The one constant in the Gundam saga is the sprawling, bureaucratic, corrupt and cowardly Earth Federation. This unified world government organized the space colonization program, and then proceeded to incur the undying enmity of the spacenoids by turning Earth into a private playground for government elites. Acronyms used in the animation imply that it might properly be referred to as the "United Nations" or "Earth Union," but the Sunrise animation studio has since decided that "Earth Federation" is to be the official translation.
Earth Federation Government
This is the central government that rules over Earth and its space territories. The Federation Government's exact structure is unclear, and at various times it appears to be run by both a cabal of cabinet ministers and a bickering mob of demogogic politicians. Our best guess, based on material published in Gundam reference books and oblique references in the animation, is that the Federation Government is organized along the lines of the modern-day United Nations.
According to this model, the highest authority is the Earth Federation Assembly, a congress of elected representatives from the Federation's member nations which meets once or twice a year to debate broad policy matters (as seen in Z Gundam). The assembly is headed by a chairman, who is the top official in the Federation Government. Meanwhile, a permanent security council takes care of day-to-day matters and supervises the Earth Federal Forces. This would presumably be the shadowy cabal we see in Gundam 0083, deciding how to respond to the threat of the Delaz Fleet.