The biggest problems with the geocentric model of the universe is age. Although the model that is two thousand years old and has been updated and error after error has been corrected, it still remains a fossilized idea. The Ptolemaic system, used until the sixteenth century, believed that "each planet orbited around a circle. . . an epicycle. . . [which encircles the earth].
The original model, although false was the first and last word of the celestial heavens. Then along came Nicolaus Copernicus and his visionary insights that contradicted the Ptolemaic view of outer space of the sun revolving around the planets. He presented his ideas and his model is known as the heliocentric view, the sun being in the center of the universe and the planets revolve around it. It was an improvement.
There have been remedial work on that view, but basically the sun is the focal point of the universe. Planets, including the third planet, the earth, orbits the sun. Then along came Kepler who corrected his mistakes and insisted that the planets did not circle in an ordinary fashion but on an axis elliptically with one of its two pole points always directed toward the sun. The sun shone in a cone like fashion and was often intercepted with another planet.
This basically, is the reason for the seasons. Sunshine means summer, absence of sunshine and far distances away from the sun means winter. The northern and southern hemispheres have opposite seasons because of their geographic placement, nearer or closer to the sun. Examples, when it is summer in the northern hemisphere, it is winter in the southern - winter in US, summer in Australia, as an example.
The along came Galileo threw his bombshell that cost him a lot of trouble. He sided with the the heliocentric view and that did not set well with the Catholic Church who had not accepted it. He is remembered and credited with his views on astronomy, but much of his fame has do do with the famous trials with the Church who made him recant his views.
In time he was proven right and his name was cleared and he was forgiven by the Church. That still remains a a black spot on the history of astronomy, and the Catholic Church is forever reminded that it too sometimes can make mistakes. Big mistakes. To their credit, when they learn they are wrong, the admit it and try to make restitution.
In reality, the problems with astronomy is not much different from problems that face the earth today. There is information and there is misinformation. There is truth of the matter and there is chaos. What is at the base of the problems is reality. The realization that the biggest obstacle facing astronomers when studying the solar system is distance. The lines drawn have to be continually redrawn when new discoveries are made.
At first, the stars closest to earth were mapped and studied and nothing was known about the far distant planets, and even then, mistakes were made in calculations, but those were eventually corrected. Enough is never enough where stars and the mysterious outer reaches of the universe is concerned.
It is clear now that some more realistic model is needed to study and to be used as a model for all studies. As it stands now, the geocentric model being used is not sufficient for the scope of future explorations. As if in truth such a model is possible. Yet there are indications that there are newer methods of learning about solar mysteries that are less invasive and yes, more realistic. Surely some bright far thinking young student one day will be able to cut through the entanglements and bring chaos out of confusion.