Earth, Moon, and Planets

, 106:1 | Cite as

A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars

  • A. A. Ardalan
  • R. Karimi
  • E. W. Grafarend


Using the shape model of Mars GTM090AA in terms of spherical harmonics complete to degree and order 90 and gravitational field model of Mars GGM2BC80 in terms of spherical harmonics complete to degree and order 80, both from Mars Global Surveyor (MGS) mission, the geometry (shape) and gravity potential value of reference equipotential surface of Mars (Areoid) are computed based on a constrained optimization problem. In this paper, the Areoid is defined as a reference equipotential surface, which best fits to the shape of Mars in least squares sense. The estimated gravity potential value of the Areoid from this study, i.e. W 0 = (12,654,875 ± 69) (m2/s2), is used as one of the four fundamental gravity parameters of Mars namely, {W 0, GM, ω, J 20}, i.e. {Areoid’s gravity potential, gravitational constant of Mars, angular velocity of Mars, second zonal spherical harmonic of gravitational field expansion of Mars}, to compute a bi-axial reference ellipsoid of Somigliana-Pizzetti type as the hydrostatic approximate figure of Mars. The estimated values of semi-major and semi-minor axis of the computed reference ellipsoid of Mars are (3,395,428 ± 19) (m), and (3,377,678 ± 19) (m), respectively. Finally the computed Areoid is presented with respect to the computed reference ellipsoid.


Areoid Areoid potential Reference ellipsoid Constrained optimization problem Lagrange method 



The authors would like to kindly acknowledge the constructive comments and corrections of the anonymous reviewer which helped to significantly improve initial version of the paper. Besides, the authors would like to thank the University of Tehran for the financial support.


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Surveying and Geomatics Engineering, Center of Excellence of Geomatics Engineering and Disaster Prevention, College of EngineeringUniversity of TehranTehranIran
  2. 2.Department of GeodesyStuttgart UniversityStuttgartGermany

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