The Eastern Alliance destroyer is a spacecraft used by the Eastern Alliance of Terra. An Eastern Alliance destroyer tracks the Lunar Avion from Lunar Seven to Paradeen where it eventually encounters the Galactica. Commandant Leiter commands the destroyer that is captured by the Colonials. Lanceman and Donner are crewmen aboard the destroyer (Greetings from Earth). The destroyer manages to escape from Galactica, and returns to Terra with the Colonials on its trail (Baltar's Escape).
The Eastern Alliance destroyer was repeatedly noted to be far smaller that a battlestar and non-threatening as a contender. In fact, a captured destroyer was briefly impounded aboard Galactica and appeared to be comparable in size to a Colonial shuttle.
Although a Viper squadron was dispatched to pursue the Alliance Destroyer in Experiment in Terra, at the end of the episode we never learn whether it reached its destination, which may have been Lunar Seven. The conclusion of the war between the Eastern Alliance and the Terrans presumably rendered both the Viper squadron's mission, and the mission of the Destroyer itself unnecessary.