Estimating asteroid density distributions from shape and gravity information

Details Estimating asteroid density distributions from shape and gravity information Estimating asteroid density distributions from shape and gravity information

Aug 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000p%26ss...48..965s&link_type=abstract

Planetary and Space Science, Volume 48, Issue 10, p. 965-971.

Computer Science

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1

Scientific paper

A least-squares approach for estimating the internal density distribution of an asteroid is presented and applied to a simple polyhedron asteroid shape. The method assumes that the asteroid gravity field is measured to a specified degree and order and that a polyhedral model of the asteroid is available and has been discretized into a finite number of constant density polyhedra. The approach is derived using several basic properties of spherical harmonic gravitational expansions and can explicitly accommodate a fully correlated covariance matrix for the estimated gravity field. For an asteroid shape discretized into /M constant density polyhedra and a gravity field measured to degree and order /N, the least-squares problem is under-determined if M>(N+1)2 and is over-determined if M<(N+1)2. For both cases a singular-value decomposition (SVD) approach will yield solutions. We apply our approach to a number of ideal test situations using an asteroid shape consisting of 508 tetrahedra. We show that the under-determined case is sensitive to non-uniform density distributions. The over-determined case shows very good performance independent of the initial density distribution guess.

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