Define few-body Milgromian gravitational-force addition

Determine how gravitational forces are to be combined in discrete few-body systems governed by the nonlinear Milgromian-dynamics field equations, where the mean-field formulation breaks down.

Background

The paper explains that Milgromian dynamics successfully describes systems that can be approximated by continuum dynamics, but that its mean-field formulation breaks down when few-body dynamics becomes important. Because the theory is nonlinear, the prescription for adding gravitational forces in such systems is unresolved, limiting reliable tests of Milgromian versus Newtonian dynamics in very wide binaries and the outer Solar System.

References

For systems in which few-body dynamics becomes important the mean-field formulation of MOND breaks down but the discrete-few-body dynamics is mathematically not well understood due to the non-linearity of Milgromian dynamics -- it is unclear how the gravitational forces are to be added.

— The relevance of the cosmic microwave background for cosmology  (2609.10672 - Kroupa et al., 9 Sep 2026) in Section 2.1, “Different models”