For thousands of years, Terra III has been the capital of the Federation and the home base of humankind. As the name implies, it is the third planet to hold such an honor as "terra" which, as in Earth's Latin, means something akin to "land."
Terra III is a technological and urban development wonder. After the first Terra, from which humanity truly thrived at the dawn of their era, became inhabitable, the space-faring race established a new home on what would become known as Terra II. Unfortunately, this was a short-lived venture, as the planet was quickly stripped of its resources and was unable to provide adequate space and sustenance for a bursting population. When the Federation decided to move once again, a planet was scouted that would become known as Terra III.
The humans of that time were dedicated to long-term planning, convinced that if they put in enough effort, it would be tens of thousands of years before a Terra IV would have to be found. Every inch of the new planet was terraformed to perfection before construction began. As humanity knew it was inclined to expand, and to make sure there was room for further technological advancement, a "thousand-year build" plan was put into place. Construction centered on what would become the core capital of the Federation before expanding in planned blocks and swathes as needed. There is no unclaimed or uninhabitable land on Terra III. Even the frigid poles belong to the humans who have been caring for it for thousands of years.
This planning also included open, public green spaces such as parks, botanical gardens, beaches and fields surrounded by low-level dwellings. The contentment and happiness of the population was well thought-out, to the point that Terra III became with a humble population of two million that turned into thirty-four billion in the present day. Ecological and environmental safety are as paramount as human satisfaction. Learning from their mistakes on Terra I and II, humanity put forth great effort into carbon-offset technology and clean energy. Most food is either grown in small, personal hydroponic gardens or imported from neighboring agrarian planets like Qahrain. There are no farms or ranches on Terra III.
Colloquially, "Terra III" refers to both the planet as a whole and the core capital at the same time. The core itself boasts nearly 20 percent of the planet's population, most of whom live in reinforced high-rises that mark the sky and underground communities. Most of the universe's news and entertainment is produced somewhere on Terra III, with over 85% of the Federation's corporations holding headquarters on the planet. The core capital also boasts some of the highest rated universities, hospitals, and resorts in the Federation.
Since so many people live in towering high-rises that reach into the sky, transportation on Terra III is not only accomplished on the ground (which must be unnaturally illuminated during both day and night cycles) but through "sky carriages" that have preset routes like a train line. These are often rideshares, although only one carriage car at at time rolls through any given designated pick-up or drop-off point. Those with the means can reserve their own carriage ahead of time.
Terra III is administered both on a local council level and a planetary-wide governance. Like every planet or unaffiliated moon/colony in the Federation, Terra III has representation in the parliament, which meets in the core capital.