is there any software library that calculates earth/moon/sun/planets positions based on the geocentric model?
if that exists, why is the heliocentric model the most popular?
I don't know any software library which does what you require. But there is an account of the geocentric model in terms of modern mathematics (vector algebra etc) written by Professor Richard Fitzpatrick of the university of Texas. It is called "A Modern Almagest. An Updated Version of Ptolemy's Model of the Solar System" and available in html or pdf at: https://farside.ph.utexas.edu/books/Syntaxis/Syntaxis.html The procedures described in this book can be used to develop such a software library.
As we know today from the works of Copernicus and his successors the heliocentric system is the right one and describes the motion of the earth/moon/sun/planets very precisely.
Kind Regards Klaus
I think no one claims that assuming the earth is at the center of everything makes orbit predictions impossible. (For that matter, the apparent homogeneity of the cosmic background radiation seems to suggest that there is no "center" of the universe, etc.) It just makes things messier. That's partly why "local" problems like getting a spaceship to the moon, or to Mars, that do need to refer to Earth as a "ground point", become crazy, in comparison to two-body or restricted three-body problems.
But/and, yes, NASA in-effect has software that does such computations for Earth-to-X stuff!
That (also!) does not mean that the Earth is anywhere near the center of mass of the solar system. The sun is. And our solar system is nowhere near the center of mass of our galaxy. And ...
So, in some regards, the whole question of geocentric versus heliocentric doesn't really have content... at least insofar as there is no center, anyway, ... That kind of thing.
EDIT: the Community Bot has made some well-intentioned "suggestions" about editing-to-improve. Ok. But I am inclined to think that my minor reframing of the question answers it better than a literal response. Sure, opinions vary...