The Orellius system was a planetary system in the Alpha Quadrant. It was relatively close to the Bajoran system, but (at least in the 2360s) far away from any trade route. The system contained an F-type star, Orellius Minor, and the M-class planet Orellius, which orbited the star at a distance of 160 million kilometers.
In 2360, the SS Santa Maria, a Federation colony ship on its way to found a colony on Gemulon V, landed on the system's M-class planet in order to fix problems that had arisen in its life support system. Once on the planet, an apparently natural duonetic field disabled all technology, including the Santa Maria, and the colonists became stranded.
Under the direction of community leader Alixus, a prolific writer and self-proclaimed philosopher, attempts to overcome the field and thus escape or send a distress signal were soon abandoned, and instead the colonists dismantled the Santa Maria for material and started their planned colony on the planet. They embraced the absence of technology and created a primitive but seemingly well-functioning society.
However, the absence of technology also resulted in multiple deaths, most notably as the result of dangerous insect bites that proved difficult to treat using only herbal medicine. Also a punishment box was in use, a small and claustrophobic box barely large enough to hold a Human, in which colonists were locked for some amount of time, without water, as punishment for crimes like stealing. However despite these issues, the colonists were in general very happy with their new life.
In 2370, Commander Benjamin Sisko and Chief Miles O'Brien of the Starfleet runabout USS Rio Grande, prospecting the area for potential new colonies, also got stranded on the planet. They discovered that the stranding of the Santa Maria was not an accident, but rather an elaborate plot by Alixus. She planned everything in advance, and used a power generator to create the duogenic field herself, in order to bring her social theories into practice and create what she perceived as a perfect community. Alixus tried to manipulate the two Starfleet officers into joining her community, using sexual favors and torture in the punishment box among other means. She also tried to auto-pilot their runabout in orbit into the system's sun in an effort to evade further discovery, but it missed the target and when it was located by Starfleet they were able to extrapolate its starting point. As a result, the Federation officially re-established contact with the colony. The deception by Alixus became known to the colony, too, but most thought that the community they had was not worth giving up. (DS9: "Paradise")