Surveys in Geophysics

, Volume 39, Issue 3, pp 313–335 | Cite as

Definition of Physical Height Systems for Telluric Planets and Moons

  • Robert Tenzer
  • Ismael Foroughi
  • Lars E. Sjöberg
  • Mohammad Bagherbandi
  • Christian Hirt
  • Martin Pitoňák


In planetary sciences, the geodetic (geometric) heights defined with respect to the reference surface (the sphere or the ellipsoid) or with respect to the center of the planet/moon are typically used for mapping topographic surface, compilation of global topographic models, detailed mapping of potential landing sites, and other space science and engineering purposes. Nevertheless, certain applications, such as studies of gravity-driven mass movements, require the physical heights to be defined with respect to the equipotential surface. Taking the analogy with terrestrial height systems, the realization of height systems for telluric planets and moons could be done by means of defining the orthometric and geoidal heights. In this case, however, the definition of the orthometric heights in principle differs. Whereas the terrestrial geoid is described as an equipotential surface that best approximates the mean sea level, such a definition for planets/moons is irrelevant in the absence of (liquid) global oceans. A more natural choice for planets and moons is to adopt the geoidal equipotential surface that closely approximates the geometric reference surface (the sphere or the ellipsoid). In this study, we address these aspects by proposing a more accurate approach for defining the orthometric heights for telluric planets and moons from available topographic and gravity models, while adopting the average crustal density in the absence of reliable crustal density models. In particular, we discuss a proper treatment of topographic masses in the context of gravimetric geoid determination. In numerical studies, we investigate differences between the geodetic and orthometric heights, represented by the geoidal heights, on Mercury, Venus, Mars, and Moon. Our results reveal that these differences are significant. The geoidal heights on Mercury vary from − 132 to 166 m. On Venus, the geoidal heights are between − 51 and 137 m with maxima on this planet at Atla Regio and Beta Regio. The largest geoid undulations between − 747 and 1685 m were found on Mars, with the extreme positive geoidal heights under Olympus Mons in Tharsis region. Large variations in the geoidal geometry are also confirmed on the Moon, with the geoidal heights ranging from − 298 to 461 m. For comparison, the terrestrial geoid undulations are mostly within ± 100 m. We also demonstrate that a commonly used method for computing the geoidal heights that disregards the differences between the gravity field outside and inside topographic masses yields relatively large errors. According to our estimates, these errors are − 0.3/+ 3.4 m for Mercury, 0.0/+ 13.3 m for Venus, − 1.4/+ 125.6 m for Mars, and − 5.6/+ 45.2 m for the Moon.


Geoid Gravity Heights Planets Moon Topography 



We thank Dr. Gregory A. Neumann (Goddard Space Flight Center of NASA) and another anonymous reviewer for their constructive comments that helped improve this manuscript.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Robert Tenzer
    • 1
  • Ismael Foroughi
    • 2
  • Lars E. Sjöberg
    • 3
  • Mohammad Bagherbandi
    • 3
    • 4
  • Christian Hirt
    • 5
  • Martin Pitoňák
    • 6
  1. 1.The Department of Land Surveying and Geo-InformaticsThe Hong Kong Polytechnic UniversityKowloonHong Kong
  2. 2.Department of Geodesy and GeomaticsUniversity of New BrunswickFrederictonCanada
  3. 3.Division of Geodesy and Satellite PositioningRoyal Institute of Technology (KTH)StockholmSweden
  4. 4.Department of Industrial Development, IT and Land ManagementUniversity of GävleGävleSweden
  5. 5.Institute for Astronomical and Physical Geodesy and Institute for Advanced StudyTU MunichMunichGermany
  6. 6.New Technologies for the Information Society (NTIS), Faculty of Applied SciencesUniversity of West BohemiaPlzeňCzech Republic

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