Mr. Jubber,
Thank you for your interest in my case on Legal Match. Here is a short explanation of my research, so you can ask questions when we talk:
If you followed the recent Artemis mission to the Moon (or the Apollo lunar missions), you might have seen a diagram of their path, a figure-eight-shaped orbit with Earth and the Moon in the loops. That path exists between any two major celestial bodies; so it also exists between the Sun and Mars. I set up my Mars computer program to target the crossing point of the figure eight (which is close to Mars). If you align the spacecraft to that flight path, it uses the “Three Body” (Sun, Mars, spacecraft) forces that are not usually accounted for – Coriolis force and centrifugal force – both of which are totally neglected in orbital mechanics (because orbital mechanics is in fixed coordinates and the Three Body Problem is solved in rotating coordinates). When the spacecraft reaches that point, Mars is going 9000 MPH faster, and it takes a huge thrust to catch up. My idea was to try to match the trajectory to the figure-8 loop to help speed up and adjust the course. In my crude approximation, I saved 10% on the energy needed to reach Mars.
“Rotating coordinates” simply means that the figure-8-shaped orbit persists as the Moon orbits Earth, following it around.
Fundamentally, I added the Centrifugal force and the Coriolis force to my non-rotating trajectory model and used them to refine a solution to Mars.
The Mars trajectory is one of the most nonlinear problems in space science. Normally, a basic trajectory model is created, and then a massive nonlinear optimization program is used to solve it. This involves millions of lines of code running for hours on a massively parallel supercomputer. However. If all the forces in your model are gravity, which is a “central force,” you can integrate backward in time. I set up my model to integrate forward to Mars from the midpoint and backward to Earth from the midpoint; I added them together for a seamless trajectory. (You can save another 10% at Earth by the same Mars approach method.) My 26 pages of FORTRAN code solved the problem, with some basic optimization, on a 486 PC running for 30 seconds. This was not a simple approximation, but using the full 3D ephemerides. I benchmarked it to confirm the model versus an industry standard. It was exact to 16 significant digits.
Astronomers use reverse integration to study the evolution of our solar system, integrating back in time. But nobody in orbital mechanics had ever done this before. All orbital optimization was going forward in time, using various nonlinear optimization programs.
I have a short AI analysis on my website at https://clark-vs-utaustin.com that looks at Cesar Ocampo’s work prior to November 2000, when I presented my research at a Department seminar (I have the flyer, my presentation notes, and notes of attendees on the website). Cesar Ocampo was my advisor at this time and, in fact, he set up the seminar- his name is on the flyer.
Dr. Ocampo graduated in 1996 with a PhD and had done some computer models in FORTRAN, standard forward-time, nonlinear optimizations. Nothing involving the figure-eight “free return orbit” or reverse integration. The Copernicus system he developed relies on “Third Body topology”, as I did with my Mars solution. Copernicus also uses a system of forward and reverse optimization, which had not been done before.
In layman’s terms, Copernicus included the Coriolis and centrifugal forces that no previous model had used and, in so doing, was able to discover many hyper-efficient trajectories. My Mars solution found one such solution, but proved the efficacy of the approach. Copernicus also uses reverse integration, which had not been done before in orbital mechanics.
I have six official US Copyrights from 1988-2000 (I solved it in the summer of 1988) with this Mars research, including the FORTRAN code. I have the original papers, a whole box full of the original notes, notebooks, and backup copies of the research at every stage. I even have the hard drives of the computers I used, which I took from the PCs when I upgraded. The original website I set up to try and get feedback from the aerospace community is back online at the original domain, https://mars-pathfinder.com/txfiles
My skill in FORTRAN is well documented going back almost ten years before I started grad school, with a dozen formal conference papers (listed on my website resume) on dBase applications I created for the commercial-quality analysis of engineered systems in buildings – HVAC, electrical, energy analysis. The dBase and FORTRAN commands are very similar, if not identical. All my engineering programs had to fit on a 3.5 in floppy, so they were very compact. The DOS version 1.0 of Mars Pathfinder was (is) only 145 KB; the full 2.0 Windows version fits on a 3.5 in floppy, which is 1.5 MB. I have most of these conference papers and all of the original dBase apps on floppies. This establishes the programming skill needed to develop my Mars solution.
Ocampo also wrote using FORTRAN, I believe.
I learned only within the last month that my Mars research was not only valid but spawned a whole new field in orbital mechanics. This was from an AI search and investigation, as I sought AI (using Jenni and Gemini) references to write up my Mars research in a formal academic paper. Then. Only a few days ago, I learned about Ocampo’s research and how closely it aligned with my own methods. Moreover, I learned that he announced Copernicus, according to AI, in the spring of 2001, only a few months after my Mars seminar, and received a massive grant from NASA in August 2001 – during which time I was being summarily expelled.
I was rated 0% for schizophrenia when I started grad school. I studied my orbits notes for a year or two; then it was too much – only brought back pain. Maybe around 2003, the VA increased my rating to 100%. After all that grief at Texas, I had a math phobia. I have written several books using the 150+ diagrams from my final dissertation, which included the Mars research, but illustrating the diagrams with psychology and philosophy analogies – no equations, no math, no orbital mechanics tech. It’s only in the last few months that I have been able to get back to my old orbital mechanics ideas to try and publish them – I had a new model of the solar system, a model of the transistor junction, and new insights into relativity.
I can talk with you at any time that is convenient. I am in North Carolina, so any time say 10 AM to 4 PM eastern is fine. LOL. I have a chalkboard in the living room, and I can draw some diagrams to help you understand. I’ll also set up some diagrams online to show you.
Bill Clark