N-Body Simulation:
While N-Body simulations are employed in both the geocentric and heliocentric models, this simulation uses only user input radius, velocity, and masses. Following are examples of Sun-Earth-Moon and Earth-Moon systems.
Sun-Earth-Moon:
Left: The dashed lines show all the places where the Moon (green) comes in front of the Earth (blue). The simulation was run for 1 year, and as you can see, Moon circles the earth 12 times (12 months). The sun did not move significantly, and does not show in the figure.
Right: If you look closely, the green line is rotating around the blue line. This represents a time period of almost 3 months.
Earth-Moon:
The figure on the left is similar to the N-body simulation for the geocentric model, however, as shown in the figure on the right, due to the movement of the Earth, the Moon moves in a helix. The Earth also moves in a helix around the Sun as it circles the Milky Way.
You are able to model any number of bodies, however it make take an large amount of time to iterate a system of many point masses. I am looking into potentially using a tree-method or figure out some simplification to apply to simulation cases with a larger number of point masses. This will be used to simulate an asteroid belt or numerous celestial bodies.
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