Final answer:
The background radiation of the Big Bang was most notably mapped in detail by the WMAP mission launched in 2001, and even more finely by the Planck mission launched in 2009.
Step-by-step explanation:
The background radiation of the Big Bang, known as the Cosmic Microwave Background (CMB), was mapped by the Cosmic Background Explorer (COBE) satellite which was launched in 1989. However, the more detailed mapping that is widely recognized happened with the subsequent satellite missions. The Wilkinson Microwave Anisotropy Probe (WMAP) was launched in 2001, and the Planck mission, which provided an even more detailed map, was launched in 2009.
These missions have delivered increasingly detailed all-sky maps of the CMB, revealing tiny temperature fluctuations that are extremely important to understand the early universe. The colors in these maps represent different temperatures, red for warmer and blue for cooler areas, and correspond to regions of slightly different densities. These densities are the seeds of all future structures in the universe such as stars, galaxies, and galaxy clusters.