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Precise Gravitational Modelling of Planetary Moons and NEO (Near Earth Objects) Asteroids

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Precise Gravitational Modelling of Planetary Moons and NEO (Near Earth Objects) Asteroids

GRAVMOD-2 is a software tool developed by Astos Solutions and GMV for ESA.

It adds guidance analysis and on-board manoeuver capabilities to the gravitational modelling core of GRAVMOD-1 originally developed by DEIMOS. The unique mathematical models and architecture make it particularly suitable for the modelling of the gravity field of highly irregular bodies such as small moons, asteroids or comets. GRAVMOD-2 is composed of two main modules:

  1.  A Gravity Modelling module: containing mathematical algorithms able to compute gravity fields as Spherical Harmonics Model (SHM) or Multiple Point Masses Model (MPMM), using as input gravity accelerations provided, geometrical models, or computed from other gravity fields (as PANGU model, polyhedron model, and ellipsoid model, along with the already mentioned SHM and MPMM). This module allows also comparing two different gravity fields, analyzing the accelerations produced or propagating a trajectory.
  2. An Orbit Propagation and Determination module: set of methods and algorithms allowing the propagation of a trajectory and an attitude profile, generation of measurements, and optimal estimation of a gravity field once a mission around a body is known. It also allows the computation of stable orbits based on simplified orbital and attitude dynamics models including the restricted three body problem. In this sense, GRAVMOD is specially indicating for the modelling of binary asteroids, providing some additional features for the proper study of such systems:
  •  Analytical and numerical ephemeris models describing the ephemeris of each one of the bodies of a binary system around its centre of mass.
  • Proper modelling of the non-spherical gravity field acting upon the S/C from the asteroid, being possible to characterise a simple asteroid or a binary system, in which both bodies simultaneously act upon the spacecraft (primary and secondary).


As a part of this tool additional features have been developed: 

  • a GNC propagator has been developed for on-board applications.
  • a link between GRAVMOD-2 and the Planetary Database has been created for the upload and download of models.
  • new NLP solvers have been added for the generation of stable orbits GRAVMOD-2 allows producing a series of gravity models for ESA internal purpose.


Those models have been made available via the ESA Planetary Database (PDB). In the scope of GRAVMOD-2, the PDB has also been extended and it now provides the capability to plot GRAVMOD-2 gravity fields and trajectories (using a simplified version of the GRAVMOD-2 propagator).

Application Domain
Space Science
Technology Domain
2 - Space System Software
Competence Domain
3-Avionic Systems
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Public Document
Executive Summary