A multiresolution model for small-body gravity estimation

  • Brandon A. JonesEmail author
  • Gregory Beylkin
  • George H. Born
  • Robert S. Provence
Original Article


A new model, dubbed the MRQSphere, provides a multiresolution representation of the gravity field designed for its estimation. The multiresolution representation uses an approximation via Gaussians of the solution of the Laplace’s equation in the exterior of a sphere. Also, instead of the spherical harmonics, variations in the angular variables are modeled by a set of functions constructed using quadratures for the sphere invariant under the icosahedral group. When combined, these tools specify the spatial resolution of the gravity field as a function of altitude and required accuracy. We define this model, and apply it to representing and estimating the gravity field of the asteroid 433 Eros. We verified that a MRQSphere model derived directly from the true spherical harmonics gravity model satisfies the user defined precision. We also use the MRQSphere model to estimate the gravity field of Eros for a simulated satellite mission, yielding a solution with accuracy only limited by measurement errors and their spatial distribution.


Gravity modeling Spherical harmonics Gravity estimation Quadratures for the sphere Multiresolution representations Asteroid Eros 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Brandon A. Jones
    • 1
    Email author
  • Gregory Beylkin
    • 2
  • George H. Born
    • 1
  • Robert S. Provence
    • 3
  1. 1.Colorado Center for Astrodynamics ResearchUniversity of ColoradoBoulderUSA
  2. 2.Department of Applied MathematicsUniversity of ColoradoBoulderUSA
  3. 3.Aerosciences and Flight Mechanics DivisionNASA Johnson Space CenterHoustonUSA

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