The interesting thing here is that he used only algebra. This model therefore occupies a sort of sweet spot, insofar as adding to the accuracy of the model requires machinery a level above what was used to get this model.

To wit: If you want to take into account eccentricity (which I think would be the biggest source of error), the steps needed are fairly involved. For one way to do it, see [0].

[0] https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_m...