English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The "point mass singularity" inherent in Newton's law for gravitationrepresents a major difficulty in accurately determining the potential andforces inside continuous bodies. Here we report a simple and efficientanalytical method to bypass the singular Green kernel 1/|r-r'| inside thesource without altering the nature of the interaction. We build an equivalentkernel made up of a "cool kernel", which is fully regular (and contains thelong-range -GM/r asymptotic behavior), and the gradient of a "hyperkernel",which is also regular. Compared to the initial kernel, these two components areeasily integrated over the source volume using standard numerical techniques.The demonstration is presented for three-dimensional distributions incylindrical coordinates, which are well-suited to describing rotating bodies(stars, discs, asteroids, etc.) as commonly found in the Universe. An exampleof implementation is given. The case of axial symmetry is treated in detail,and the accuracy is checked by considering an exact potential/surface densitypair corresponding to a flat circular disc. This framework provides new toolsto keep or even improve the physical realism of models and simulations ofself-gravitating systems, and represents, for some of them, a conclusivealternative to softened gravity.

A substitute for the singular Green kernel in the Newtonian potential of celestial bodies