Amelia Earhart was one of the first female pilots in Earth history. In the mid-20th century she became famous for being the first woman to fly across the Atlantic Ocean. In 1937 she attempted to fly around the world, and on July 2nd, she and her navigator, Fred Noonan, took off from New Guinea and headed east, around the equator. Somewhere in the South Seas, however, they vanished, never to be heard from again, and their disappearance became one of the most celebrated mysteries of the 20th century.
Although the most commonly-held theory was that they simply ran out of fuel and crashed, numerous searches of the area failed to produce the wreckage of an aircraft, leading many to speculate as to the true nature of their disappearance. Among the theories were that they had been shot down and captured by the Japanese navy, that Earhart and Noonan had eloped together, and, the most fringe theory, that they had been abducted by aliens. (VOY: "The 37's")
In 2151, while discussing the disappearance of the human colony at Terra Nova, Ensign Travis Mayweather compared the mystery to the disappearance of Amelia Earhart and Judge Crater. (ENT: "Terra Nova")
In 2371, the crew of the USS Voyager discovered that Earhart and Noonan had, in fact, been abducted by aliens known as the Briori, along with over three hundred other people in 1937, to be utilized as slave labor on a planet in the Delta Quadrant. The Voyager crew discovered Earhart and Noonan, along with six other humans, in a state of suspended animation, the only abducted humans who had been left in stasis. By this time, the humans had long since overthrown their Briori masters, and their descendants had established a thriving community on the planet. Upon being revived by the Voyager crew, Earhart and the others, who had come to be known as "the 37's" by the human colonists, were given the option of joining the crew on their long journey back to the Alpha Quadrant. Earhart and the others declined, however, and elected to remain on the planet with the other human colonists. (VOY: "The 37's")