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  • ESA' s Novel Gravitational Modelling of Planetary Bodies

    Paper number



    Ms. Ana Blasco, European Space Agency (ESA)/ESTEC, The Netherlands


    Dr. Guillermo Ortega, European Space Agency (ESA)/ESTEC, The Netherlands


    Mr. Juan-Carlos Bastante, DEIMOS Engenharia, Portugal




    The European Space Agency has initiated in 2004 an activity to develop a mathematical model and a software tool for the entire gravitational field of celestial bodies. This model should allow ESA’s spacecraft and vehicles to maneuver around planets, moons asteroids, etc.

    A detailed understanding and modeling of the gravitational modeling is required for realistic investigation of the dynamics of orbits close to irregularly shaped bodies. Gravity field modelling up to a certain maximum spherical harmonic degree N involves N 2 unkown spherical harmonic coefficients or complex harmonics. The corresponding number of matrix entries reaches till N 4. For missions like CHAMP, GRACE or GOCE, the maximum degree of resolution is 75, 150 and 300 respectively. Therefore, the number of unknowns for a satellite like GOCE will be around 100.000. Since these missions usually fly for a period of time of several years, the number of observations is huge. Hence, gravity field recovery from these missions is a high demanding task. The classical approaches like spherical expansion of the potential lead generally to a high number of coefficients, which reduce the software computational efficiency of the orbit propagation and which have mostly a limited physical meaning.

    All celestial bodies are irregular by definition. However, the scope of the activity is broad enough as to be able to use the models and the software in quasy-regular bodies as well. Therefore the models and tools could be used for bodies such as the Moon, Mars, Venus, Deimos, Europa, Eros, Mathilda, and Churyumov-Gerasimenko, etc., being these applications relevant for scientific (Rosetta, Bepi Colombo), exploration (Exo-Mars), NEO mitigation (Don Quijote) and Earth observation (GOCE) missions of ESA.

    The code name for this ESA activity is GRAVMOD. The main objectives of GRAVMOD are as follows:

    • Analysing and trading-off the different possible options for modelling irregular gravity fields with the aim to consolidate the state of the art on gravitational modelling methods.
    • A detailed software requirement specifications of a simulation tool that should include a propagation method. This tool shall not only simulate (i.e. orbit propagation), but also allow to estimate the gravity model parameters based on local and gravimetric measurements.
    • The activity will take into account that the optimality criteria to use in this work as to achieve minimum computational time and high accuracy.
    Abstract document


    Manuscript document

    IAC-07-C1.4.09.pdf (🔒 authorized access only).

    To get the manuscript, please contact IAF Secretariat.