The Ptolemaic model’s main error was holding that everything went around the earth when only the projected position of the moon matched observations and all the other planets go around the sun (and their moons go around their respective planets – which was one of the main points Galileo discovered) but the model is excellent if you then still have the sun go around the earth. This is still the model we use for star observations. It is also the model used in planetariums where a devise projects the universe from the center of the room.

The Copernican model initially was not as accurate but as it was updated and improved it became an excellent model and the one most useful for space flight. It is mathematically most simple which made it appealing to the mathematically minded modern philosophers that considered it superior to the Ptolemaic system for that reason.

With the Einsteinian model space is curved – earth goes straight, as do all objects in space/time. With his concept of symmetry the equations are even simpler than with the Copernican model and is more accurate. It is also more like the Ptolemaic system than the Copernican system.

There are other models. One at least: neither the sun goes around the earth, nor the earth goes around the sun but both remain on the same plane.

I am sure there are other models I have not heard of, and that there will be more.

The contemporary pragmatic view is that all the different models have their usefulness and in that respect may be considered true to observations. Each model may be interpreted as a perspective. Interesting to note here is that the Geocentric model of Ptolemy and the Heliocentric model of Copernicus can only each be a good model if both are correct, each from a different perspective! The Geocentric model is the view from here on earth looking up and the Heliocentric model is the view from the perspective of space (you have to picture yourself off the earth to visualize the “solar system.” Each is the mirror model of the other.

Some other interesting things not directly associated with this: models of the universe at least to include those in ancient Egypt, South America, and observatories such as Stonehenge clearly indicate the people thought of the earth as a sphere and while certainly some people –children and uneducated at least, thought of the earth as flat, some, such as Aristotle came close to figuring the size of the sphere. Columbus’ remarkable trip to “India” was successful despite the fact that he was not as good a mathematician as those that insisted India was farther. They were right about that, but lucky for him and his expedition there was another continent in between! He still called the natives “Indians.”