Earth

Every space cartoon needs a home port it can point back at, and SilverHawks puts Earth in that job and then almost never goes there. It is where the five recruits volunteer, where Professor Ghemakain and his assistant Mabis do the surgery that makes them partly metal, and where General Rawlings gives the order that sends them across the galaxy. After the first episode the series leaves it behind.

That distance is the point. Limbo is roughly forty thousand light years out and the trip takes the Mirage most of episode two, so once the team arrive at Hawk Haven they are on their own. No cavalry arrives from Earth. When the show does come back it is usually for a flashback or a briefing, and the appearance lists bear that out: seven episodes out of sixty-five, five of which also visit Federal Interplanetary Force 1 Headquarters.

Nobody on the team is homesick out loud. Bluegrass keeps a Tennessee accent and a guitar, Quicksilver keeps the command habits, and that is as close as the writing gets to the subject.

Sources: the aired episodes, the appearance lists on thundercats.fandom.