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Amelia Earhart - Death by Parallax?
Amelia Earhart's disappearance on 2 July, 1937 has been the subject of much speculation over the years, with theories ranging from the plausible to the wildly fantastic. Here is a look at a reasonable explanation of why Earhart and navigator Fred Noonan failed to reach Howland Island on that fateful day1.
Human 'Depth Perception'
Parallax allows us to estimate the distance of objects that we can see. Hold up a finger approximately three inches in front of your nose and look at it closely. Then close first your left eye and then your right. Repeat this rapidly. Notice how your finger rapidly moves (or appears to move) from right to left, depending on which eye you use to observe the finger. Our brains deftly integrate information received from the parallax of our two eyes, and this allows us to estimate distances to objects. Parallax is therefore very useful in surviving on the motorway, picking fruit, playing games involving balls and in numerous other ways.
Stellar parallax is another use of parallax and was an early method of estimating the distance of nearby stars. In this case, the angles for a nearby star are measured six months apart while the Earth is on opposite sides of its orbit. This parallax error defines a parsec2, which is one second of arc and a little over three light years. This method of measuring stellar distances is useful for up to about 11 parsecs.
Photographic Parallax Errors
Here parallax begins to reveal its darker side. We find that what the observer views through the eyepiece may not exactly correspond to the size and dimension of the image that will end up travelling though the lens and falling upon the camera's film. This type of parallax error may be most noticeable on close-up photography when the viewfinder and lens of the cameras are on different lines of sight. Better cameras provide help with parallax correction features, which may be as simple as a visual box in the viewfinder indicating the size and shape of the eventual photographic image.
Geocentric Parallax Errors
Geocentric parallax can have fatal consequences for the unwary traveller. An adjustment is required to compensate for a false apparent angle between a celestial body and a human observer. The moon's observed altitude angle is usually misleading due to parallax because the moon is very close to the Earth. The sun and the stars do not require a correction because they are so far away that the parallax error approaches total insignificance. Failing to apply the parallax correction to celestial navigation observations can result in a really bad sun/moon fix or just a wildly incorrect speed-line or course-line3 from the moon alone.
The amount of the celestial parallax error is at a minimum when the moon passes through the meridian and is also directly overhead (ie, on the same latitude as the observer). The amount of the parallax error can be as much as much as 60 minutes4 (60 nautical miles or about 69.046767 English miles) when the moon is near the observer's horizon.
A 60-mile error on the moon observation can become a much greater error in determining your position on the Earth if the moon and a second body being observed have lines of position that cross at other than a 90-degree angle, which is almost always the case.
To get a picture of how it works, think of an observer on the equator, and the sun and the moon both circling about the equator on one of the equinox days. The moon rises exactly in the east and passes directly overhead to set in the west. The sun follows the same path. We will ignore the sun's insignificant parallax, due to its greater distance from the Earth. However, the moon can have an error in the observed altitude angle of approximately one degree (60 nautical miles) on the horizon. There is no geocentric parallax error at all when the moon is directly overhead and the observer is on a direct line between the moon and the Earth's centre.
The need for the parallax correction arises because navigation tables compute the altitude angle of the moon based on an angle between the celestial body and the exact centre of the Earth. The navigator/observer is hopefully somewhere else and on (or above) the surface of the Earth, so there will always be an 'error' in the observed angle of nearby bodies (ie, the moon) unless the body is conveniently passing exactly over the observer's head. The amount of the error can be computed from a table which is provided to all navigators who have not yet transitioned to the use of the infinitely more convenient and inexpensive handheld GPS devices.
A Researcher's Experience with Geocentric Parallax
In 1966, as we prepared for a 4.00am local time take off from Wake Island, heading to Guam, the pre-flight revealed that our APN-9 LORAN5 was broken. The APN-9 LORAN is perhaps good for 150 miles near an island under ideal conditions, but that can be critical if one is looking for an island from an 8,000 foot altitude. Islands usually pop into sight about 30 miles out. The LORAN is the somewhat inappropriately named 'Long range Over water Aid to Navigation'. In 1966 the 'Long' part of the name was certainly optimistic.
Amelia Earhart and Parallax
Amelia and Fred had been flying though the night toward dawn7. Fred should have had good celestial observations from stars and later the sun and moon8.The sun rose near Howland 6.10am local time (Howland had an 11.5 hour time difference from GMT), about two hours before Amelia was due at (and still about 300 miles away from) Howland. The last quarter-moon rose at 12.18am. The moon transited overhead and about 20 degrees to the south at 7.01am and set at 12.43pm local time. Fred would certainly have used both the sun and moon9. Both celestial bodies were available, it was an historic flight, the first of its type, and Fred would not have ignored the moon in the early daylight morning hours almost directly overhead (and to the south) or the sun rising in the east nearly dead ahead while making the final three-hour run into Howland. Fred probably got a several final fixes that morning using both bodies.
As Fred and Amelia approached Howland island after a gruelling 21-hour flight from Lae City in New Guinea, her last words indicated that she was at 1,000 feet (one explanation for flying that low would be to get under the scattered cumulus clouds while searching for a small island)10 and running on a line (157-337) north and south. This researcher's theory is that Fred, clouds permitting, would have had a shot at the sun in the east and the moon in the south and would have been able to get a set of perfectly crossed lines of position any time after sunrise from those two bodies. However, Fred would have been relying on the moon for the course line and parallax error could have caused him to veer off course enough to miss the island by a fairly large margin. It is certain that, as Fred approached where he thought Howland should be, heading east, he failed to see the island appear where his sun/moon observation and dead reckoning indicated that it should be. Fred must have logically assumed that they had missed the island to the north or south. Amelia then began her run on a line 'north and south' hoping Howland would come into view.
The Electra used by Amelia had a speed of about 150 MPH and an endurance about 24 hours11. The flight from Lae to Howland was 2,556 miles. In this researcher's view, it is totally improbable that Amelia would have agreed to add over six hours12 to the flight by diverting to over-fly Truk to make clandestine photographs of Japanese military installations for the American military, as some conspiracy theory enthusiasts have suggested13.
While she was alive, she was celebrated for what she accomplished and for what her example meant to women and aviation. Once she was presumed missing, Amelia Earhart the role model for women was increasingly replaced by Amelia Earhart the lost aviator, and attention was shifted away from her strongly articulated feminism to speculation about the circumstances of her fateful last flight.
Earhart's Electra had a new radio direction finder but Amelia was not trained on the use of the new RDF and failed to use it effectively. Her additional inability to receive voice messages may have been caused by damage on takeoff.Here is a link to a takeoff video, which may show the belly mounted voice antenna breaking off on takeoff. These critical problems, combined with the scattered cloud cover, low cloud bases, very small island, sun in the eyes, possibly inaccurate charts, lack of an alternate landing site, crew exhaustion, a possible hangover14, an inadequate fuel reserve, no autopilot to maintain a consistent track. 15 and Fred's possible parallax correction error, certainly resulted in enough cumulative issues to kill the crew several times over.
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