Every planet exterts a torque on every ring of the 1D grid, given by the well-known expression of the Lindblad torque density, proportional to , with , where is the radius of the ring, and the radius of the planetary orbit. This is implemented in the procedure
Reciprocally, every planet recieves the opposite torque from the rings of the 1D grid. This is implemented in
This prescription is only an approximation, and it can’t replace the 2D decription of the planet-disk interactions. The planet should remain sufficiently far away from the grids interface for an accurate simulation.