Gravity simulation with arbitrary geometries

In summary: That will give you the gravitational field at every point on the body, no matter how far away.Are there methods to avoid calculating the field in all the pure space to focus on the field in the plane?There are a few ways to do this. You could use a boundary condition that says the field inside the boundary is zero, or you could use a mesh that is very tiny compared to the size of the body.
  • #1
debilo
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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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  • #2
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?
 
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Likes aaroman
  • #3
Hello,

thank you for your answer.

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.
 
  • #4
It depends what you want. You can, of course, split your object up into a cubical grid and pretend each little cube is a point mass at its center. That will get more accurate the smaller your cubes are - in fact, the limiting case of infinitely small cubes is an integral over the volume, which is exactly what I was proposing.

Algorithms to divide a polygon up into triangles are easy to find online. Imagine drawing a wireframe of your object looking down on it from above - you immediately get a set of polygons that you can triangulate. That gives you the simple polygons. The only question then is if you can write down and/or do the integral to get the gravitational force from such a prism.

However, if you are not going for an analytical solution, then you will have to balance precision (more and smaller cubes) versus the computational cost of doing so.
 
  • #5
debilo said:
I thought I'd solve Poisson's equation in 3D.

How about a 2D integration over the surface of the body using the divergence theorem?
 

1. What is gravity simulation with arbitrary geometries?

Gravity simulation with arbitrary geometries is a computer model that simulates the behavior of objects under the influence of gravity, allowing for the use of non-uniform shapes and geometries for the objects involved.

2. How does gravity simulation with arbitrary geometries work?

Gravity simulation with arbitrary geometries uses mathematical equations and algorithms to calculate the gravitational forces between objects of varying shapes and sizes. These calculations are then used to predict the movement and interactions of the objects over time.

3. What are the applications of gravity simulation with arbitrary geometries?

Gravity simulation with arbitrary geometries has a wide range of applications in various fields such as astrophysics, aerospace engineering, and planetary science. It can be used to study the behavior of celestial bodies, the dynamics of spacecraft, and the formation of planetary systems.

4. What are the limitations of gravity simulation with arbitrary geometries?

Gravity simulation with arbitrary geometries is a simplified model and does not take into account other factors such as air resistance and friction. It also requires a significant amount of computational power and may not be able to accurately simulate complex systems with numerous objects.

5. How accurate is gravity simulation with arbitrary geometries?

The accuracy of gravity simulation with arbitrary geometries depends on the complexity of the system being simulated and the precision of the initial conditions and parameters used. With proper input, it can produce results that closely match real-world observations, but it is not a substitute for experimental data and observations.

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