measured from the photographs was used to establish a rough “line of position.”

Thank you, Mark

Answer
Hello Mark,

I'm not sure I understand what they did either. It seems that they didn't really even try to explain it. I'm not sure I can make sense of it either. I'm sorry. National Geographic is actually more of a common knowledge thing. They don't really explain too much in detail since they want it to be attractive to someone who either doesn't know much science or just isn't that curious.



I'm Sorry,
Robi