The NKTg Law on Varying Inertia

A novel formulation of orbital dynamics that describes how an object's motion in space depends on its position, velocity, and mass — through a new quantity called NKTg.

📌 Overview

The NKTg Law proposes a relationship that governs an object's movement tendency based on three parameters:

NKTg = f(x, v, m)

Where: - x: Position or displacement of the object relative to a reference point. - v: Velocity of the object. - m: Mass of the object.

🔬 Extended Description

Unlike classical Newtonian mechanics which assumes constant inertia, the NKTg Law introduces a dynamic view of inertia — influenced by mass variation and positional momentum. This law is particularly valuable for modeling systems such as spacecrafts, satellites, or even planets where mass is not constant over time.

The law defines two components that determine an object's movement tendency:

• NKTg₁ = x × p — evaluates whether momentum and position drive the object toward or away from equilibrium.
• NKTg₂ = (dm/dt) × p — measures how a change in mass affects the motion, either amplifying or resisting it.

By integrating these two components, the NKTg Law offers a more complete interpretation of motion in dynamic systems, verified through real NASA and GRACE satellite data.

📐 Core Formulas

Let p = m × v be the linear momentum.

🔸 Component 1: Position-Momentum Interaction

NKTg₁ = x × p

• If NKTg₁ > 0: The object tends to move away from its stable state.
  
• If NKTg₁ < 0: The object tends to return toward the stable state.

🔸 Component 2: Mass Variation Effect

NKTg₂ = (dm/dt) × p

• If NKTg₂ > 0: Mass change supports the movement.
  
• If NKTg₂ < 0: Mass change resists the movement.

📏 Unit of measure: NKTm — a proposed unit representing varying inertia.

🔧 Stable State Definition

A stable state is a dynamic configuration where the object’s position (x), velocity (v), and mass (m) interact in such a way that motion is preserved without uncontrolled deviation. This concept is key to understanding orbital sustainability.

📂 Applications

This theoretical framework can be applied to: - 🛰 Predicting orbital behavior of satellites and planets - 🚀 Reinterpreting spacecraft trajectory dynamics - 🌌 Modeling mass-variable systems such as migrating celestial bodies - 📉 Diagnosing inertial stability in gravitationally active environments

📁 Resources

• CITATION.cff – Citation metadata
  
• README.md – Project summary and formulas

👤 Author

Nguyen Khanh Tung
🔗 https://traiphieu.com
✉️ traiphieu.com@gmail.com

📜 License

This work is licensed under a Creative Commons Attribution 4.0 International License.

📝 How to Cite

Nguyen Khanh Tung (2025). The NKTg Law on Varying Inertia.

📌 DOI (Primary – Figshare): https://doi.org/10.6084/m9.figshare.29481710.v1
📌 DOI (Zenodo mirror): https://doi.org/10.5281/zenodo.15808498