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Earth's rotational and orbital motions interrelated byLoitsyanskii's turbulence theorem

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Summary

The Loitsyanskii theorem for turbulent fluid motion is presented in simplified form from the viewpoint of angular momentum conservation and extended by a normalization with respect to total mass. When the new parameter thus obtained is evaluated for a gas cloud of the size and mass of the present Sun-Earth system, and this is equated to the corresponding parameter for the Earth-Moon configuration, an accurate equation between independently determined astronomical constants is found. The Earth's rotational speed is expressed in terms of its mean orbital motion, the Sun-Earth mass ratio, the ratio of separation distances, and the Earth's radius. The most simple form of the algebraic relationship (10) is believed unique in linking planetary orbital dynamics to motion about the center of gravity.

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References

  1. [1]

    L. G. Loitsyanskii,Some basic laws of isotropic turbulent flow, Rep. Cent. Aero Hydrodyn. Inst. (Moscow), No. 440 (Translated as Tech. Memor., Nat. Adv. Comm. Aero., Washington, No. 1079) (1939).

  2. [2]

    C. F. von Weizsäcker,Das Spektrum der Turbulenz bei grossen Reynolds'schen Zahlen, Z. Phys.124 (1948), 614.

  3. [3]

    I. Michelson,Augmented lunar tide heights in barycentric motion, Mon. Not. R. astr. Soc.132 4 (1966), in press.

  4. [4]

    I. Michelson,Sun, earth and moon masses related by reciprocity principle, J. de Mécanique,5, 3 (1966), in press.

  5. [5]

    E. Schatzman (editor),Astronomie, encyclopédie de la pléiade, Librairie Gallimard (1962). 1150.

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Michelson, I. Earth's rotational and orbital motions interrelated byLoitsyanskii's turbulence theorem. PAGEOPH 65, 164–167 (1966). https://doi.org/10.1007/BF00874963

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Keywords

  • Angular Momentum
  • Rotational Speed
  • Total Mass
  • Simple Form
  • Separation Distance