This is one of the photos used by astronomers  Von Del Chamberlain and David J. Krause to triangulate the trajectory of a large fireball  with a smoke trail that passed near Detroit, Michigan and Windsor, Ontario, at 4:43 p.m., December 9, 1965,  The results were written up in the Journal of the Royal Astronomical Society of Canada (JRASC) in 1967.

The photo was taken near Pontiac, Michigan, about 20 miles north of downtown Detroit, and shows the smoke trail after the fireball disappeared following an explosion.  Point B at the end of the trail was thought to be the puff of smoke created by the final explosion. Supposedly this photo was taken within about a minute of the end of the event.  Point A is a kink in the trail also visible in another photo taken about 8 miles southwest in Orchard Lake, Michigan.  These two points were what was used for triangulating a trajectory.

This is a working diagram of the triangulation that I lifted directly off the above graphic.  

This fireball was also associated with something that came down a few minutes later in Kecksburg, Pennsylvania, about 240 miles distant.  Note that the straight-line direction to Kecksburg (see map below) is nearly at right angles to what the JRASC article claimed was the true fireball direction.  If that was the case, then obviously the fireball couldn't have anything to do with Kecksburg.  It would be just an amazing coincidence.

But just how reliable and accurate was the triangulated trajectory in the JRASC article?
An Analysis of the "Kecksburg UFO" Fireball Trajectory and Possible Error

Skeptics of the 1965 Kecksburg crash love to cite a 1967 astronomical journal article as "proof" that there was no Kecksburg object, but analysis shows numerous faults in in the paper, including an impossible result of zero error in determining trajectory
Because of the small triangulation base, the range of possible trajectories increases very rapidly even for very small errors in determining directions of less than ± 0.5°.  As seen from the graph, a straight-line trajectory to Kecksburg is still possible with an error of about ± 0.6°.

There are other possibilities as well if one assumes the fireball could have been a controlled spacecraft of some kind and could change trajectories, just as the space shuttle does to some extent during re-entry.  E.g., if the Detroit-Windsor trajectory was directly West to East, or azimuth 90°, this could be accommodated with only ± 0.25° error.  Perhaps later a turn was made towards Kecksburg (pure speculation).

Descent Angle

This also has important implications for the steepness of the trajectory.  The JRASC article has the smoke trail diving toward the ground at a 52° angle relative to the horizontal.  The altitude at point A is 20 miles and about 4.5 miles away at B it is about 14 miles.
 If the JRASC trajectory were correct, one would expect the smoke trail to be of about even thickness between points A and B, since the fireball would be moving sideways to the camera and maintaining about an equal distance at all times. Instead, the trail near A is noticeably thicker than most of the trail approaching B (except in the "puff" at B where the trail ends).  A simple explanation of this would be that the trail near A is much closer to the camera than the trail at B.  In other words, the trail would again be steeply slanted away from the camera (the fireball was moving off into the distance) instead of being at nearly right angles, as the JRASC article has it. 

Kecksburg fireball 2
However, if the object was moving away instead of sideways, part of the dip in elevation angle for point B is due to the object being further away from the camera.  This is illustrated in the graph at the right.  Assuming a "Kecksburg-directed" trajectory at an azimuth of about 124°, the object instead descends one-third as much, from about 18 miles down to 16 miles over 9 miles of travel, for an angle of 13° to the horizontal, only one-quarter of the 52° in the JRASC article.

The descent angles for the blue curve assume zero error in determining elevation angles for points A and B.  However, if the range of error were as great as that for determining the trajectory's azimuth, then the descent angles would be represented by the red curve.  At a "Kecksburg trajectory" under the maximum error assumption, the descent angle could be as low as 7°.

However, this is still too steep to get all the way to Kecksburg, as illustrated in the next graph indicating approximate impact point at the given angle of descent.  (Note:  This calculation assumes a constant angle of descent, such as for a powered object like an airplane, instead of a curved trajectory caused by gravity, such as for a passive object like a meteor.)  On a straight-line Kecksburg trajectory, the object would impact about 70 miles away assuming zero error in finding elevation angles and about 180 miles away assuming maximum error.

