The moon

, Volume 8, Issue 4, pp 539–545 | Cite as

Orientation of the moon by numerical integration

  • H. B. Papo


The differential equations of rotational motion of the Moon are solved by numerical integration methods. Euler's dynamical equations transformed to a convenient form are treated by techniques analogous to ordinary orbit determination procedures. The proposed method is fully consistent with the ephemeris of the Moon and can utilize a variety of observational material for the solution of the selected parameters. The parameters are grouped into three distinct groups, namely:
  • --The physical libration angles of the Moon and their time rates at an arbitrary initial epoch.

  • --Physical constants featuring the principal moments of ineria of the Moon.

  • --Parameters associated with the particular observational material being used.

Examples are given of comparison between the proposed method and Eckhardt's 1970 model of the physical librations of the Moon. The merits of the new method are discussed in the light of conventional data sources like Earth-based or satellite-based photography as well as newly available data types like Laser ranging to retroreflectors on the Moon.


Dynamical Equation Integration Method Photography Rotational Motion Time Rate 
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  1. Eckhardt, D. H.: 1967, in Z. Kopal and C. L. Goudas (eds.),Measure of the Moon, D. Reidel Publ. Co., Dordrecht, Holland, p. 40.Google Scholar
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  3. Eckert, W. J. Jones, R. B., and Clark, H. K.: 1954,Improved Lunar Ephemeris 1952-1959. U.S. Naval Observatory, Washington.Google Scholar
  4. Papo, H. B.: 1971, ‘Optimal Selenodetic Control’, Reports of the Department of Geodetic Science, No. 156, The Ohio State University, Columbus, Ohio.Google Scholar
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Copyright information

© D. Reidel Publishing Company 1973

Authors and Affiliations

  • H. B. Papo
    • 1
  1. 1.Department of Geodetic ScienceThe Ohio State UniversityColumbusUSA

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