How do the geocentric and the heliocentric descriptions of the solar system differ?

Answer 1

The geocentric view is the view of "Well, DUH!"; the one we can see happening all around us, even with (or ESPECIALLY with!) no scientific training. We see ourselves standing on the Earth, which clearly IS NOT moving, and the Sun and Moon rise and set. What, this isn't obvious?

The heliocentric view requires an external viewpoint, a look at the bigger picture. The Earth IS spinning, even though we can't feel it or see it; careful instruments can measure it, and devices such as the Foucault Pendulum can make it obvious. It's the Sun that's standing still (well, it isn't, but that's another external viewpoint and an even bigger picture) and the Earth spinning to create days and nights. Careful measurement of the movements of the planets can clearly prove that the heliocentric view is easier to explain, but farmers generally don't measure the positions of the planets that accurately.

We can use both. The geocentric view is accurate enough for most people, for most purposes. When you drive down the street, you don't REALLY need to calculate how fast the Earth is spinning in order to find your way to the grocery store, because the street is spinning at the same speed.