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| HAL: hal-00685411, version 1 |
| arXiv: 1203.6822 |
| DOI: 10.1051/0004-6361/201118443 |
| Detailed view |  Export this paper |
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| Astronomy and Astrophysics 541 (2012) A130 |
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| A substitute for the singular Green kernel in the Newtonian potential of celestial bodies |
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| J.-M. Huré 1, 2, 3, 4Andreas Dieckmann |
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| (2012) |
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| The "point mass singularity" inherent in Newton's law for gravitation represents a major difficulty in accurately determining the potential and forces inside continuous bodies. Here we report a simple and efficient analytical method to bypass the singular Green kernel 1/|r-r'| inside the source without altering the nature of the interaction. We build an equivalent kernel made up of a "cool kernel", which is fully regular (and contains the long-range -GM/r asymptotic behavior), and the gradient of a "hyperkernel", which is also regular. Compared to the initial kernel, these two components are easily integrated over the source volume using standard numerical techniques. The demonstration is presented for three-dimensional distributions in cylindrical coordinates, which are well-suited to describing rotating bodies (stars, discs, asteroids, etc.) as commonly found in the Universe. An example of implementation is given. The case of axial symmetry is treated in detail, and the accuracy is checked by considering an exact potential/surface density pair corresponding to a flat circular disc. This framework provides new tools to keep or even improve the physical realism of models and simulations of self-gravitating systems, and represents, for some of them, a conclusive alternative to softened gravity. |
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| 1: | Observatoire aquitain des sciences de l'univers (OASU) |
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CNRS : UMS2567 – INSU – Université Sciences et Technologies - Bordeaux I |
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| 2: | Laboratoire d'Astrophysique de Bordeaux (LAB) |
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CNRS : UMR5804 – INSU – Université Sciences et Technologies - Bordeaux I |
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| 3: | Université Sciences et Technologies - Bordeaux 1 |
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Université Sciences et Technologies - Bordeaux I |
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| 4: | Laboratoire d'astrodynamique, d'astrophysique et d'aéronomie de bordeaux (L3AB) |
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CNRS : UMR5804 – INSU – Université Sciences et Technologies - Bordeaux I |
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| FORMATION STELLAIRE 2012 |
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| Subject | : | Physics/Astrophysics/Instrumentation and Methods for Astrophysic Sciences of the Universe/Astrophysics/Instrumentation and Methods for Astrophysic Physics/Mathematical Physics Mathematics/Mathematical Physics |
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| Astrophysics - Instrumentation and Methods for Astrophysics – Mathematical Physics |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1203.6822 |
| hal-00685411, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00685411 | |
| oai:hal.archives-ouvertes.fr:hal-00685411 | |
| From: Marie-Paule Pomies | |
| Submitted on: Thursday, 5 April 2012 09:49:17 | |
| Updated on: Tuesday, 29 May 2012 13:26:48 | |
