# Ptolemaic planetary models and Kepler’s laws

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## Abstract

In this article, we aim at presenting a thorough and comprehensive explanation of the mathematical and theoretical relation between all the aspects of Ptolemaic planetary models and their counterparts which are built according to Kepler’s first two laws (with optimized parameters). Our article also analyzes the predictive differences which arise from comparing Ptolemaic and these ideal Keplerian models, making clear distinctions between those differences which must be attributed to the structural variations between the models, and those which are due to the specific parameters Ptolemy determined in the Almagest. We expect that our work will be a contribution for a better understanding not only of the Ptolemaic theories for planetary longitudes through a clearer perception of the way in which Keplerian features are present—or absent—in Ptolemy’s models, but also for a more balanced judgement of different aspects of the contribution of the first two laws of Kepler to the modern astronomical revolution.

## Notes

### Acknowledgements

We want to thank Alexander Jones, Dennis Duke, Diego Pelegrin, Sandra Ponce and Gustavo Zelioli for their comments and suggestions of earlier versions of this paper. We would also like to express our thanks for the support of Research Projects PICT-2014-1741, PICT-2014-0775 and PICT-2016-4487 of the Agencia Nacional de Promocion Cientifica y Tecnológica of Argentina.

### Compliance with ethical standards

### Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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