Lunar Gravity Model Obtained by Using Spherical Harmonics with Mascon Terms

  1. Soren W. Henriksen,
  2. Armando Mancini and
  3. Bernard H. Chovitz
  1. Marshall H. Kaplan and
  2. Bohdan G. Kunciw

Published Online: 15 MAR 2013

DOI: 10.1029/GM015p0265

The Use of Artificial Satellites for Geodesy

The Use of Artificial Satellites for Geodesy

How to Cite

Kaplan, M. H. and Kunciw, B. G. (1972) Lunar Gravity Model Obtained by Using Spherical Harmonics with Mascon Terms, in The Use of Artificial Satellites for Geodesy (eds S. W. Henriksen, A. Mancini and B. H. Chovitz), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM015p0265

Author Information

  1. Department of Aerospace Engineering Pennsylvania State University, University Park, Pennsylvania 16802

Publication History

  1. Published Online: 15 MAR 2013
  2. Published Print: 1 JAN 1972

ISBN Information

Print ISBN: 9780875900155

Online ISBN: 9781118663646



  • Keplerian elements;
  • Lunar gravity model;
  • Lunar orbiter data;
  • Mascons;
  • Moon


The lunar gravitational potential must be accurately known in order to carry out near-surface orbital missions and perform precision landings automatically. Previous investigations by the Jet Propulsion Laboratory and Langley Research Center have concentrated on using a pure spherical harmonic expansion (Legendre polynominal series) to model this potential. This approach has not yielded entirely satisfactory results, because near-surface concentrations (mascons) do not permit rapid convergence of the series expansion. Mascons discovered through recent studies of gravimetry maps cause the moon to be gravitationally ‘rough,’ thus requiring use of high degree and order coefficients even to obtain a poor potential model. The work reported here is concerned with methods for obtaining models of lunar gravity by using a truncated spherical harmonic expansion with a finite number of mascon terms. To test this formulation, rates of change of the ascending node due to asphericity, mascons, sun and earth attraction, and solar pressure were used with measured data from the Lunar Orbiter series. Values of unknown coefficients in the potential model were calculated and were used to generate predictions of perturbation effects. Comparisons with Lunar Orbiter data indicate the validity of this approach. Determination of the lunar density distribution is also discussed.