# Gravity simulation with arbitrary geometries

## Main Question or Discussion Point

Hello,

I want to study the trajectory of planets (considered as points) around a body with arbitrary geometry (cube,...). I would like to restrict the simulation to a 2D plane, which would be a plane of symmetry of the 3D object (for example a plane that would cut the cube into two equal parts). I thought I'd solve Poisson's equation in 3D. But my computer is not very efficient (and I only know Finite difference methods).

Are there methods to avoid calculating the field in all the pure space to focus on the field in the plane? I couldn't find any articles on this subject.

Thanks.

Edit : I want to do the simulation with Python.

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Ibix
When I did this for 2d polygonal gravity sources, it turned out to be possible to write an analytical expression for the gravitational field of a parallelogram. Any polygon can be divided into parallelograms, and then calculating the total field was just the sum of the parallelogram fields.

Can you find an algorithm to break your shape into standard simpler shapes - triangular prisms with sloped ends, for example? Can you write down an expression for the gravitational field of that kind of simple shape?

Hello,

Can you find an algorithm to break your shape into standard simpler shapes - triangular prisms with sloped ends, for example?
I really don't know how to do these things.

I had a new idea. Instead of solving the Poisson equation I consider that each point of my grid is Dirac-mass and I calculate the potential on the whole space using the well-known formula : $$V(r)=\sum Gm(r')/|r-r'|$$ I don't know if it's a good idea.

Ibix