Unification and Support: Harmonic Law Ratios Measure the Mass of the Sun

  • William Harper
  • Bryce Hemsley Bennett
  • Sreeram Valluri
Part of the Synthese Library book series (SYLI, volume 236)


Newton’s inferences to inverse square centripetal forces from Kepler’s areal and harmonic laws illustrate an ideal of scientific explanation according to which the phenomenon to be explained measures the theoretical parameter which explains it.’ This ideal suggests a corresponding type of unification which is realized when two or more phenomena yield agreeing measurements of the same theoretical parameter. Such successful unification generates empirical support for estimates of that theoretical parameter. An example is that the harmonic law ratios of the several planets all measure the mass of the sun. This example will help us explore the way in which such unification brings empirical support to the estimation of the parameter. It will clarify what we regard as the great empirical significance of the role of phenomena as generalizations specified by best fitting curves for open-ended bodies of data. When such a phenomenon yields an agreeing measurement of a theoretical parameter the estimate of that parameter can be backed up by the whole body of data which the phenomenon fits. The open-endedness makes new data relevant; if the phenomenon continues to fit new data they will augment the empirical support that could be appealed to in backing up the estimate of the theoretical parameter.


Astronomical Unit Centripetal Force Keplerian Orbit Empirical Success Theoretical Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Butts, R.E. (ed.) William Whewell’s Theory of Scientific Method, Hackett Publishing Company, Indianapolis, Indiana 1989Google Scholar
  2. Cajori, F. (1962) Sir Isaac Newton’s Mathematical Principles of Natural Philosophy, University of California Press, BerkeleyGoogle Scholar
  3. Casper, M. Johannes Kepler Gesammelte Werke, C.H. Beckische Verlags Buchhandlung MünchenGoogle Scholar
  4. Clemence, G.M. (1961) “Theory of Mars-Completion”, Astron. Pap. Amer.Jour.Eph., Vol.161 pt. 2Google Scholar
  5. Danby, J.M.A. (1988) Fundamentals of Celestial Mechanics,. 2nd edition. Willmann-Bell Inc. Richmond, VirginiaGoogle Scholar
  6. Gurnette, B.L. and Woulley, R. (1974) Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, Nautical Almanac Offices of the U.K. and U.S.Google Scholar
  7. Harper, W.L. (1991) “Newton’s Classic Deductions from Phenomena” PSA 1990, Volume 1, pp. 183–196.Google Scholar
  8. Harper, W.L., (1993) “Reasoning from Phenomena: Newton’s Argument for Universal Gravitation and the Practice of Science”, pp.144–182 in Action and Reaction: Proceedings of a Symposium to Commemoratethe Tercentenary of Newton’s Principia, University of Delaware Press, Eds. Paul Theerman and Adele F. Seeff.Google Scholar
  9. Herivel, J.W. (1965) The Background to Newton’s Principia, Oxford, Clarendon Press.Google Scholar
  10. Laskar, J. (1990) “The chaotic behaviour of the solar system: A numerical estimate of the size of the chaotic zones”, Icarus 88, 266–291.Google Scholar
  11. Laubscher, R.E. (1981) “The Motion of Mars 1751–1969”, pp. 363–490, Astronomical Papers prepared for the use of the American Ephemeris and Nautical Almanac, Nautical Almanac Office, U.S. Naval ObservatoryGoogle Scholar
  12. Meeus, J. (1988) Astronomical Formulae for Calculators, 4th ed. WillmannBell, Inc. Richmond, VirginiaGoogle Scholar
  13. Moulton, F.R. (1914) An Introduction to Celestial Mechanics, 2nd revised edition, Dover (edition 1970 ), New York.Google Scholar
  14. Skyrms, B. (1980) Causal Necessity, Yale University Press, New Haven.Google Scholar
  15. Taton, R. and Wilson, C. (eds) (1989) Planetary Astronomy from the Renaissance to the rise of astrophysics. Part A: Tycho Brahe to Newton, Cambridge University Press, Cambridge.Google Scholar
  16. Thoren, V. The Lord of Uraniborg, Cambridge University Press, CambridgeGoogle Scholar
  17. Wilson, C. (1989) “Horrocks, Harmonies, and the Exactitude of Kepler’s Third Law”, in Astronomy from Kepler to Newton, Variorum Reprints, London.Google Scholar
  18. Wilson, C., (1989) “Predictive Astronomy in the Century after Kepler”, pp.162–206 in Taton R. and Wilson, C. op.citGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • William Harper
    • 1
  • Bryce Hemsley Bennett
    • 1
  • Sreeram Valluri
    • 1
  1. 1.University of Western OntarioCanada

Personalised recommendations