pure and applied geophysics

, Volume 63, Issue 1, pp 109–120 | Cite as

On a refinement of the theory of the Moon's physical librations

  • Irving Michelson


The standard formulation of the dynamics of physical librations of the Moon is re-examined in the light of currently accepted reduced estimates of the mechanical ellipticity of the lunar equator. It is seen that a more complete mathematical model is required which accounts for centrifugal couples and in which the sum of inclinations of lunar orbit (5°9′) and equator (1°30′) is not regarded as an infinitesimal quantity. Although it remains doubtful whether linearized differential equations can be expected to yield a quantitatively useful theory, a preliminary to more accurate calculation consists in analyzing the motion with fewer restrictions than has been customary. The main features of such a treatment are given which unify the classical analysis by showing how the afore-mentioned inclinations can be used to estimate the two principal mass parameters that affect physical librations. When accurate short-period libration data become available, the constants in question can be evaluated without recourse to orbital data used in the past.


Differential Equation Mathematical Model Standard Formulation Orbital Data Mass Parameter 
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  1. J. L. Lagrange,Théorie de la Libration de la Lune, Nouv. Mém. Acad. Roy. des Sciences de Berlin (1780).Google Scholar
  2. P. S. Laplace,Mécanique Céleste, Livre V, Chap. II (Gauthier-Villars, 1798).Google Scholar
  3. H. Jeffreys,Dynamics of the Earth-Moon System, Chapter 2 ofThe Earth as a Planet, Edited by G. P. Kuiper. The Solar System II (University of Chicago, 1954).Google Scholar

Copyright information

© Birkhäuser Verlag 1966

Authors and Affiliations

  • Irving Michelson
    • 1
  1. 1.Illinois Institute of TechnologyChicago

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