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The softened point mass model is commonly used in simulations of gaseousdiscs including self-gravity while the value of associated length \lambdaremains, to some degree, controversial. This ``parameter'' is however fullyconstrained when, in a discretized disc, all fluid cells are demanded to obeyNewton's law. We examine the topology of solutions in this context, focusing oncylindrical cells more or less vertically elongated. We find that not only thenominal length depends critically on the cell's shape (curvature, radialextension, height), but it is either a real or an imaginary number. Setting\lambda as a fraction of the local disc thickness -- as usually done -- isindeed not the optimal choice. We then propose a novel prescription validirrespective of the disc properties and grid spacings. The benefit, whichamounts to 2-3 more digits typically, is illustrated in a few concrete cases. Adetailed mathematical analysis is in progress.

A truly Newtonian softening length for disc simulations