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The two-body interaction potential in the STF tensor formalism: an application to binary asteroids. (English) Zbl 1298.70014

Summary: The symmetric trace free (STF) tensor formalism, developed by T. Hartmann et al. [Celest. Mech. Dyn. Astron. 60, No. 1, 139–159 (1994; Zbl 0818.70014)], is a nice tool, not much used in Celestial Mechanics. It is fully equivalent to the usual spherical harmonics but permits more elegant and compact formulations. The coupling between the gravitational fields of extended bodies with this formalism has been used in [S. Mathis and C. Le Poncin-Lafitte, “ Tidal dynamics of extended bodies in planetary systems and multiple stars”, Astron. Astrophys. 497, No. 3, 889-910 (2009; doi:10.1051/0004-6361/20079054)] for binary stars or planetary systems, but not yet applied to binary asteroids. However, binary asteroids are common in the Solar System and usually their study requires a full two rigid body approach. The formulation of the two-body interaction potential in the STF formalism in the full two rigid body problem is detailed and completed in this article. An application to the binary asteroid (66391) 1999 KW4 is presented with a comparison of our results with other results of the literature for validation.

MSC:

70F15 Celestial mechanics
70F05 Two-body problems
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics

Citations:

Zbl 0818.70014

Software:

NIMASTEP
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Full Text: DOI

References:

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