The Federation of Planets is an interstellar federation on South Park. It is only mentioned in the episode "Pinewood Derby".
Little is known of the Federation of Planets. It is supposedly a benevolent governing body that presides over an ever-expanding assortment of species and planets across the galaxy. All member species are capable of traveling at warp speed. Many of its member species, although not human, are humanoid in appearance.
Membership for the Federation of Planets revolves around warp speed. Whenever a new species discovers warp speed, they are immediately eligible to join the Federation. However, they must first be tested for worthiness through the "space money test". They trick the species into accepting space money and if that species returns the money to the proper authorities, they may join the Federation. Those who keep it for their own selfish needs are punished by becoming permanently isolated from the universe in a cubical force field surrounding their homeworld.
In "Pinewood Derby", Randy Marsh inadvertently discovered warp speed when he stole a proton accelerator particle from the accelerator in Switzerland to use in Stan's pinewood derby car to beat one of his rivals. The car ended up speeding into outer space and was retrieved by the Federation. They sent Baby Fark McGee-zax, the Ambassador to New Planet Testing, to test Earth for membership with the space money test.
Kevern, under the guise "Baby Fark McGee-zax", posed as a criminal and held Earth hostage while demanding a new warp drive-capable vehicle to escape the Space Cops. The humans supposedly killed him and they took the space cash as planned, and were monitored by the Space Cops, who asked if the humans knew of the space cash. They claimed not to know what happened to it, and instead used it to satisfy their own needs, at Randy's insistence. When Finland tried to confess to the aliens, the world leaders, once again on Randy's insistence, nuked Finland. The Space Cops grew suspicious and asked if they knew of this tragedy. The humans lie to the aliens about this and denied any knowledge of Finland's destruction.
Stan confessed to having cheated in the derby, but his dad refused to confess about the space cash, prompting the Space Cops to reveal that "Baby Fark" was alive and that the whole series of events was an elaborate test. They weren't Space Cops and space cash was only worth what humans decided it was worth. Because the humans refused to come clean and destroyed one of their own countries, they were denied entry into the Federation. Even worse, the Federation punished Earth by isolating it from the universe in a force field, leaving the people of Earth stunned.