Empirical Evidence for the NKTg Law from the 2025 RUS Mercury Dataset

[NKTgLaw]

Experimental Verification of the NKTg Law Using NASA Mercury Data in 2025​

Table 1 – Actual orbital and mass data of Mercury in 2024 from the NASA JPL Horizons System
Thời điểm​	x (m)​	v (m/s)​	m (kg)​	p = m·v​
1/1/2024​	5.16E+10​	5.33E+04​	3.30E+23​	1.76E+28​
4/1/2024​	6.97E+10​	3.90E+04​	3.30E+23​	1.29E+28​
7/1/2024​	5.36E+10​	5.20E+04​	3.30E+23​	1.72E+28​
10/1/2024​	6.95E+10​	3.92E+04​	3.30E+23​	1.30E+28​
12/31/2024​	4.64E+10​	5.81E+04​	3.30E+23​	1.92E+28​
Table 2 – Simulated orbital and mass data of Mercury in 2025 according to the NKTg law
Thời điểm​	x (m)​	v (m/s)​	m (kg)​	p = m·v (kg·m/s)​
1/1/2025​	5.16E+10​	5.22E+04​	3.301E+23​	1.72E+28​
4/1/2025​	6.97E+10​	3.87E+04​	3.301E+23​	1.28E+28​
7/1/2025​	5.49E+10​	4.91E+04​	3.301E+23​	1.62E+28​
10/1/2025​	6.83E+10​	3.95E+04​	3.301E+23​	1.30E+28​
12/31/2025​	4.61E+10​	5.85E+04​	3.301E+23​	1.93E+28​
Table 3 – Actual orbital and mass data of Mercury in 2025 from the NASA JPL Horizons System
Thời điểm​	x (m)​	v (m/s)​	m (kg)​
1/1/2025​	5.16E+10​	5.34E+04​	3.30E+23​
4/1/2025​	6.97E+10​	3.89E+04​	3.30E+23​
7/1/2025​	5.49E+10​	5.04E+04​	3.30E+23​
1/10/2025​	6.83E+10​	3.98E+04​	3.30E+23​
12/31/2025​	4.61E+10​	5.89E+04​	3.30E+23​
Table 4 – Comparison between NKTg Simulation and NASA Data in 2025
Thời điểm​	v – NKTg​	v – NASA​	Sai lệch v tương đối (%)​
1/1/2025​	5.22E+04​	53400​	-2.15461​
4/1/2025​	3.87E+04​	38900​	-0.562786​
7/1/2025​	4.91E+04​	50400​	-2.561981​
1/10/2025​	3.95E+04​	39800​	-0.819213​
12/31/2025​	5.85E+04​	58900​	-0.707806​

SCIENTIFIC CONCLUSION
On the experimental verification of the NKTg Law on planetary orbits​

Abstract: This report presents the results of the experimental verification of the NKTg law through the simulation of Mercury’s orbit in 2025, using reference data from NASA JPL Horizons and the MESSENGER spacecraft.
1. Conservation of motion tendency through the quantity NKTg₁
The study confirms that the quantity NKTg₁ = x × p (the product of position and momentum) is the fundamental parameter determining the motion tendency of an object in space. The experimental results show that:
• Establishing NKTg₁ = x × p as a target constant (8.90E+38 NKTm) allows the prediction of orbital velocity with high accuracy, with an average relative error of only 1.3% compared to NASA data.
• The interaction between position (x) and momentum (p) self-adjusts to maintain this constant, enabling the object to preserve its motion structure and maintain a stable state without the need for external force parameters.
2. Experimental verification of mass variation (dm/dt) from MESSENGER data
The model integrates the actual mass variation coefficient dm/dt = -0.5 kg/s, established from measured data of the atmospheric escape phenomenon by the MESSENGER spacecraft. According to the NKTg law, this variation leads to:
• The formation of the quantity NKTg₂: The product of the rate of mass change and momentum (NKTg₂ = (dm/dt) × p) carries a negative value throughout the orbit.
• Resisting effect: The negative value of NKTg₂ confirms that the mass loss process plays a resisting role against changes in the state of motion, accurately reflecting the nature of varying inertia.
3. Consistency and applicability
The experimental results on Mercury confirm that the NKTg law has consistency and high applicability. The system demonstrates the capability to:
• Fully describe planetary dynamics solely through the interaction between fundamental quantities (x, v, m).
• Eliminate dependence on approximation methods, without using force expressions in the calculation process, ensuring the reproducibility of results across different computational platforms.



// ... ...
use std::f64;

struct MercuryData {
date: &'static str,
x: f64, // position (m)
v: f64, // velocity (m/s)
m: f64, // mass (kg)
}

fn main() {

// ================================
// 1. NASA 2024 Reference Data
// ================================
let reference_2024 = MercuryData {
date: "31/12/2024",
x: 4.64e10,
v: 5.81e4,
m: 3.30e23,
};

let p_ref = reference_2024.m * reference_2024.v;
let nktg1_constant = reference_2024.x * p_ref;

println!("NKTg₁ reference constant: {:.3e}", nktg1_constant);
println!("========================================\n");

// ================================
// 2. NASA 2025 Real Data
// ================================
let nasa_2025 = vec![
MercuryData { date: "01/01/2025", x: 5.16e10, v: 5.34e4, m: 3.30e23 },
MercuryData { date: "01/04/2025", x: 6.97e10, v: 3.89e4, m: 3.30e23 },
MercuryData { date: "01/07/2025", x: 5.49e10, v: 5.04e4, m: 3.30e23 },
MercuryData { date: "01/10/2025", x: 6.83e10, v: 3.98e4, m: 3.30e23 },
MercuryData { date: "31/12/2025", x: 4.61e10, v: 5.89e4, m: 3.30e23 },
];

// Mass variation rate (MESSENGER data)
let dm_dt = -0.5_f64; // kg/s

println!("Date\t\tv_NKTg\t\tv_NASA\t\tRel.Error(%)\tNKTg₂");
println!("-----------------------------------------------------------------------");

for data in nasa_2025 {

// Interpolated velocity from constant NKTg1
let v_nktg = nktg1_constant / (data.x * data.m);

// Relative error
let rel_error = ((v_nktg - data.v) / data.v) * 100.0;

// Momentum
let p = data.m * v_nktg;

// NKTg2 calculation
let nktg2 = dm_dt * p;

println!("{:<12} {:>10.3e} {:>10.3e} {:>12.4} {:>15.3e}",
data.date,
v_nktg,
data.v,
rel_error,
nktg2);
}

println!("\n========================================");
println!("Interpretation:");
println!("NKTg₁ maintained as constant.");
println!("NKTg₂ negative → mass variation resists motion.");
}

Output:
NKTg₁ reference constant: 8.896e38
========================================

Date v_NKTg v_NASA Rel.Error(%) NKTg₂
-----------------------------------------------------------------------
01/01/2025 5.224e4 5.340e4 -2.1630 -8.620e27
01/04/2025 3.868e4 3.890e4 -0.5713 -6.382e27
01/07/2025 4.910e4 5.040e4 -2.5703 -8.102e27
01/10/2025 3.947e4 3.980e4 -0.8277 -6.513e27
31/12/2025 5.848e4 5.890e4 -0.7163 -9.649e27

========================================
Interpretation:
NKTg₁ maintained as constant.
NKTg₂ negative → mass variation resists motion.