It's mentioned that the Babylonians decreed that there were exactly 360 days in a year. This statement was based upon the utilization of 360 as a standard (based on the sexagesimal system) i.e., they divided the circle into 360 equal parts. Although, there is a mention about the Sun making one full circle across the sky in one year (as estimated by them), but, how were they able to measure it? And did they believe in the Heliocentric version of the solar system?
In 150 BC a babylonian heliocentric model is documented. Heliocentric models were not uncommon historically, but Ptolemaios geocentric model was actually better at predicting the movements of the planets until Kepler came up with the idea of elliptic rather than circular orbits in the early 1600s. In the 1500s Copernicus hesitated to publish his heliocentric ideas because they did not improve predictions.