We do know that Airi Masaki is a native of the world call Airai. Tenchi is part Airain. We do know that Airai is a theoracy. the best information about Airai comes from the Astronerdboy Anime and Magna Blog website.
Airai is a planet with the greatest concentration of precursur artifacts. By studying the artifacts, the Airain have extremely advanced technology that makes them one of the greatest antions in the galaxy. Additionally, they are aware of the 'Three Lives,' the Chousin. Airai is also the center of the largest religion in the galaxy and while they have pwoerful religious leaders, they are seeking for the "true god." The Airians belived that Tsunami is one of the three great goddesses, and are convinced that Jurai selfishly keeping her to themselves. The Airians thus plan to gain access to and 'acquire' Tsunami.
The use of overt force is not their chief method in this undertaking. Instead, the Airains are using diplomaic and undercover methods. For example, Airi Magma ,the daughter of their cheif leader, was to marry a member of the Amaki House of Jurai. By doing so, they hoped to someday have an Airain on the throne of Jurai. Instead, Airi had a relationship with Yosho and broke off the engagement to the man from Hosue Amaki. About 140 years later, Airi would married Yosho, and evntually giving birth to Kiyone, the mother of Tenchi Masaki.
It is very odd that Airai had wanted to take Tsunami form Jurai. While Airai is the center of the largest reliigion, why they were willing to start a war with Jurai over Tsunami. There seem to have been a group of Airain leaders who have become too powerful and currupt. Airain and Jurain relations were at a low point when Airi had fallen in love with Yosho. It seem that Airi's parents and a few trusted allies have intentionally plotted to bring Yosho and Airi together to prevent a major war. The plot of Airi's parents had succeeded as a result of Airi falling in love with Yosho. Unknown to Airi's parents and Yosho, Airi became pregnant with Yosho's child. Fear that her child will be kill by her people, Airi had surgically remove the fetus and place it in stasis. Airi had return to Airai to break off her engagement to the man form the Amaki House. After defecting the Galaxy Acamedy, Airi had the child replace back into the womb. A few months later, the child was born and named Minaho.
Sometime after Airi ahd defected to the Galaxy Academy, Lady Kimiko Jurai had learn of Airi's plight. Lady Seto decided to place Airi under her wing. Both have become very close friends.
While the plans of Airi's parents seem to have avoided a war, it was likely Ryoko's attack on Jurai which had stop the war as wel as Tsunami's disappearance.. We can suspect that Airain and Jurain relations have improve over the alst seven hundred years, The Seniwan Empire have play their part in the improvement of relations between Jurai and Airai.
If there is an OVA 4, I will like to see Airai playing a major role in the series. Instead of trying to get Tsunami, the Airains may have spent the last seven hundred years in studying a set of prophecies which focus on the emergance of the myerious Third Power. The Third Power is the mythical world which one day become the greatest and friendly rival power of Jurai and the Seniwan Empire.