The theory, explored further in the documentary, argues that Earhart and Noonan crashed near the Marshall Islands, about 1,000 miles away from their intended target of Howland Island, and were captured by the Japanese.
But that theory is dismissed by other Earhart investigators, and it's just one of a number of possible ideas speculating what happened to Earhart.
Earhart, the first woman to fly across the Atlantic solo and one of the most famous people in the world when she disappeared, has been a continual source of fascination in life and in death.
"I don't blame people for wanting to know (what happened), and it is one of the greatest mysteries of the 20th century because she was so well known," said Dorothy Cochrane, the curator for the Aeronautics Department at the Smithsonian National Air and Space Museum.
"The world was following her. So it is really someone drops off the face of the earth, naturally everyone wants to know what happens."
Here's a look at some of the most prominent of those theories surrounding what happened to Earhart, which range from a fatal crash to a conspiracy that she lived out her days under a new alias in New Jersey.
Crash and sink
As part of her attempt to become the first woman to fly around the world, Earhart and Noonan took off in a Lockheed Electra airplane on July 2, 1937, from Lae, New Guinea, intending to reach Howland Island in the Pacific Ocean.
They were in radio contact with the US Coast Guard cutter Itasca, which was just offshore Howland Island. The aviators radioed that they were low on fuel and unable to find the tiny island.
They were never seen again.
Based on those agreed-upon facts, the most basic theory posits that Earhart and Noonan ran out of fuel, crashed into the Pacific Ocean near Howland and died. That's the theory officially held by the US government as well as the Smithsonian.
"It's not the exciting theory. It's not the attention grabber," said Cochrane.
The US government spent $4 million searching for Earhart, Noonan and the Electra over about two weeks, at that point the most expensive search in history. Their search of a wide area near Howland Island came up empty.
Earhart was declared legally dead
on January 5, 1939, according to the History Channel.
Died as a castaway
Theorizing from The International Group for Historic Aircraft Recovery, or TIGHAR, argues that Earhart survived a rough landing on a remote atoll in the Pacific but died soon after.
"We believe she died as a castaway," said TIGHAR board member Richard Gillespie.
The idea is that Earhart and Noonan landed safely on a reef
in the ocean, and unsuccessfully attempted to radio for help. The Electra was eventually washed into the ocean by rising tides, leaving the aviators alone on the uninhabited island of Nikumaroro, or Gardner Island, about 350 miles south of Howland Island, TIGHAR claims.
In October 1937, months after Earhart went missing, Colonial Service Cadet Officer Eric Bevington took an image of the shoreline of Gardner Island. TIGHAR claims that a blurry form in that photo
may show landing gear components from the Electra.
TIGHAR also claims that a skeleton of a castaway
found on the island in 1940, tested decades later, is consistent with a female of Earhart's height and ethnic origin.
Taken prisoner by the Japanese
Another popular theory is that Earhart and Noonan landed in the Marshall Islands, were taken prisoner by the Japanese, and died in captivity in Saipan.
This is the theory put forth by the History Channel documentary, which argues that a newfound photo of Jaluit Atoll in the Marshall Islands shows Earhart and Noonan alive and well near the Japanese ship the Koshu.
The documentary cites investigators and facial recognition experts who argue the figure at the left in the photo has the same hairline as Noonan, while the figure sitting and facing away from the camera has the same hair length and body size as Earhart.
As the theory goes, the US search did not find Earhart because the Japanese had already taken her into custody.
A number of residents of the Marshall Islands have claimed they witnessed the aviators land there. The Marshall Islands even issued stamps commemorating the 50th anniversary
of her flight, which show Earhart's plane "crash landing at Mili Atoll" and "recovery of the Electra by the Koshu."
So why would the Japanese take her captive? That leads us to another related theory.
Earhart was a spy
Earhart and Noonan were spies shot or forced down on a secret mission to gather intelligence about the Japanese in the Marshall Islands, according to one set of theories.
Supporters argue their secret mission, approved by President Franklin Roosevelt, was kept under wraps after they were captured.
The theory was given attention due to a 1943 fictional movie "Flight for Freedom," which was loosely based on Earhart's story.
In the film, the female pilot is to issue a distress signal and land her plane near Japanese Islands so US Navy surveillance planes can fly over them.
One particularly outlandish variation of the spy theory holds that Earhart survived World War II, returned to the United States and lived under the assumed name Irene Bolam until her death in 1982.
That's the idea outlined in books like "Amelia Earhart Lives
" by Joe Klaas and "Amelia Earhart Survived" by Col. Rollin C. Reineck.
"Amelia Earhart was captured, and taken first to Saipan and then to Tokyo where she was kept prisoner in the Imperial Palace until 1945," Klaas' 1970 book concluded, as quoted by The New York Times at the time.
The theory held that Earhart's secret was used as a bargaining chip after the war to allow the Japanese Emperor to remain in power.
Bolam sued the book publishers for $1.5 million, maintaining she was not Earhart and had evidence from the 1930s to prove it.
"Utter nonsense," she called the book in an interview with the Times. "A poorly documented hoax."
The book was later withdrawn, but the theory persisted.