Before the asteroid-sensing mission, a probe orbit intended to fly over or land on an asteroid should be more perceptive to the effects of the irregular asteroid’s non-spherical gravity field. A multi-body spherical harmonic gravity field (MSHGF) method is proposed here. First, the irregular asteroids are evenly divided into several sub-partitions to reduce the irregular shape of each. Then, models of spherical harmonic gravity field (SHGF) are developed for each subset of the divided asteroids, and all the subpart SHGF models are superimposed to form a MSHGF of the asteroid. After that, using the polyhedral model, the potential energy of the asteroid gravity field at the test locations is determined, and a correlation between the multi-body spherical harmonic coefficient (SHC) and the gravitational potential energy is established. Finally, using the least squares method, the super-definite linear system of equations is resolved to yield the multi-body SHCs. The MSHGF method can greatly increase the accuracy of the gravity field model, improving it compared to the traditional simulation of the SHGF model for the asteroid (433) Eros, for example, by reducing the mean error by 94% and reducing the maximum error by 64%. The MSHGF approach can deliver more accurate gravity field data for the design and orbital control of asteroid detection missions, according to numerical simulations.

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A Multi-body Spherical Harmonic Gravity Field Method for Irregular Asteroid

  • Shaoliang Zhang,
  • Ying Nan,
  • Guochuan Yu

摘要

Before the asteroid-sensing mission, a probe orbit intended to fly over or land on an asteroid should be more perceptive to the effects of the irregular asteroid’s non-spherical gravity field. A multi-body spherical harmonic gravity field (MSHGF) method is proposed here. First, the irregular asteroids are evenly divided into several sub-partitions to reduce the irregular shape of each. Then, models of spherical harmonic gravity field (SHGF) are developed for each subset of the divided asteroids, and all the subpart SHGF models are superimposed to form a MSHGF of the asteroid. After that, using the polyhedral model, the potential energy of the asteroid gravity field at the test locations is determined, and a correlation between the multi-body spherical harmonic coefficient (SHC) and the gravitational potential energy is established. Finally, using the least squares method, the super-definite linear system of equations is resolved to yield the multi-body SHCs. The MSHGF method can greatly increase the accuracy of the gravity field model, improving it compared to the traditional simulation of the SHGF model for the asteroid (433) Eros, for example, by reducing the mean error by 94% and reducing the maximum error by 64%. The MSHGF approach can deliver more accurate gravity field data for the design and orbital control of asteroid detection missions, according to numerical simulations.