The Queen of the Moon, Dianna Soreil is the hereditary ruler of the Moonrace. Now that the Earth has regenerated from the destruction wrought by the Dark History, she believes that it is time for her subjects to return to Earth. Dianna lands a colonial force on the Earth in the hopes that they will be allowed to live in America&#039;s sparsely-populated sunbelt area. Unfortunately, she fails to take Terran resistance to the migration into account, and does not anticipate that her more ambitious subjects might turn against her in her absence. Events quickly spiral out of her control.    Dianna has lived for centuries using the Moonrace&#039;s cryogenic techniques. Her desire to live on Earth is a product of her weariness with her unchanging life on the Moon. She is an intelligent and commanding leader, but she lacks the drive of her young double, Kihel Heim. Dianna is overjoyed when assuming Kihel&#039;s identity allows her to lead a simple life with Loran. She only returns to the Moon in order to correct the mistakes she made in her rash rush towards repatriation.     ~!At the end of the series Dianna permanently switches places with Kihel, and lives out the rest of her days in a small cabin with Loran.!~

This story is set thousands of years in the future. The people of Earth have forgotten the space wars of the past, reverting back to a pre-industrial existence. But the lunar settlers known as the Moonrace, who have retained their high technology, now plan to seize their mother planet for themselves. As the war of the worlds begins, a young Moonrace citizen named Loran Cehack, pilot of the legendary Turn A Gundam, struggles to bridge the gap between humanity's long-separated branches. 
(Source: GundamOfficial)

Several hundred years have passed since the fierce battles using Mobile Suits throughout the universe. After many wars, earthlings forgot how to make developments in their own civilization. Some humans moved to the moon. For a very, very long time, they dreamed about returning to earth. When Planet Earth regained its standard of living to that of the days of the Industrial Revolution, Diana Soler, the Queen of the Moon entered into negotiations with the head of Planet Earth so that the Moon Race could return. She also secretly dispatched a reconnaissance troop to check the environmental and living conditions on Planet Earth. Rolland Seac came to Earth as part of the troop. Almost drowned in a river, he was saved by two beautiful sisters, Kiel and Sosie. After the accident, he started working for a mine, owned by the father of these sisters. He soon gets used to living on Planet Earth. 
Two years pass and the Moon Race who are becoming impatient with the slow negotiations takes action and forcefully tries to return to Earth. Flames engulf the streets. The "Turned 'A' Gundam" appears from the White Doll Ruins and Rolland finds himself riding it. He becomes the savior of Planet Earth. Rolland's struggle to avoid war between the Moon and Planet Earth begins.

Two thousand years ago since the war, the people of the moon are hoping to return to Earth. Loran, a boy who cannot find his place in the unnatural moon society, decides to become a "volunteer" for the Earth descent experiment. He wants to lie down on the earth, and hopefully see the Queen of the Moon. 
 
In addition to the story of Loran, included are the stories of six people including Sochie, Keith, and Kihel-Diana, set before the TV anime. 
(Source: Bookwalker, translated)

Several hundred years have passed since the fierce battles using Mobile Suits throughout the universe. After many wars, earthlings forgot how to make developments in their own civilization. Some humans moved to the moon. For a very, very long time, they dreamed about returning to earth. When Planet Earth regained its standard of living to that of the days of the Industrial Revolution, Dianna Soreil, the Queen of the Moon entered into negotiations with the head of Planet Earth so that the Moonrace could return. She also secretly dispatched a reconnaissance troop to check the environmental and living conditions on Planet Earth. Loran Cehack came to Earth as part of the troop. Almost drowned in a river, he was saved by two beautiful sisters, Kihel and Sochie. After the accident, he started working for a mine, owned by the father of these sisters. He soon gets used to living on Planet Earth.

Two years pass and the Moonrace who are becoming impatient with the slow negotiations takes action and forcefully tries to return to Earth. Flames engulf the streets. The "Turn 'A' Gundam" appears from the White Doll Ruins and Loran finds himself riding it. He becomes the savior of Planet Earth. Loran's struggle to avoid war between the Moon and Planet Earth begins.

The story takes place in unnamed timeline, where humanity has highly advanced technology. However, the human population is decreasing and it seems that they're on their way to extinction. 
The protagonists are Leos Alloy, Sthesia Awar and their Haro. They work on a Jupiter base called "Jupiter X", using "General Answer" (or "GA") which contains a massive repository of data about the alternate history of Humanity, Leos travels to the Earths' of the alternate timelines in an effort to collect data that might give them a hint for the evolution of mankind. 
(Source: Gundam Wikia)

For more than 2,000 years, there are people who have been waiting patiently to return to the earth. The people of the moon. When the Moonrace, led by the Dianna Counter, began executing their mission to return to Earth, Loran Cehack, who had descended from the Moon to Earth two years earlier, underwent a coming-of-age ceremony. That night, he encountered the Turn A Gundam.