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Inertia: A Millennia-Long Journey
Inertia, the ability to maintain an object’s motion, has existed since ancient times. Aristotle viewed motion as an inherent property; an object stops only when the force disappears. For thousands of years, inertia remained an abstract concept, impossible to measure.
Galileo and Newton initiated a revolutionary leap. Newton defined inertia through the first law, but humans could only measure mass indirectly. In modern physics, inertia exists more in theory than in experiment; it is still not directly quantifiable.
NKTg Law: A Great Leap in Quantifying Inertia
NKTg Law – the Law of Varying Inertia allows for the measurement of inertia. Inertia becomes a variable quantity, depending on position, velocity, and mass:
NKTg=f(x,v,m)
NKTg₁ = x × p
NKTg₂ = (dm/dt) × p
With the NKTm unit, inertia becomes a measurable entity, both theoretical and practical. NKTm is the bridge between classical thinking and modern experimentation, enabling simulation, calculation, and deployment across all physical and engineering systems.
NKTg Law is implemented in 150 leading programming languages, from Python, C++, Java, MATLAB, R, Swift, Go to PL/I, PL/SQL, ASP.NET, Assembly. This enables:
- Support for all software ecosystems, from desktop to web and mobile.
- Direct integration with inertia-measuring sensors.
- Simulation of objects from fundamental particles to planets and galaxies on a unified algorithmic platform.
Core Library & API: Global Knowledge of Inertia
Another historic advancement is the implementation of NKTg Law in 150 leading programming languages. From Python, C++, Java, MATLAB, R, Lua, Swift, Go to rarer languages like PL/I, PL/SQL, ASP.NET, Assembly, or COBOL, NKTg Law becomes a common language for modern simulation and computation systems.
This wide deployment allows:
- Support for all software ecosystems, from desktop, server, to web and mobile.
- Direct integration with sensors to measure inertia experimentally.
- Easy simulation of objects, from fundamental particles to planets and galaxies, on the same algorithmic platform.
This is supported by the Core library & API of NKTg Law on GitHub: https://github.com/NKTgLaw/NKTgLaw, which provides:
- Core implementation: core algorithms for calculating varying inertia,
- REST/gRPC API: access to inertia data and system integration,
- 150+ client wrappers: deployment support for over 150 programming languages, from infrastructure to application, from physics simulation to robotics, aviation, and astronomy.
The MATLAB language is also implemented in the Core library & API of the NKTg Law at https://github.com/NKTgLaw/NKTgLaw/tree/main/clients/matlab.
Thus, NKTg Law becomes a global digital science platform, where inertia is no longer a theoretical concept but data that can be analyzed, shared, and applied instantly.
Historical Significance and Cosmic Vision
Quantifying inertia is a milestone of knowledge, leading humanity into a new era of understanding the universe. With NKTg Law, NKTm, 150 programming languages, and sensor systems:
- Inertia can be measured directly, no longer an abstract unknown.
- All motion models – from elementary particles to galaxies – can be simulated and predicted accurately.
- Understanding of nature and the universe enters a new era, where intrinsic properties of objects become scientific data.
Inertia, once theoretical, is now a numerical entity, opening doors for humanity to explore and understand the universe more deeply.
Conclusion
From Aristotle to Newton and modern physics, inertia has always been an abstract concept, not directly measurable. Thanks to NKTg Law and NKTm, along with 150 programming languages and sensor devices, inertia is now a practical measurable quantity, ushering in a new era of universal understanding, transforming physical knowledge from theory to data, from abstraction to measurement, from reasoning to discovery.
Independent researcher: Nguyễn Khánh Tùng
ORCID: 0009-0002-9877-4137
Email: traiphieu.com@gmail.com
Website: https://traiphieu.com
Abstract
Every fundamental law of physics has a characteristic quantity and a unit of measurement (e.g., Newton for force, Joule for energy). The NKTg Law (Law of Varying Inertia) introduces a new physical quantity — varying inertia — defined by the interaction between position, velocity, and mass.
To measure this new quantity, I propose the NKTm unit, verified with NASA JPL Horizons data (Neptune, 2023–2024). Results indicate that NKTm is an independent fundamental unit, comparable in significance to Newton, Pascal, Joule, and Watt, with applications in astronomy, aerospace, and engineering.
This article clarifies the measurement unit of the NKTg Law (NKTm) and highlights its applications, many of which I have already implemented and shared as code examples on MATLAB Central.
1. Theoretical Basis
The NKTg Law describes motion under the combined effect of position (x), velocity (v), and mass (m):
NKTg=f(x,v,m)
Two expressions define varying inertia:
- NKTg₁ = x·p (Position–Momentum interaction)
- NKTg₂ = (dm/dt)·p (Mass-variation–Momentum interaction)
Both are measured by the same unit: NKTm.2. Dimensional Analysis
- From NKTg₁: [M⋅L2/T][M·L²/T][M⋅L2/T]
- From NKTg₂: [M2⋅L/T2][M²·L/T²][M2⋅L/T2]
Thus, NKTm is a unique unit that can take different dimensional forms depending on which component dominates.
For comparison:
QuantityUnitDimensionForceNewton (N)[M·L/T²]EnergyJoule (J)[M·L²/T²]PowerWatt (W)[M·L²/T³]Varying inertia (NKTg₁)NKTm[M·L²/T]Varying inertia (NKTg₂)NKTm[M²·L/T²]
3. Verification with NASA Data (Neptune, 2023–2024)
- Position (x): 4.498×1094.498 \times 10^94.498×109 km
- Velocity (v): 5.43 km/s
- Mass (m): 1.0243×10261.0243 \times 10^{26}1.0243×1026 kg
- Momentum (p = m·v): 5.564×10265.564 \times 10^{26}5.564×1026 kg·m/s
Results:
- NKTg₁ = x·p ≈ 2.503 × 10³⁶ NKTm
- NKTg₂ ≈ -1.113 × 10²² NKTm (assumed micro gas escape)
- Total NKTg ≈ 2.501 × 10³⁶ NKTm
4. Applications
- Astronomy: describe planetary mass variation, star/galaxy formation, and long-term orbital stability.
- Aerospace: optimize rocket fuel usage, account for mass leakage, design ion/plasma engines.
- Earth sciences: analyze GRACE-FO data, model ice melting, sea-level rise, and mass redistribution.
- Engineering: variable-mass robotics, cargo systems, vibration analysis, fluid/particle simulations.
👉 Many of these applications are already available as MATLAB code examples that I have uploaded to MATLAB Central, showing how NKTm can be computed and applied in practice.5. Scientific Significance
- Establishes a new fundamental unit (NKTm), independent of Newton and Joule.
- Provides a theoretical framework for variable-mass dynamics, beyond Newton and Einstein.
- Supports accurate computation and simulation of real-world systems with mass variation.
Conclusion
The introduction of the NKTm unit demonstrates that varying inertia is a measurable, independent physical quantity. Like Newton or Joule, NKTm lays the foundation for a new reference system in physics, with applications ranging from planetary mechanics to modern space technology.
This article not only clarifies the measurement standard of the NKTg Law, but also connects directly with practical MATLAB implementations for simulation and verification.
Discussion prompt:
What do you think about introducing a new physical unit like NKTm? Could it be integrated into MATLAB-based simulation frameworks for variable-mass systems?
You can refer to the following four related articles to gain a deeper understanding of the NKTg Law and its applications
