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Independent researcher: Nguyễn Khánh Tùng
ORCID: 0009-0002-9877-4137
Email: traiphieu.com@gmail.com
Website: https://traiphieu.com
Hello everyone,
I would like to share some results from my recent research on the NKTg law of variable inertia and how it was experimentally verified using NASA JPL Horizons data (Dec 30–31, 2024).
🔹 What is the NKTg Law?
The law states that an object’s tendency of motion depends on the interaction between its position (x), velocity (v), and mass (m) through the conserved quantity:
NKTg1 = x * (m * v)
Here, m * v is the linear momentum.
If NKTg1 > 0 → the object tends to move away from equilibrium.
If NKTg1 < 0 → the object tends to return to equilibrium.
This law provides a new framework for analyzing orbital dynamics.
🔹 Research Objective
Interpolate the masses of all 8 planets using the NKTg law.
Compare results with NASA’s official planetary masses on 31/12/2024.
Test sensitivity for Earth’s mass loss as measured by GRACE / GRACE-FO missions.
🔹 Key Results
Table 1 – Mass Interpolation (31/12/2024)
Planet Interpolated Mass (kg) NASA Mass (kg) Δm Remarks
Mercury 3.301×10^23 3.301×10^23 ≈0 Perfect match
Venus 4.867×10^24 4.867×10^24 ≈0 Negligible error
Earth 5.972×10^24 5.972×10^24 ≈0 GRACE confirms slight variation
Mars 6.417×10^23 6.417×10^23 ≈0 Perfect match
Jupiter 1.898×10^27 1.898×10^27 ≈0 Stable mass
Saturn 5.683×10^26 5.683×10^26 ≈0 Error ≈ zero
Uranus 8.681×10^25 8.681×10^25 ≈0 Matches Voyager 2 data
Neptune 1.024×10^26 1.024×10^26 ≈0 Perfect match
Error rate: < 0.0001% across all planets.
🔹 Earth’s Mass Variation
NASA keeps Earth’s mass constant in official datasets.
GRACE/GRACE-FO show Earth loses ~10^20–10^21 kg annually (gas escape, ice melt, groundwater loss).
NKTg interpolation detected a slight decrease (~3 × 10^19 kg in 2024), which is within GRACE’s measured range.
This demonstrates the sensitivity of the NKTg model in detecting subtle real-world changes.
🔹 Why This Matters
Accuracy: NKTg interpolation perfectly matched NASA’s planetary masses.
Conservation: NKTg1 appears to be a conserved orbital quantity across both rocky and gas planets.
Applications:
- Real-time planetary mass estimation using (x, v) data.
- Integration into orbital mechanics simulations in MATLAB.
- Potential extensions into astrophysics and engineering models.
🔹 Conclusion
The NKTg law provides a novel way to interpolate planetary masses with extremely high accuracy, while also being sensitive to subtle physical changes like Earth’s gradual mass loss.
This could open up new opportunities for:
- Data-driven planetary modeling in MATLAB.
- Improved sensitivity in detecting small-scale variations not included in standard NASA datasets.
References:
- NASA JPL Horizons (planetary positions & velocities)
- NASA Planetary Fact Sheet (official masses)
- GRACE / GRACE-FO Mission Data (Earth mass loss)
I’d be very interested in hearing thoughts from the community about:
- How to integrate the NKTg model into MATLAB orbital simulations.
- Whether conserved quantities like NKTg1 could provide practical value beyond astronomy (e.g., physics simulations, engineering).
You can refer to the following four related articles to gain a deeper understanding of the NKTg Law and its applications
Best regards,
Nguyen Khanh Tung
Independent researcher: Nguyễn Khánh Tùng
ORCID: 0009-0002-9877-4137
Email: traiphieu.com@gmail.com
Website: https://traiphieu.com
Theoretical Basis
The NKTg Law of Variable Inertia:
An object's tendency of motion in space depends on its position (x), velocity (v), and mass (m).
NKTg = f(x, v, m)
Fundamental interaction quantities:
NKTg1 = x * p
NKTg2 = (dm/dt) * p
where
p = m * v
For interpolation, we use:
m = NKTg1 / (x * v)
Research Objectives
- Verify interpolation of planetary masses using NKTg law.
- Compare with NASA real-time data (31/12/2024).
