In "On the Revolutions of the Heavenly Spheres" Book 5. chapter 16, Copernicus appears to acknowledge a discrepancy between the old Ptolemy observation and the model. Here is a Google Translate from a German translation:

if one calculates back, it turns out that the location of the apogeum of the eccentric circle was in 119 ° 40 ′ of the fixed star sphere at this last observation. Ptolemy found this place at the time of Antoninus at 108 ° 50 ′; so it has moved forward by 10 ° 50 ′ except for us. We have found the distance between the centers to be 40 such parts smaller, of which 10,000 come to the radius of the eccentric circle. Not as if Ptolemy or we were wrong, but to prove that the center of the earth's orbit has approached the center of the orbit of Mars while the sun has remained immobile...

Copernicus seems to be saying neither he nor Ptolemy were in error, but that the "center of the Earth's orbit" has moved. Did Copernicus ever try to explain how the "center of the Earth's orbit" moved? or to investigate the nature of the movement?

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    $\begingroup$ Apparently, he does not. Mazer in Shifting the Earth only remarks that "Copernicus' conclusion must have been most disturbing as it presents a movement that his model does not explain". $\endgroup$
    – Conifold
    Jul 16, 2021 at 2:23

1 Answer 1


There is really no sign here of any 'discrepancy' at all. In the quoted/translated passage from 'De Revolutionibus', Copernicus is pointing out that the apogee of Mars' orbit has shifted between the time of the observation reported by Ptolemy and his own time. The quoted passage then goes on to refer to Copernicus' theoretical mechanistic ideas for the celestial motions, which explain this motion as well.

Insofar as these ideas and mechanisms involved circles and epicycles, they have become obsolete since Copernicus' time, but that is of course different from any matter of discrepancy. 'Discrepancy' normally implies some kind of incompatibility or contradiction. But the slow motions of apogees over time contradict nothing: planetary tables from Ptolemy's day to the present acknowledge and incorporate such motions. They are part of the natural order, not any sort of discrepancy or mistake.

It may help any further discussion to quote a somewhat better English translation of the passage in question (i.e. not subject to the hazards of machine translation). This is from Edward Rosen, "Nicholas Copernicus on the Revolutions. Translation and commentary", (Polish Scientific Publishers, Warsaw/Cracow; also Macmillan; also Johns Hopkins, Baltimore; 1978). The reference to an apogee is to the apogee of Mars' orbit ('eccentric') around the sun:-

... computed backwards, the place of the eccentric's apogee in this last observation obviously = 119°40' [ = 133°20'- 13°40'] in the sphere of the fixed stars. In Antoninus [Pius'] time Ptolemy found the apogee at 108°50' [Syntaxis, X, 7 : 25°30' within the Crab = 115°30'- 6°40']. It has therefore shifted eastward 10°50' [= 119°40'- 108°50' from that time] to ours. I have also found the distance between the centers smaIler by 40P [1460P as compared with 1500P] whereof the eccentric's radius = 10,000P. The reason is not that Ptolemy or I made an error, but that, as is clearly proved, the center of the earth's grand circle has approached the center of Mars' orbit, with the sun meanwhile remaining stationary. For, these conclusions are mutuaIly consistent to a high degree, as will become plainer than daylight hereafter [V, 19].

Clearly, in the final sentence included here, in the quotation from the Rosen translation (omitted by the questioner), Copernicus was saying that everything is consistent, and at the end of the later chapter (V, 19) to which he refers, he concludes:--

Thus also in the case of Mars the sizes and distances of its motion have been explained through sound computation by means of the earth's motion.

  • $\begingroup$ Thanks you very much for this answer. I agree the term "discrepancy" is not the best here. However, for the eye of the reader it is indeed discrepancy that N.C explained by a physical cause (so no "true" discrepancy ) as Mazer writes in his book (see Coinfold comment) it seems the movement of the apogee was not 100% established in the scientific atmosphere of that time. $\endgroup$
    – d_e
    Dec 27, 2022 at 18:06
  • $\begingroup$ Also, it is interesting that for that, N.C needed to shift the Center of Earth orb while the True Sun remained in place. If I read that right it means that N.C thought the eccentricity of Earth has changed during that time? At any case this is a big movement his model indeed does not explain. And By moving the MeanSun to account for Mar's apogee, should it not "break" the apogee movement of the other planets? I wonder if N.C wrote about this movement in other planets. $\endgroup$
    – d_e
    Dec 27, 2022 at 18:11
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    $\begingroup$ @d_e : Thanks for your comments and reaction. I agree, of course, that Copernicus' explanations did not solve all problems of planetary measurement. From a modern point of view, one can distinguish results of old theories that would give differences in observable quantities, from results that would give differences in theoretical constructs. Apogees and centers are remoter from observation and thus in a sense secondary/theoretical compared with planetary positions and motions. Historically it took much work, especially from Tycho and Kepler, to improve on problematic points left by Copernicus. $\endgroup$
    – terry-s
    Dec 27, 2022 at 18:33

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