However, the graphs also show that for azimuths only a little beyond a straight-line Kecksburg trajectory,  somewhere between about 126° and 131° azimuth (depending on elevation angle error), the object would descend at only about 4-5° to the horizontal and would impact at about the 220 mile distance to Kecksburg (assuming the simplistic constant descent).   
Thus, if the object was really flying at a sharp angle away from the camera, it could be slowly descending in near level flight instead of being in a steep dive, as in the JRASC article.  Furthermore, it could fly all the way to Kecksburg instead of impacting nearby. To accommodate the greater azimuths required in this near-level-flight, distant-impact scenario, the errors in determining triangulation directions would have to be increased to about  ± 0.7 degrees       (above graph).

Another possibility, if the object had controlled flight, is a straight-Kecksburg trajectory at a steeper angle initially followed by the object leveling out at lower altitudes, just as the Space Shuttle does at times as it comes in for a landing.  There are, of course, an infinite number of other possible variable descent scenarios.

Change in smoke trail thickness:  implications for trajectory

Another possible indication that the JRASC trajectory could be in error can be seen by examining the smoke trail in the photo above and an enhanced, rotated blowup below.
(See also composite image below of three smoke trails pictured in JRASC article.)  
It is interesting that this result is only a few degrees more than the azimuth found for the shallow descent, distant Kecksburg impact scenario.

In March 1966, researcher Ivan Sanderson compiled newspaper and  eyewitness reports to the fireball.  Sanderson concluded that the fireball took a more southerly route initially rather than making a "bee-line" for Kecksburg.  Somewhere over Ohio it changed course to a more easterly direction towards the region near Kecksburg. (By Sanderson's reckoning, the course change was about 25°.)  Sanderson's trajectory findings are thus consistent with the more southerly trajectory results derived here from changes in smoke trail thickness plus the constant slow-descent, distant-impact scenario based on the smoke trail elevation angles and triangulation.   These assumptions and results would point to the initial trajectory azimuth being about 140° instead of about 124° for a straight-line Kecksburg trajectory.

In the graphic below, the straightline Kecksburg trajectory at 124° is shown in red from point A of the smoketrail to Kecksburg. (Photo sites 1 & 2 also depicted above Detroit).  In addition, a possible more southerly route in green is shown, along the lines proposed by Ivan Sanderson, with an initial azimuth of 135°, and after a 25° turn, an azimuth of 110° towards Kecksburg.  Note this trajectory takes it directly over Lorain and Elyria, Ohio (southern shore of Lake Erie) where metal debris was reported raining down and grass fires being started.  (Map generated by Topo USA)
The graph at right shows the expected perspective change in trail thickness as a function of the azimuth or direction of the trajectory.  Note the JRASC trajectory at 40° azimuth (or pointing nearly Northeast) has a trail thickness ratio close to 1.0, what would be expected for an object moving sideways to the camera.  (If anything, with the JRASC ratio of about .92 between beginning and end thickness, the graph shows the trail should have gotten slightly thicker as the fireball progressed, not thinner.)  

However for a trail thickness ratio of 1.5 (as determined by linear regres-sion above), the graph  indicates the trajectory as being around 140° (or to the Southeast), assuming the ratio is due to the object moving sharply away fro the camera from points A to B ), or due only to  perspective and not some other confounding factor, like the fireball "fizzling out".
In making the above graphic, the three trails were rotated about 45° to a horizontal position.   For comparison purposes, features A & B in all three pictures were made level and scaled to be the same distance apart (although the equi-distance assumption is itself in question.)

Red horizontal lines mark extreme positions of trail drift in features common to all three photos.  The photos of the first two trails (1a & 1b) were both taken from the same site, while trail 2 was taken at a separate site about 8 miles northeast (see triangulation details above).  According to the JRASC article, photo 1a was taken "within a few seconds" of the end of the fireball, while 1b was taken about 15 seconds afterwards.  Photo 2 was supposedly taken about 45 seconds after the fireball.

