The gravitational potential of axially symmetric bodies from a regularized green kernel

Details The gravitational potential of axially symmetric bodies from a regularized green kernel The gravitational potential of axially symmetric bodies from a regularized green kernel

Dec 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011sf2a.conf..685t&link_type=abstract

SF2A-2011: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics Eds.: G. Alecian, K. Belkacem,

Astronomy and Astrophysics

Astrophysics

Gravitation, Methods: Analytical, Celestial Mechanics

Scientific paper

The determination of the gravitational potential inside celestial bodies (rotating stars, discs, planets, asteroids) is a common challenge in numerical Astrophysics. Under axial symmetry, the potential is classically found from a two-dimensional integral over the body's meridional cross-section. Because it involves an improper integral, high accuracy is generally difficult to reach. We have discovered that, for homogeneous bodies, the singular Green kernel can be converted into a regular kernel by direct analytical integration. This new kernel, easily managed with standard techniques, opens interesting horizons, not only for numerical calculus but also to generate approximations, in particular for geometrically thin discs and rings.

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