This is actually related to Galileo. What he said is irrelevant. What he did was pick a point of reference without a reason, the sun, and that was of course immediately denied by both the church and all science to this day.
Speaking practically, when calculating satellite orbits one uses a two body universe, Earth and Moon. To include the Sun, other planets, the Milky Way or distant galaxies would be inefficient and not yield a result different enough to bother. So many people legitimately treat the Earth as the center of the universe every day and to do otherwise would be inappropriate.
Science of course, pretty much since G went out on a limb, says that planets don't orbit. All heavenly bodies are affected by all others based on formulas that we've got figured out pretty accurately. But we teach orbits because the additional forces are tiny enough that orbits work very well.