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I am a professional scientist (biologist), statistician and a computer programmer, but an amateur physicist so pardon me if this question appears silly. In order to understand general relativity (a truly inspiring theory, btw), I would like to create a computer simulation of the solar system using gravity as defined by the general relativity theory (not Newtonian gravity). I am thinking about following steps for the process:
- Introduce the XYZ locations, masses, and tangential velocities for celestial bodies
- Calculate the curvature of spacetime introduced by these celestial bodies at time
- Remove the curvature caused by each celestial body for their own path, but include all other curvatures.
- Increase time to
t1, iterate the new position of celestial bodies based on conditions set in step 1 and 3 (and those in general relativity).
- Calculate steps 2 and 3 for the new position. Repeat 4. Etc.
After using half a day online, I am still unsure whether Einstein Field Equations (EFEs) let me derive the new XYZ locations in step 4. Does General relativity let me do calculations outlined above using computational power in a modern laptop?
My background in physics and maths fails me here (this is part of the fun in learning something new). If doing the above is theoretically possible and not too computationally intensive, figuring out how to do each step is just details. I might ask such details in separate questions, but here I am after whether my understanding is completely off (never worked with partial differential equations before).