In Copernicus’ model a spherical Earth rotates daily on it axis whilst it and the other planets each orbit the Sun. The period of the planets’ orbits increases with increasing distance from the Sun. The Sun was not exactly at the centre of the planetary orbits thus strictly speaking the model is heliostatic rather than heliocentric.
There were several advantages of Copernicus’ model over that of Ptolemy:
It could predict planetary positions to within 2°, the same as that of Ptolemy.
Retrograde motion of planets was explained by the relative motion between them and the Earth.
Distances between planets and the Sun could be accurately determined in units of the Earth-Sun distance (ie Astronomical Units).
Orbital periods could be accurately determined.
It explained the difference between the inferior planets (Mercury and Venus) that were always observed close to the Sun and the superior ones (Mars, Jupiter and Saturn).
It preserved the concept of uniform circular motion without the need for equants.
It preserved Aristotle’s concept of real spheres nestled inside one another.
Unlike Ptolemy’s model it did not require the Moon to change in size.
Copernicus’ model also had several problems which contributed to its failure to immediately supplant Ptolemy’s model:
No annual stellar parallax could be detected. Copernicus explained this as due to the fact that the stars were a vast distance hence any parallax would be very small and difficult to detect.
It required a moving Earth, This would contradict Aristotelian physics and Copernicus presented no new laws of motion to replace Aristotle.
By removing the Earth from its natural place it was philosophically and theologically unacceptable to many scholars.
It was no more accurate than Ptolemy’s in predicting planetary positions.
It was actually more complicated then Ptolemy’s model. In his efforts to avoid the equant but retain uniform circular motion he had to introduce more devices to fit his observations.
http://www.atnf.csiro.au/outreach/education/senior/cosmicengine/renaissanceastro.html
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