Interestingly, the separation between the red lines in 1b is about double that of 1a, while the separation in 2 is about triple of 1a.  Assuming a constant lateral rate of spread of the trail and that photo 2 was indeed taken at 45 seconds, this would suggest that photos 1a and 1b were more likely taken at about 15 seconds and 30 seconds after the disappearance of the fireball.

By photo 2, the distance between the red marked extremes is already about one sixth of the distance between points A & B.  In the JRASC article trajectory, A & B are separated by about 4.5 miles.  Thus, even in the JRASC article, the trail has departed from straightness by 1/6 x 4.5 = 0.75 miles in 45 seconds, or at a rate of about 1 mile a minute or  60 miles an hour.

If the trajectory is instead slanted steeply away from the camera, as the analysis above suggests, then the distance between A & B would be much greater and the relative dispersal of the trail proportionately faster.  E.g., at a trajectory azimuth of 130°, the distance between A & B is more like 9 miles, or double that of the JRASC value, and the high altitude winds would be dispersing the trail at about 120 miles an hour.

Thus this analysis indicates that there were high-altitude shear winds on the order of 60-120 mph, causing the trail to rapidly disperse and depart from its initial straightness.  Even if photos 2 and 1b were taken only 15 seconds apart, this still raises the possibility that points A & B could have shifted relative to one another by one quarter to half a mile.
The triangulation diagram from the JRASC article is shown directly below, noting the location of the two photo sites (1 & 2), and the two triangulation points in the trail (A & B).  The authors claimed the triangulation showed the fireball trajectory ran from the Southwest to the Northeast (dark line between points A & B)
(Among a number of problems with the paper, the coordinates of points A & B were reversed, meaning the fireball would have been racing upward rather than downward and in the opposite direction.  The mistake was corrected in a later edition of JRASC.)
Possible sources of error in JASC article

That the fireball could assume such a trajectory taking it ultimately to Kecksburg depends on the triangulated JRASC trajectory being seriously wrong.  As previously noted, this would involve significant errors in determining directions of their triangulation points. Sources of potential error in the JRASC article are numerous and include tiny errors in reading compass directions in on-site surveys or not locating the exact sites to within inches of where the photos were taken during the same surveys.  (For example, one of the photographers, the one quoted by Sky and Telescope, was driving his car when the fireball happened; his photo was taken by the side of the road in the middle of the country--see photo at top.  Under these circumstances, it would be extraordinarily difficult  to precisely determine where the photo was taken.)

This could throw off the proper scaling of the photos if the position was wrong in the radial direction, resulting in the calculated angular distance between points A and B being either slightly too small or large.  In addition, the location being off laterally (or if compass readings were slightly off) would cause systematic error in the directions even if the photo scaling was correct.  Another possible source of scaling error would be not taking into account possible camera lens distortion in the photos.

The overall thinning of the trail before the puff at the end is illustrated in the plot of trail thickness as the fireball moved from right to left in the photo (note direction of red arrow).  Obviously the thickness is erratic, but taking a linear regression through the scatter of points   (red line) shows that on average, the thickness is about 1.5 times greater at the beginning of the trail (right) than at the end (left).
A huge problem with the JRASC article was no included error analysis.  Note that photo sites 1 & 2 are relatively close together compared to the distance to the fireball trail (A & B), creating a narrow triangulation base.  This diagram shows the possible effect of 1 degree of error in determining the directions of points A & B.  As a consequence,  the resulting trajectory instead of being well-defined can instead vary over about 150°!  A Kecksburg trajectory would fall well within this error range.

