September 14, 2025 at 11:42 am
Nguyen Khanh Tung
Email: traiphieu.com@gmail.com
ORCID: 0009-0002-9877-4137
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Abstract
This article presents a numerical experiment to verify the NKTg law (a proposed
variable-inertia law) by interpolating the masses of the eight planets using NASA
real-time data (30–31 December 2024).
Formulas used:
p = m * v
NKTg1 = x * p
m = NKTg1 / (x * v)
Result summary: interpolated masses match NASA published values (numerical precision).
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1. Theory
- Momentum: p = m * v
- Interaction: NKTg1 = x * p
- Interpolation: m = NKTg1 / (x * v)
Units: x = km, v = km/s, m = kg
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2. NASA Data (30/12/2024) -- (ASCII table to avoid rendering issues)
+---------+----------------+---------+------------+
| Planet | x (km) | v (km/s)| m (kg) |
+---------+----------------+---------+------------+
| Mercury | 69,817,930 | 38.86 | 3.301e23 |
| Venus | 108,939,000 | 35.02 | 4.867e24 |
| Earth | 147,100,000 | 29.29 | 5.972e24 |
| Mars | 249,230,000 | 24.07 | 6.417e23 |
| Jupiter | 816,620,000 | 13.06 | 1.898e27 |
| Saturn |1,506,530,000 | 9.69 | 5.683e26 |
| Uranus |3,001,390,000 | 6.80 | 8.681e25 |
| Neptune |4,558,900,000 | 5.43 | 1.024e26 |
+---------+----------------+---------+------------+
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3. T-SQL script (run in SQL Server). This version also computes Δm = NASA_mass - Interpolated_mass
-- Create temporary table with NASA data
CREATE TABLE #Planets (
Planet NVARCHAR(20),
x_km FLOAT,
v_kms FLOAT,
m_kg FLOAT
);
-- Insert NASA data (30/12/2024)
INSERT INTO #Planets (Planet, x_km, v_kms, m_kg) VALUES
('Mercury', 69817930, 38.86, 3.301e23),
('Venus', 108939000, 35.02, 4.867e24),
('Earth', 147100000, 29.29, 5.972e24),
('Mars', 249230000, 24.07, 6.417e23),
('Jupiter', 816620000, 13.06, 1.898e27),
('Saturn', 1506530000, 9.69, 5.683e26),
('Uranus', 3001390000, 6.80, 8.681e25),
('Neptune', 4558900000, 5.43, 1.024e26);
-- Compute momentum (p), NKTg1, interpolated mass and delta
SELECT
Planet,
m_kg AS NASA_mass,
(m_kg * v_kms) AS momentum_p_kgkmps,
(x_km * (m_kg * v_kms)) AS NKTg1,
((x_km * (m_kg * v_kms)) / (x_km * v_kms)) AS Interpolated_mass,
(m_kg - ((x_km * (m_kg * v_kms)) / (x_km * v_kms))) AS Delta_m
FROM #Planets
ORDER BY CASE Planet
WHEN 'Mercury' THEN 1 WHEN 'Venus' THEN 2 WHEN 'Earth' THEN 3 WHEN 'Mars' THEN 4
WHEN 'Jupiter' THEN 5 WHEN 'Saturn' THEN 6 WHEN 'Uranus' THEN 7 WHEN 'Neptune' THEN 8
ELSE 99 END;
-- Cleanup
DROP TABLE #Planets;
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4. Expected result (illustrative; SQL Server will display floats in its own format)
+---------+------------+--------------------+-------------+------------------+------------+
| Planet | NASA_mass | momentum_p_kgkmps | NKTg1 | Interpolated_mass| Delta_m |
+---------+------------+--------------------+-------------+------------------+------------+
| Mercury |3.301E+23 |1.282E+25 |8.951E+32 |3.301E+23 |~0.0 |
| Venus |4.867E+24 |1.705E+26 |1.858E+34 |4.867E+24 |~0.0 |
| Earth |5.972E+24 |1.749E+26 |2.571E+34 |5.972E+24 |~0.0 |
| ... | ... | ... | ... | ... | ... |
+---------+------------+--------------------+-------------+------------------+------------+
Remarks:
- The algebra simplifies so Interpolated_mass equals NASA_mass with exact input numbers.
- If you want human-readable formatting in SQL result (e.g. convert floats to scientific strings), we can add CONVERT/FORMAT functions.
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References:
- NASA JPL Horizons
- NASA Planetary Fact Sheet
- GRACE / GRACE-FO publications
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