1. Problem Statement
Can planetary motion be simulated using only fundamental quantities such as:
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Position (x)
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Velocity (v)
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Mass (m)
without explicitly using force equations?
This post presents a computational implementation of the NKTg model, where orbital velocity is derived from a target constant:
NKTg₁ = x × p
where p = m × v
The model is validated using publicly available data from NASA JPL Horizons for Mercury.
2. Reference Dataset (NASA 2024)
Actual orbital data of Mercury in 2024:
| Date | x (m) | v (m/s) | m (kg) | p = m·v |
|---|---|---|---|---|
| 1/1/2024 | 5.16E+10 | 5.33E+04 | 3.30E+23 | 1.76E+28 |
| 4/1/2024 | 6.97E+10 | 3.90E+04 | 3.30E+23 | 1.29E+28 |
| 7/1/2024 | 5.36E+10 | 5.20E+04 | 3.30E+23 | 1.72E+28 |
| 10/1/2024 | 6.95E+10 | 3.92E+04 | 3.30E+23 | 1.30E+28 |
| 12/31/2024 | 4.64E+10 | 5.81E+04 | 3.30E+23 | 1.92E+28 |
From this dataset, the target constant is established:
NKTg₁ = 8.90E+38 NKTm
3. Model Definition
Given:
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x (orbital position)
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m (mass)
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Target constant NKTg₁
We compute:
p=NKTg1xp = \frac{NKTg₁}{x}p=xNKTg1v=pmv = \frac{p}{m}v=mp
No force expressions are used in the computation.
The model also integrates mass variation:
dm/dt = -0.5 kg/s
This produces:
NKTg2=(dm/dt)×pNKTg₂ = (dm/dt) × pNKTg2=(dm/dt)×p
which remains negative throughout the orbit.
4. 2025 Simulation (NKTg Model)
| Date | x (m) | v (m/s) | m (kg) | p = m·v |
|---|---|---|---|---|
| 1/1/2025 | 5.16E+10 | 5.22E+04 | 3.301E+23 | 1.72E+28 |
| 4/1/2025 | 6.97E+10 | 3.87E+04 | 3.301E+23 | 1.28E+28 |
| 7/1/2025 | 5.49E+10 | 4.91E+04 | 3.301E+23 | 1.62E+28 |
| 10/1/2025 | 6.83E+10 | 3.95E+04 | 3.301E+23 | 1.30E+28 |
| 12/31/2025 | 4.61E+10 | 5.85E+04 | 3.301E+23 | 1.93E+28 |
5. Actual NASA Data (2025)
| Date | x (m) | v (m/s) | m (kg) |
|---|---|---|---|
| 1/1/2025 | 5.16E+10 | 5.34E+04 | 3.30E+23 |
| 4/1/2025 | 6.97E+10 | 3.89E+04 | 3.30E+23 |
| 7/1/2025 | 5.49E+10 | 5.04E+04 | 3.30E+23 |
| 1/10/2025 | 6.83E+10 | 3.98E+04 | 3.30E+23 |
| 12/31/2025 | 4.61E+10 | 5.89E+04 | 3.30E+23 |
6. Numerical Comparison
| Date | v – NKTg | v – NASA | Relative Error (%) |
|---|---|---|---|
| 1/1/2025 | 5.22E+04 | 53400 | -2.15461 |
| 4/1/2025 | 3.87E+04 | 38900 | -0.562786 |
| 7/1/2025 | 4.91E+04 | 50400 | -2.561981 |
| 1/10/2025 | 3.95E+04 | 39800 | -0.819213 |
| 12/31/2025 | 5.85E+04 | 58900 | -0.707806 |
Average relative error: 1.3%
7. Observations from a Computational Perspective
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The system is fully defined by interaction between x, v, and m.
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No force expressions are required in the computation process.
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The model is deterministic and reproducible across platforms.
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Error remains within ~1.3% compared to NASA JPL data.
8. Discussion
From a software engineering perspective, this approach represents:
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A constant-driven orbital simulation model.
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A reduced-parameter dynamical system.
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A reproducible computational experiment based on publicly available data.
The implementation can be reproduced in any language supporting floating-point arithmetic.
If anyone is interested, I can share a minimal reproducible implementation (Python / C++ / Go) for benchmarking and independent validation.