As an example of just how uncertain such a fireball trajectory calculation can be,  the famous Tagish Lake fireball of 2000 in Canada left a much longer smoke trail about 100 miles in length, was photographed from multiple angles from beginning to end, including an overhead satellite photo (thus a very wide base of triangulation) and left a linear debris field of meteorites on Tagish Lake, by itself defining an approximate trajectory, yet various astronomers   (12) who calculated the trajectory gave it an accuracy of no more than ±2.2°-2.4° azimuth angle  (and  ±1.2° -1. horizontal entry angle).
(Math note:  "Azimuth" represents the degrees measured from North in a clockwise direction.  Thus North is 0°, East is 90°, South 180°, etc.)
Yet the JRASC article, with far less information to go on, assumes ZERO error, which is unscientific not to mention impossible.   There is always measurement error; a key component to determining whether a result is valid or not is estimating the degree of error. (For a rebuttal to a debunker's silly, pseudoscientific claim that there was absolutely zero error and it is up to me to prove there was any, click here.)

The graph immediately below shows a more quantitative analysis of the effects of differing direction errors on final trajectory.  This was done using basic high school Algebra and trigonometry (plus an Excel spreadsheet)  to determine intersection points of the error lines and the range of angles of possible trajectories that can result.
The Sky and Telescope article

JRASC wasn't the only astronomical journal to publish an article on the fireball.  Sky and Telescope magazine published an earlier article in February 1966 ("Great Lakes fireball"), in which they contradicted the JRASC trajectory conclusion.  As the caption of their diagram below reads, "The path of the fireball extended roughly northwest to southeast..."  This is exactly the same conclusion reached above based on the analysis of trail thinning.

In addition, they cited the impressions of one of the photographers of the photos used by JRASC (the one who took the photo at the top).  According to S&T, "The fireball traveled toward the EAST [emphasis mine]… Although when first seen the fireball APPEARED TO BE FADING [emphasis mine], it ended with a burst of light.”  This again is consistent with the photos indeed seeming to show the trail thinning and fading, at least leaving the impression of the object moving away from the photographer in the distance, roughly toward the east, not sideways from southwest to northeast.  And in a letter to the USAF only 2 days after the incident, the same photographer similarly said it was moving "to the east" but on an estimated trajectory of 110° azimuth (so more to the ESE than E), even closer to the straight-line trajectory to Kecksburg of about 124°.
Further possible error could be added to the mix if "points" A & B weren't truly fixed in space.  The JRASC article also seemed to assume no significant shifts in the smoke trail between photos, and therefore A & B remaining in the same positions.  However, the composite image below, showing three trails from the JRASC article, calls this assumption into serious doubt. Were there no significant shifts in the smoke trail, then the trail should remain nearly straight.  Instead, it obviously departs very rapidly from straightness, even in the first photo supposedly taken only seconds after the fireball disappeared.  In the third photo, taken roughly 45 seconds after the fireball, the trail is already very twisted.  This could indicate significant turbulence or high-altitude shear winds causing the trail to depart quickly from straightness.  If that was the case, then the locations of points A & B were NOT the same in photos 1 & 2.
This next illustration shows how random measurement error or a systematic photo scaling error can likewise dramatically shift the trajectory.  Again, for simplicity, the errors are assumed only from one photo position, in this case #1.  Here, small errors are shown to shift directions of "points" A & B laterally outward, creating falsely triangulated "points" A' & B'.

As noted, to simplify illustrations these types of potential error are assumed from one photo point only.  But such errors are likely at both photo positions. Thus errors are likely to compound.  It was the responsibility of the authors to estimate the degree of such errors since they could potentially have a very significant impact on the outcome, but this was not done.
The diagram at the right illustrates how a simple error in determining the exact photo position could cause a small lateral shift in the directions of fireball trail "points" A & B, creating a false trajectory (A'®B').  For simplicity in illustration, the lateral errors are considered only for photo position 2, with directions for position 1 presumed to be "exact".  The real "points" A & B are indicated with solid red and blue starburst symbols, whereas the falsely triangulated ones are open symbols.  
As an example of how this could affect the trajectory calculation, the distances from the photographers to the midpoint of the smoke trail is on the order of 45 miles.  1 mile lateral change in position represents about 1.25°.  A lateral shift of 0.25-0.50 miles between photos 1a & 2 would thus represent an angular shift between A and B of about 0.3-0.6°; whereas ~1.2° total direction error is all that would be needed to sent the fireball on a possible trajectory headed straight for Kecksburg.  

