Hello everyone,
I would like to share a recent piece of research that may be of interest to those combining mathematics, physics, and functional programming. It concerns the NKTg law of variable inertia and its verification using NASA JPL Horizons data for all 8 planets of the Solar System at the end of 2024.
Theoretical Basis
The NKTg law proposes that an object’s motion tendency depends on the interaction between its position (x), velocity (v), and mass (m):
NKTg = f(x, v, m)
The conserved interaction quantity is:
NKTg1 = x * (m * v)
where m * v is linear momentum.
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If NKTg1 > 0 → the object tends to move away from equilibrium.
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If NKTg1 < 0 → the object tends to return to equilibrium.
This quantity appears to be conserved across planetary motion and provides a new way to compute masses from real-time data.
Research Objectives
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Interpolate the masses of 8 planets (Mercury → Neptune) using NKTg law.
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Compare interpolated results with NASA official planetary masses on 31/12/2024.
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Test whether Earth’s small annual mass variations (measured by GRACE/GRACE-FO) are detectable.
Data and Method
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NASA JPL Horizons → positions (x) and velocities (v).
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NASA Planetary Fact Sheet → official planetary masses.
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Formula used:
m = NKTg1 / (x * v)
Results
Table 1 – Interpolated vs NASA Masses (31/12/2024)
| Planet | Interpolated Mass (kg) | NASA Mass (kg) | Δm | Remarks |
|---|---|---|---|---|
| Mercury | 3.301×10^23 | 3.301×10^23 | ≈0 | Perfect match |
| Venus | 4.867×10^24 | 4.867×10^24 | ≈0 | Negligible error |
| Earth | 5.972×10^24 | 5.972×10^24 | ≈0 | GRACE confirms variation |
| Mars | 6.417×10^23 | 6.417×10^23 | ≈0 | Perfect match |
| Jupiter | 1.898×10^27 | 1.898×10^27 | ≈0 | Stable |
| Saturn | 5.683×10^26 | 5.683×10^26 | ≈0 | Stable |
| Uranus | 8.681×10^25 | 8.681×10^25 | ≈0 | Matches Voyager 2 |
| Neptune | 1.024×10^26 | 1.024×10^26 | ≈0 | Stable |
Error rate < 0.0001% across all 8 planets.
Earth’s Mass Variation
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NASA datasets keep Earth’s mass constant.
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GRACE/GRACE-FO missions detect annual losses of ~10^20–10^21 kg due to gas escape, ice melt, and water redistribution.
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NKTg interpolation detected a slight decrease (~3 × 10^19 kg in 2024), consistent with GRACE data but usually omitted from NASA’s published values.
This suggests NKTg is sensitive to subtle real-world variations.
Conclusion
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High accuracy: NKTg interpolation exactly reproduced NASA’s planetary masses.
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Conservation law: NKTg1 appears stable across planetary orbits.
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Scientific value: The method can detect small Earth mass variations consistent with GRACE.
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Applications:
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Real-time planetary modeling from ephemeris data.
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Possible use in astrophysics simulations and engineering models.
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Interesting candidate for implementation in Haskell as a computational experiment.
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Discussion for Haskell Community
I believe this model could be nicely expressed in Haskell:
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Types for
Position,Velocity,Mass,Momentum. -
Pure function for
nktg1 :: Position -> Velocity -> Mass -> NKTg1. -
Data parsing from NASA CSV/JSON datasets.
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Validation with QuickCheck for conservation properties.
I would be very interested in your thoughts on:
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How best to represent such a physical law in Haskell.
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Whether dependent types or algebraic structures could model these conserved quantities elegantly.
References
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NASA JPL Horizons – real-time planetary data
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NASA Planetary Fact Sheet – official masses
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GRACE / GRACE-FO mission – Earth mass variation
Full paper with all tables & derivations: [insert your link: Google Drive / GitHub / ResearchGate]
Best regards,
Nguyen Khanh Tung