Orbital Simulations

Gravitational and atomic orbital simulations based on the Planck-scale model described in Article 3 and Article 4. Code is written in C and Python; C is faster and preferable for large orbital radii and heavy centre masses. Animations were generated with gnuplot.

Model philosophy: The universe does not require an external set of commands. Rather, it is a geometrically autonomous computer — electrons orbit protons not because of pre-programmed force rules, but due to geometrical imperatives. The incremental expansion of the hyper-sphere universe does the rest.
Tools

Getting Started

C Compiler

The author uses Code::Blocks. Any C/C++ compiler works. C is recommended for computationally intensive runs.

Python

Spyder IDE is used for Python, but any environment works. Python versions are easier to modify and plot.

Animations

gnuplot for animations, Python (matplotlib) for static plots.

Licence

All code is available under CC BY-NC-SA 4.0 — free to modify with attribution.

Sections

Simulation Categories

Each section contains source code files and, where available, sample output images.

Atomic Orbitals

2-photon gravitational orbital atom simulations for H-atom electron transitions. Includes C and Python code, transition animations, and momentum plots.

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Elliptical Orbits

Gravitational elliptical orbit simulations with extrapolation. Demonstrates that the model reproduces Kepler's laws without a force term.

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N-Body Simulations

Multi-point gravitational orbital simulations. The central mass is discretised into Planck-mass points, each forming independent orbital pairs.

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Newton vs Orbital

Side-by-side trajectory comparison between the classical Newtonian approach and this geometric orbital model.

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Kepler Derivation (Maple)

Step-by-step Kepler's formula derivation in Maple computer algebra system. The derivation shows $G$ emerges from $\alpha$ and $\pi$ alone.

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Reference

Common Simulation Variables

  • 📌
    ipoints Number of Planck-mass points in the central mass (the Schwarzschild radius)
  • 📌
    jpoints Total number of points — in a 2-body orbit, the orbiting point is 1 mass unit; jpoints = ipoints + 1
  • 📌
    kr Sets orbital radius as multiples of ipoints (quantises radius as a function of the Schwarzschild radius)
  • 📌
    x[0], y[0] Start coordinates for the orbiting point
  • 📌
    x[1], y[1] Start coordinates for the orbited mass centre point

Note: points may also be assigned random co-ordinates for complex orbits. The simulation itself doesn't distinguish between points — they all rotate around each other.