pure and applied geophysics

, Volume 63, Issue 1, pp 105–108 | Cite as

Moon mass approximation in algebraic form analogous to activity sphere formula

  • Irving Michelson


The concept of comet orbit activity sphere as introduced byD'Alembert and developed byLaplace is modified and applied to the Sun-Earth-Moon system, leading to a new approximate relationship between astronomical constants usually regarded as independent quantities. When Sun-Earth mass ratio, the astronomic unit, and Earth-Moon separation distance are taken as known, an elementary algebraic formula gives the Earth-Moon mass ratio in terms of these. Despite the inherently imprecise character of this type of calculation, surprisingly close numerical agreement with independently determined values is obtained. The great simplicity and directness of the result contrast with ardous orthodox inference procedures for the lunar mass, suggesting that newer methods of general dynamic analysis are required in the study of asymptotic states of the three-body problem.


Asymptotic State Algebraic Form Inference Procedure Astronomic Unit Orbit Activity 
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  1. [1]
    P. S. Laplace,Traité de Mécanique Céleste, Tome Quatrième, Livre IX, Oeuvres Complètes, T. IV, Gauthier-Villars (1880), 219.Google Scholar
  2. [2]
    E. Schatzman (Ed.),Astronomie, Encyclopédie de la Pléiade, Librairie Gallimard (1962), 1150.Google Scholar

Copyright information

© Birkhäuser Verlag 1966

Authors and Affiliations

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

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