Astronomia nova

  • Bruce Stephenson
Part of the Studies in the History of Mathematics and Physical Sciences book series (HISTORY, volume 13)


In 1609 Kepler published the Astronomia nova, the record of a decade’s intense labor. The full title of the work1 proclaims that his new astronomy is causal, that it is a physics of the heavens based upon an examination of the motions of the planet Mars. This book is the pinnacle of pre-Newtonian astronomy, and points the way toward modern astronomy as established by Newton. Yet the material treated is scarcely that of a definitive treatise. No trace does one find, in this book, of the assurance with which Ptolemy had explained his predecessors’ models, and his own, and no trace of the orderly and comprehensive arrangement of Ptolemy’s Almagest. The Astronomia nova is instead the account of a trip into unknown territory. We enjoy today a comfortable familiarity with the end results, the area law and the ellipse, so that the journey narrated by Kepler seems even more circuitous than it really is.


Optical Equation Equant Center Eccentric Anomaly Distance Theory Planetary Theory 
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    G. W., 3: 311:40–312:1. For Kepler, remember, forces caused motion rather than acceleration. The planet’s velocity from its own moving virtue could be simply added to its circumsolar velocity (even though each of these motions was curvilinear), just as a Newtonian physicist would add accelerations.Google Scholar
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    Near the apsides the distances changed very little in any plausible theory, so that one could not be badly mistaken about the increments. (No comparison of different increments was needed.) Kepler made the curious statement that the increments were also known, reasonably well, in the mean distances. G. W., 3: 337: 33–338: 1.Google Scholar
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    W. Donahue has shown that the numbers Kepler published in Chapter 53 were not all derived from any one set of assumptions, and that the table published in that chapter probably represents Kepler’s attempt, after discovering his final distance law, to smooth the exposition leading up to it. “The Peccadillo of Johannes Kepler,” read at the meetings of the History of Science Society, Bloomington, Indiana, 2 November 1985.Google Scholar
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    C. Wilson has correctly emphasized both the impossibility of determining the true orbit from distance calculations alone, and the role of the equations of center alongside the rough distance calculations in suggesting the kind of improvements needed: “Kepler’s Derivation of the Elliptical Path,” Isis 59 (Spring 1968): 4–25.Google Scholar
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    C. Wilson (“Kepler’s Derivation,” p. 12, n. 32) appears to believe that since the libration theory supplied the distances in the table of Chapter 53, these distances, or at least the twenty of them not calculated explicitly in the text, were not observationally determined. On the contrary, the technique of that chapter was a way of using observations to confirm or refine a postulated distance. Although obtained initially from the libration theory, the distances in Chapter 53 really had been confirmed as (approximately) correct by the observations.Google Scholar
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    Copernicus had hypothesized an annual rotation of the earth to account for its axis being always pointed in the same (tropical) direction. Kepler, whose frame of reference for the earth’s motion around the sun was no longer that of a rotating shell, asserted that mere constancy of direction of the axis did not require a special cause, although the very slow precession of the equinoxes perhaps did. G. W., 3: 350: 30–41.Google Scholar
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    Kepler was for a while concerned over the disagreement between his physics, which indicated a libratory force proportional to the sine of the eccentric anomaly, and his distance law, which indicated that the completed libration was in fact proportional to the versed sine of that angle, until he realized that the latter represented the cumulative effect of the former. G. W., 15:252–255.Google Scholar
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    Aiton apparently missed this consideration, which is left largely implicit in Kepler’s very brief argument in G. W., 3: 354: 27–40. See “Kepler’s Second Law,” p. 83, n. 51, and “Infinitesimals,” p. 298.Google Scholar
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    Aiton believes that, at this time, Kepler conceived the sun’s rotating virtue to act along the oval path, “as if the magnetic force just steered [the planet] in the right direction” (“Infinitesimals,” pp. 298–299). Certainly Kepler realized later that the circumsolar force should be responsible only for the component of motion perpendicular to the radius. I believe that he had not worked out this distinction when he wrote Chapter 57, and that we should regard his later revision as mathematical rather than physical; but Aiton may be correct.Google Scholar
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    G. W., 3: 360: 8–32. Since the versed sine of the coequated anomaly was needed, we may presume that the anima would hold these fibers perpendicular to the apsidal line. The sine of the angle between the solar radius and the fibers would then be the cosine of the coequated anomaly; and changes in the cosine mirror the changes in the versed sine.Google Scholar
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    The final stages in Kepler’s work on Mars are recounted in a long letter to Fabricius (#358 in G. W., 15: 240–280) dafed 11 October, 1605, which reveals little more than the account published in the Astronomia nova. Google Scholar
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    For example, Koyré, Astronomical Revolution, p. 259 (“a mistake”), p. 261 (“unfounded”); Aiton, “Second Law,” p. 83 (“gratuitous”). Aiton later corrected his opinion, recognizing that the placement was “natural”: “Infinitesimals,” p. 299.Google Scholar
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    D. Whiteside has calculated that the via buccosa was observationally indistinguishable from the final ellipse. At any given time the planet’s distance from the sun differs on the two orbits, but because the motion around the sun depends on the distance, the two positions lie within three quarters of a minute of arc in true anomaly. “Keplerian Planetary Eggs,” Journal for the History of Astronomy 5 (1974): p. 14, and “Newton’s Early Thoughts on Planetary Motion,” British Journal for the History of Science 2 (1964): p. 129 n. 42. Kepler himself never paused to make such calculations. Once he realized how to combine his physics with his distances—as discussed in the following pages—he knew that the combination was correct.Google Scholar
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    C. Wilson has quite properly emphasized that Kepler’s distance calculations did not nearly suffice to define the orbit, and that an essential element was his realization that the circle and the earlier ellipse gave opposite and roughly equal equal errors in the equations of center: “Kepler’s Derivation,” passim. I cannot agree, however, with his implication that this realization sufficiently determined the shape of the orbit (p. 18).Google Scholar
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    See the discussion in Whiteside, “Keplerian Planetary Eggs,” especially pp. 13–15.Google Scholar
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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Bruce Stephenson
    • 1
  1. 1.Department of Astronomy and AstrophysicsUniversity of ChicagoChicagoUSA

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