From point electrostatic sources to extended electrostatic architectures near Lagrange points

Abstract Electrostatic forces can modify the motion of a charged body near a collinear libration point in the circular restricted three-body problem (CRTBP). This study examines how two equal repulsive sources placed symmetrically about this point affect the number, spatial arrangement, and stability of equilibria. The local model combines a quadratic approximation of the gravitational field with the full unscreened electrostatic potential of the sources. After nondimensionalization and parameter reduction, the model depends on two parameters: the local gravitational curvature and the reduced charge strength. Explicit expressions describe the equilibrium branches along the three coordinate axes and identify the critical parameter values at which bifurcations occur.The analysis also examines how Debye screening changes the equilibrium configuration, bifurcations, and local dynamics, and how a small charge asymmetry displaces the central equilibrium from the midpoint. A numerical example in the Mars–Phobos system illustrates the relationship between stability and equilibrium separation. The critical Jacobi levels are computed, and conjectures concerning the model’s nonlinear dynamics are discussed.These results provide a basis for further studies of local motion and controlled insertion. Nonlinear confinement and finite-conductor effects require further investigation, while asymptotic capture requires additional dissipative or feedback mechanisms.