Another indication that there is probably a shift in the positions of "points" A & B can be seen by examination of the size of the puff of smoke at B in the composite above of the smoke trails.  It lengthens about 50% in size between photos 1a and 2, or about 3% of the distance between A & B, or about 0.3°.

All that is said in the JRASC article about all this is that they compared 4 photos taken from site 2, covering a span of about 80 seconds (therefore, from about 45 seconds to 125 seconds).  The article claims that these four photos "reveal that the total drift of the cloud was minimal, although disintegration of the train is evident."

However, the comparison of the three photos above, taken perhaps only 30 seconds apart, instead reveals that relative drift of the cloud was anything but "minimal."  Winds on the order of 60 miles an hour or higher were causing rapid trail distortion and disintegration.  The whole premise that triangulation points A & B remained in the same positions between the two used triangulation photos is thus highly questionable.

Other problems with the paper

1. As mentioned briefly before, the triangulated points A & B were reversed in the paper, giving a fireball going in the opposite direction and upward.  Although the mistake was ultimately corrected in a later issue and has nothing to do with the accuracy of the intended trajectory, it does point to further sloppiness in the editing and the peer review process (which should have picked up on such a glaring mistake).  The review process also didn't seem to insist on even a token error analysis, as should have been done by any normal scientific paper standards with quantitative data.

2.  The paper, which was "Part I" of the analysis, mentions a "Part II", which was supposed to be an analysis by two other astronomers (Dr. J.A.V. Douglas and Henry Lee) of 66 detailed eyewitness case reports that were collected.  "Part II" should have been the next paper, but for reasons never explained was NEVER published in that issue or any later issue.  This isn't so much a problem with the accuracy of Chamberlain and Krause's trajectory analysis, but with the overall handling of the data in this fireball case.  Why did the second paper disappear?

3.  In trying to estimate the speed of the fireball, the authors did state that a "majority" of these same 66 witnesses estimated a duration of the optical phenomenon of 3 to 4 seconds.  In line with this, the Sky & Telescope article mentions over 100 eyewitness reports collected by Chamberlain himself immediately afterward.  Chamberlain was quoted by S&T likewise giving a duration of "about 4 seconds" based on this collection of his own witnesses.  Despite this, the authors instead took only the estimates of the two photographers of 1 and 4 seconds, made this into an "average" of 2 seconds (why not the true average of 2.5 sec?), which then gave the fireball a "typical" meteor speed.  Their given rationale for this was that, in their opinion, the two photographers were "in the best position to judge."  This makes no sense since the two differed in their duration estimates by a factor of four.  Further, one of them (1 sec. estimate) was driving in his car on the Interstate, and may well have been unable to see the full course of the visible phenomenon.  Surely a few of the other 64 ignored eyewitnesses must have had at least as good or better vantage points and views of the phenomenon. Why weren't they used?  

4.  Photographer and self-described skeptic Rand McNatt was very critical of their assumption, believing they were force-fitting the "average" duration to give a meteor speed, instead of using the true average duration, which would have given a much lower object speed, below meteor range, but more in line with what would be expected for re-entering satellite or missile debris.  McNatt's theory (which he admits there is very little evidence for) was that the fireball was actually created by a faulty/errant re-entering U.S. ICBM armed with nukes, and that's why it was hushed up.  

5.  It is thus pretty clear and Chamberlain and Krauss deliberately ignored the vast bulk of eyewitness estimates of duration in order to force-fit a much higher "meteor" speed rather than the lower one consistent with something else entering the atmosphere from Earth orbit (not the depths of space), which would almost certainly be artificial in origin, whatever it was.
This diagram illustrates how possible
wind shear could shift the true INITIAL
positions of points A & B in photo 1 to NEW positions A2 & B2 between when photos 1 & 2 where taken.  This again can result in false triangulation points A' & B' and a radically different false trajectory.

Again, real world total error is likely to be combinations of multiple sources of error, not just these simplified illustrated examples.
Triangulation errorKecksburg rebuttalTrail photos
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