Author: Nguyễn Khánh Tùng
ORCID: 0009-0002-9877-4137
Website: https://traiphieu.com
✨ Abstract
Every fundamental law of physics comes with a quantity and its unit:
- Newton for force,
- Pascal for pressure,
- Joule for energy.
The NKTg Law (Law of Varying Inertia) introduces a new physical quantity — varying inertia — which reflects the combined effect of position, velocity, and mass.
To measure this, I propose the NKTm unit, verified using NASA JPL Horizons data (Neptune, 2023–2024).
📖 Theoretical Basis
The NKTg Law defines motion as:
math
NKTg = f(x, v, m)
where
x: position [L]
v: velocity [L/T]
m: mass [M]
p = m·v: momentum [M·L/T]
Two main forms:
NKTg₁ = x · p (Position–Momentum interaction)
NKTg₂ = (dm/dt) · p (Mass-variation–Momentum interaction)
Both share the same unit: NKTm.
📐 Dimensional Analysis
From NKTg₁: [M·L²/T]
From NKTg₂: [M²·L/T²]
Comparison with classical units:
Quantity Unit Dimension
Force Newton [M·L/T²]
Energy Joule [M·L²/T²]
Power Watt [M·L²/T³]
NKTm₁ NKTm [M·L²/T]
NKTm₂ NKTm [M²·L/T²]
🛰️ Verification with NASA Data (Neptune 2023–2024)
Position (x): 4.498e9 km
Velocity (v): 5.43 km/s
Mass (m): 1.0243e26 kg
Momentum (p = m·v): 5.564e26 kg·m/s
Results:
NKTg₁ = x·p ≈ 2.503 × 10³⁶ NKTm
NKTg₂ ≈ -1.113 × 10²² NKTm (assuming micro gas escape)
Total NKTg ≈ 2.501 × 10³⁶ NKTm
🔧 Applications
Astronomy: planetary mass variation, stellar evolution, orbital stability.
Aerospace: rocket trajectory optimization, ion/plasma engines, mass leakage effects.
Earth Sciences: climate modeling, ice melting, sea-level rise, mass redistribution.
Engineering: robotics with variable load, cargo systems, nonlinear vibrations, nanomaterials.
🎯 Why NKTm Matters
A new fundamental measurement unit, independent of Newton or Joule.
Provides a framework for systems with variable mass — beyond Newtonian mechanics or relativity corrections.
Opens new perspectives in cosmology (dark matter, dark energy) and advanced mechanics.
💬 Closing Note
This article aims to clarify the measurement unit of the NKTg Law and show its wide applications — from planetary motion to engineering systems.
My hope is that the developer & science community can see not only the formulas, but also the physical meaning behind them.
🙏 What do you think about introducing a new physical unit like NKTm? Could it be useful for future physics simulations or space exploration models?
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