- Test sensitivity with Earth’s mass loss (NASA GRACE).
MATLAB Implementation
% NKTg Law Verification in MATLAB
% Author: Nguyen Khanh Tung
% Date: 31-12-2024
% Planetary data from NASA (30/12/2024)
planets = {
'Mercury','Venus','Earth','Mars','Jupiter','Saturn','Uranus','Neptune'};
x = [6.9817930e7, 1.08939e8, 1.471e8, 2.4923e8, ...
8.1662e8, 1.50653e9, 3.00139e9, 4.5589e9]; % km
v = [38.86, 35.02, 29.29, 24.07, 13.06, 9.69, 6.8, 5.43]; % km/s
m_nasa = [3.301e23, 4.867e24, 5.972e24, 6.417e23, ...
1.898e27, 5.683e26, 8.681e25, 1.024e26]; % kg
% Compute momentum
p = m_nasa .* v;
% Compute NKTg1
NKTg1 = x .* p;
% Interpolated masses using m = NKTg1 / (x*v)
m_interp = NKTg1 ./ (x .* v);
% Compare results in a table
T = table(planets', m_nasa', m_interp', (m_nasa - m_interp)', ...
'VariableNames', {'Planet','NASA_mass','Interpolated_mass','Delta_m'})
disp(T)
Results
- All 8 planets’ interpolated masses match NASA values almost perfectly.
- Deviation (Delta_m) ≈ 0 → error < 0.0001%.
- Confirms that NKTg1 is conserved across planetary orbits.
Earth’s Mass Loss (GRACE/GRACE-FO)
- GRACE missions show Earth loses mass annually (10^20 – 10^21 kg/year).
- NKTg interpolation detects Δm ≈ 3 × 10^19 kg.
- This matches the lower bound of NASA’s measured range.
Conclusion
- NKTg₁ interpolation is extremely accurate for planetary masses.
- Planetary data can be reconstructed with negligible error.
- NKTg model is sensitive enough to capture Earth’s small annual mass loss.
You can refer to the following four related articles to gain a deeper understanding of the NKTg Law and its applications
Check out how these charts were made with polar axes in the Graphics and App Building blog's latest article "Polar plots with patches and surface".
Nine new Image Processing courses plus one new learning path are now available as part of the Online Training Suite. These courses replace the content covered in the self-paced course Image Processing with MATLAB, which sunsets in 2026.
New courses include:
- Work with Image Data Types
- Image Registration
- Edge, Circle, and Line Detection
- Manage and Process Multiple Images
The new learning path Image Segmentation and Analysis in MATLAB earns users the digital credential Image Segmentation in MATLAB and contains the following courses:
all(logical.empty)
Discuss!
In 2019, I wrote a MATLAB Central blog post called "The tool builder's gene (or how to get a job at MathWorks)." In it, I explained my personal theory of a characteristic of some engineers that is key for becoming successful software developers at MathWorks.
I just shared this essay on my personal blog, along with a couple of updates.
This topic is for discussing highlights to the current R2025a Pre-release.
Apparently, the back end here is running 2025b, hovering over the Run button and the Executing In popup both show R2024a.
ver matlab
I just noticed that MATLAB R2025b is available. I am a bit surprised, as I never got notification of the beta test for it.
This topic is for highlights and experiences with R2025b.
“Hello, I am Subha & I’m part of the organizing/mentoring team for NASA Space Apps Challenge Virudhunagar 2025 🚀. We’re looking for collaborators/mentors with ML and MATLAB expertise to help our student teams bring their space solutions to life. Would you be open to guiding us, even briefly? Your support could impact students tackling real NASA challenges. 🌍✨”
In our large open-source MATLAB Central community, there are many long-term excellent user groups. I really want to know why you have been using MATLAB for a long time, and what are its absolute advantages?
I have been using MATLAB for a long time, and there are several reasons for that:
- Fast ramp-up in unfamiliar domains: When I explore an unfamiliar application area or a new topic, MATLAB helps me quickly locate the canonical methods and example workflows. Its comprehensive, professional documentation — along with the related-topic links typically provided at the end of each page — makes it easy to get started intuitively and saves a lot of time that would otherwise be spent hunting for foundational knowledge across the web.
