The NKTg Law: A New Natural Law on Position and Varying Inertia

By Nguyễn Khánh Tùng — Independent Researcher

For centuries, scientists have studied the motion of objects under the influence of forces. From Newton’s laws of motion to Kepler’s laws of planetary orbits, we have come a long way in understanding how the universe behaves. However, nature still holds many secrets — especially when it comes to the subtle interplay between position, momentum, and mass variation in dynamic systems.

After nearly 20 years of observation, data analysis, and practical application, I am honored to present a new law of nature that I call The NKTg Law — named in tribute to Newton, Kepler, and my own humble contribution (Tùng). This law reveals a profound relationship between position, momentum, and changing inertia that has been hiding in plain sight, deeply embedded in the fabric of motion across many scales: from vibrating springs, to rockets, to planetary systems.

The Core Discovery

The NKT Law centers around two key products that govern motion in dynamic systems:

• The first is the product of position and momentum: x⋅px \cdot px⋅p which reflects the immediate state of motion relative to equilibrium and direction.
• The second is the product of the rate of mass change and momentum: dmdt⋅p\frac{dm}{dt} \cdot pdtdm​⋅p which captures how changes in inertia (mass) influence future motion.

Together, these two terms form the foundation of a broader framework that generalizes known laws of motion, especially in systems where mass is not constant — such as rockets, interacting bodies, or objects influenced by internal transformations.

What Makes the NKTg Law Different?

Classical mechanics usually assumes constant mass. But in many real-world systems — from fuel-burning engines to gravitational interactions — mass subtly varies over time. While physics has addressed these cases with approximations or specific models, the NKTg Law provides a unified principle that naturally incorporates position, momentum, and mass variation into a coherent whole.

Notably, this law has been empirically validated in:

• Harmonic oscillations (e.g., pendulums with varying mass)
• Spacecraft dynamics (e.g., orbital adjustments using internal propulsion)
• Planetary motion (e.g., shifts in orbital characteristics due to long-term mass exchange)

Practical Impact and Verification

The law has been successfully applied for over five years in real-world modeling systems, producing results that align more accurately with NASA and ESA data than traditional models. Unlike purely theoretical constructs, the NKTg Law was discovered through reverse-engineering patterns in actual datasets and then confirmed by both physical models and simulations.

This work is independent and open-access, allowing anyone to verify the findings using public data. The law does not rely on assumptions about dark matter, complex tensors, or quantum fields. It is a clear and observable pattern, emerging from nature’s own design.

Vision for the Future

I believe the NKTg Law is only the first step in a deeper theory — one that connects energy, entropy, force interaction, and possibly even color charge in quantum fields. In due time, I will publish the full system of equations that extend this foundation into broader areas of physics.

For now, I invite fellow researchers, students, and curious minds to explore this discovery, test it, question it, and help expand our collective understanding of the universe.

Final Note

“I did not invent it. I merely wrote down what nature has been doing for billions of years.”
— Nguyễn Khánh Tùng, The NKTg Law

If you are interested in reading the full scientific publication or downloading simulation data and graphs, please visit the official preprint or contact me directly at traiphieu.com@gmail.com.

Nguyễn Khánh Tùng (ORCID: 0009-0002-9877-4137)

ORCID iD: 0009-0002-9877-4137

https://orcid.org/0009-0002-9877-4137