They had almost completed their around-the-world flight. It was supposed to be the first of its kind completed by a woman.
One last hurdle remained.
Taking off from New Guinea, the pair set out for Howland Island.
It's a speck in the vastness of the Pacific Ocean. But it was a necessary stopover refuelling point for Earhart's Lockheed Model 10 Electra aircraft on the way to Hawaii.
And, for 80 years since, all attempts to find them have also failed.
Next week, world-famous wreck hunter Robert Ballard hopes he will be the one to find conclusive evidence of Earhart and Noonan's fate.
On August 7, his exploration vessel Nautilus will depart Samoa for the cluster of islands that is the Micronesian nation Kiribati. One particular uninhabited speck — one of the remotest places on the planet — is their destination.
Nikumaroro.
So why does Ballard believe Earhart and Noonan ended up on a remote beach some 650km off course?
"I'm a hunter — you have to become the prey that you're hunting," 77-year-old Ballard told National Geographic.
"I put myself in that cockpit, and I began becoming Amelia."
WITHOUT A TRACE
A US Coast Guard vessel searched the waters around Howland Island for a fortnight after the Electra failed to make its scheduled stopover. Earhart's husband, George Putnam, paid contractors to continue the hunt.
Earhart and Noonan were declared missing, presumed dead.
Confusing the matter was a barrage of unconfirmed radio messages. Many were said to have been heard days after the plane was sure to have come down.
Were they really from an increasingly desperate Earhart, broadcasting pleas for help before the rising water flooded her downed aircraft?
The last confirmed message, received by the US Coast Guard cutter Itasca, heard Earhart saying they would follow a flight line of 157SE 337NW.
The featureless coral reef that is Nikumaroro is close to that path, southeast of Howland Island, which is why it has been the subject of several expeditions in the past.
"I have always been intrigued by the story of Amelia Earhart because she shocked the world doing what everyone thought was impossible," Ballard says in a statement.
"We have an incredible team in place of experts, scientists and explorers who are working diligently to map out this ambitious expedition. Using state-of-the-art technology and decades of evidence collected in regard to her disappearance, I would say we have a real shot at rewriting history by solving one of the greatest mysteries of our time."
BEYOND REASONABLE DOUBT
There are many theories about Earhart's disappearance. That her aircraft broke up upon crashing into the ocean, taking its crew into the depths with it. That Earhart and Noonan were captured and interned by the Japanese during World War II.
But the International Group for Historic Aircraft Recovery (TIGHAR) has been on Earhart's trail for decades. It's convinced she and Noonan ended up on this desert island.
It all sounds plausible enough. At low tide, a rugged but relatively flat reef is exposed on the island's northwest side — offering something approaching an emergency airstrip.
A previous National Geographic expedition used forensic dogs to find human remains. While homing in on an abandoned castaway campsite, no bones were found.
An unfortunately blurry photo of the island taken in 1937 could potentially show a piece of the Lockheed Electra's landing gear jutting out from among the coral. Taken by a British colonial officer, he also reported finding what he called a temporary "bivouac".
Bones were found there in 1940. But these have long since vanished.
However, the autopsy report made by two doctors on Fiji survive. Measurements were taken of a skull, as well as humerus, radius and tibia leg bones. Initially, one doctor believed they belonged to an elderly Polynesian. The other, however, postulated they came from a European male.
Without the bones themselves, the best modern science can offer is that the dimensions of the bones match those of Earhart.
"If the bones do not belong to Amelia Earhart," forensic anthropologist Richard Jantz wrote in Forensic Anthropology last year, "then they are from someone very similar to her".
EVIDENCE HUNT
This time, Ballard's team will be searching on both sea and land.
The expedition is funded to last one month.
Advanced sonar will map the ocean floor in search of 'solid' objects. Robotic drones with cameras will zoom in on potential contacts for a closer look. It's not as easy as it sounds: the coral reef quickly plunges 3000m to the sea floor, which is itself a maze of volcanic gullies and valleys.
Ballard says he will be searching one site in particular — a "very high energy" beach where the collision of open sea with solid reef would quickly grind an aircraft into pieces.
"Push a plane off the cliff, and it will leave stuff all along the way," Ballard told the Washington Post. "And all you need is one piece."
Meanwhile, search teams and forensic dogs will scour the rough coral beaches, bushes and dunes.
With the team will be archaeologist Fredrik Hiebert. In particular, he will be seeking any evidence of human remains — along with any aircraft parts that can be explicitly traced back to a Lockheed Electra.
This is because visitors in the late 1930s had reported finding scattered aircraft parts. And TIGHAR, which has been exploring the island since 1989, has found the remains of several campsites and 1930s-era glass bottles. Given the number of recorded visits during that era, these cannot be used to point expressly at Earhart and Noonan. But one tantalising bottle appears to have been used for freckle cream — a cosmetic Earhart may have used.
The hope is further items, which can be tied more directly to Earhart and Noonan, can be found.
"Amelia Earhart has been on my sonar screen for a long, long time. And I've passed on it," he said. "I'm in the business of finding things. I don't want to not find things."
The documentary is scheduled to air for the first time on Sunday, October 20.