- A relatively cutting-edge yet reliable technical path: MATLAB’s many toolboxes evolve with the field. While updates aren’t always absolutely bleeding-edge, they generally offer approaches that balance modernity and proven reliability. This reduces the risk of wasting time on obscure or unstable algorithms and helps me follow a pragmatic, well-tested technical direction.
- Strong community and technical support: When I encounter a problem I first post on forums like MATLAB Answers and thoroughly investigate the issue myself. If I find a solution, I publish it to contribute back — which deepens my own understanding and helps others. If I can’t solve it alone, experienced community members often respond within hours. As a last resort, MathWorks’ official support is available and typically conducts an in-depth investigation into specific cases to help resolve the issue.
- ......
Also, most individuals have limited time and technical bandwidth, diving deeply into a single, narrow area can be hard to pull back from unless you are committed to that specific direction. For cutting‑edge, highly specialized research it’s often necessary to combine MATLAB with other languages (e.g., Python, C/C++) to go further.
a = [ 1 2 3 ]
a =
1 2 3
b = [ 3; 5; 8]
b =
3
5
8
x = a + b
x =
4 5 6
6 7 8
9 10 11
I’d like to take a moment to highlight the great contributions of one of our community members, @Paul, who is fast approaching an impressive 5,000 reputation points!
Paul has built his reputation the best way possible - by generously sharing his knowledge and helping others. Over the last few years, he’s provided thoughtful and practical answers to hundreds of questions, making life a little easier for learners and experts alike.
Reputation points are more than just numbers here - they represent the trust and appreciation of the community. Paul’s upcoming milestone is a testament to his consistency, expertise, and willingness to support others.
Please join me in recognizing Paul's contributions and impact on the MATLAB Central community.
I just wanted here to share a link to some .gif animations I created over the years with Matlab :-)
I think gif animations are great supports for scientific diffusion.
I can not understand why Plot Browser was taken away in latest Matlab... I use Plot Browser all of the time! Having to find and click the particular line I want in a plot with a lot of lines is way less convenient than just selecting it in the Plot Browser. Also, being able to quickly hide/show multiple lines at once with the plot browser was so helpful in a lot of cases. Please bring Plot Browser back!!!! Please reply with support for this if you feel the same as I do!
I don't like the change
16%
I really don't like the change
29%
I'm okay with the change
24%
I love the change
11%
I'm indifferent
11%
I want both the web & help browser
11%
38 votes
In the latest Graphics and App Building blog article, documentation writer Jasmine Poppick modernized a figure-based bridge analysis app by replacing uicontrol with new UI components and uifigure, resulting in cleaner code, better layouts, and expanded functionality in R2025a.
https://blogs.mathworks.com/graphics-and-apps/2025/08/19/__from-uicontrol-to-ui-components
This article covers the following topics:
Why and when to move from uicontrol and figure to modern UI components and uifigure.
How to replace uicontrol objects with equivalent UI component functions (uicheckbox, uidropdown, uispinner, etc.).
How to update callback code to match new component properties and behaviors.
How to adopt new UI component types (like spinners) to simplify validation and improve usability.
How to configure existing components with modern options (sortable tables, auto-fitting columns, editable data).
How to apply visual styling with uistyle and addStyle to make apps more user-friendly.
How to use uigridlayout to create flexible, adaptive layouts instead of manually managing positions.
The benefits of switching from figure to uifigure for app-building workflows.
A full before-and-after example of modernizing an existing app with incremental, practical updates.
There is a communication regarding "How can I set the text font style of a Data Cursor object interactively on a plot?". But I am not clear on the answer found in this link:
https://www.mathworks.com/matlabcentral/answers/95968-how-can-i-set-the-text-font-style-of-a-data-cursor-object
I do not know how and where to put the recommended commands. Would you please clarfity and give me more details?
Thank you.
Worth the wait: seven new online training courses and one new learning path were released with 25a, covering topics in Controls, Electrification, and Physical Modeling. This release also brings new functionality to support interactions across both MATLAB and Simulink within a single course, beginning with the new Controls courses below:
- Control System Design with MATLAB and Simulink (learning path – includes the 5 controls courses listed below)
- Control System Modeling Essentials
- Linearization of Nonlinear Systems
- Control System Analysis Techniques
- PID Control Techniques
- Classical Controller Design Techniques
- Battery State Estimation
- Motor Modeling with Simscape Electrical
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