Beta moon was the inner 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 Alpha moon, but ambassador Odan managed to negotiate a peace in 2337. During those negotiations Lathal Bine's aunt was the representative of Beta moon and Kalin Trose was the representative of Alpha 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.
In 2367 Alpha moon 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 its 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 after a six-hour long meeting, with Lathal Bine as the representative of Beta moon this time. (TNG: "The Host")