Alpha moon was the outer moon of the planet Peliar Zel II. It was colonized by the Peliar Zel natives sometime in the 19th century. Throughout their history they had been at war with Beta moon, but ambassador Odan managed to negotiate a peace in 2337. During the negotiations Kalin Trose was the representative of Alpha moon and the aunt of Lathal Bine was the representative of Beta moon. The peace was accomplished by letting the two representatives switch places for a week to understand each other's situation with more informed eyes. During those negotiations Kalin Trose quelled a plot, by a radical from his own moon, to assassinate the Beta moon delegate.
In the 2360s, Alpha Moon's government had developed a way to tap into the energy from Peliar Zel's magnetic field and relied exclusively on that energy source. It caused environmental damage on the Beta moon when their orbit passed through the energy beam, and started the process of global warming. That strained relations again and both moons started to arm for war. Odan negotiated a new peace treaty in 2367 after a six hour long meeting, with Kalin Trose as the representative of Alpha moon this time as well. (TNG: "The Host")