You came up with an expression for the gravitational potential. Did you ever convert the earth’s geopotential into your form?
[ My son and his small family live in Japan. He decided to go to college there and never came back to the USA. ]
I worked with Steve Klosko on the early NASA geopotential models back in the late 1970’s when I was studying dynamic gravitational field detection at the University of Maryland at College Park when Charles Misner and Joseph Weber were there. Joe recommended I follow what his student, Robert Forward was doing in his dissertation, “Detectors for Dynamic Gravitational Fields” Robert wanted to combine gravitation and electromagnetism at a practical level — by finding common sets of units and overall to simplify the calculations and methods to an engineering level.
The current geopotentials most used are the ones derived from the GRACE Follow-on satellites. Those give up to 2160×2160 spherical harmonic models that are updated monthly. With Mathematica or similar tools you might convert the spherical harmonics to your representation. Yours sort of reminds me of the quantum chemistry models. They approximate the full Schrodinger solutions for practical calculations.
For the last 10 years or so, I have been working informally with many different groups who use gravimeters arrays with a variety of detectors. They need better ways to represent the field in small areas at high resolution. 1 meter seems to be desired. Regional gravity surveys are much finer grained than the global geopotential model. Your representation of the field might work for them.
I had about 100 groups in a project up until this March 31 on ResearchGate., but RG decided to drop support for projects. I have not been able to get all the people and groups connected again. Several in Japan and China.
If you reply and are interested, I have a number of things you might find useful. I read several of your papers, starting with Spectrum Generating Algebra for Charged Strings. My current best nanoscopic model for gravity is chains (magnetic chains, hyperelastic fields) of charged Fermions with permanent magnetic moments. So I was checking the string theories to see if anyone had worked out the details from that side. Your 1/r^3 potential fits well as a local magnetic dipole potential, in a more complete multipole expansion.
The energy density of the gravitational field at the earth’s surface is equivalent to a magnetic field of about 380 Tesla. That corresponds to a black body with a peak at about 1500 electron volts covering most of the XUV and soft x-ray spectral region. I think the geopotential is grainy and fluctuating and might explain some of the data gathered as “quantum fluctuations”. I am asking groups doing quantum detection or quantum computing to correlate their noise with gravitational variations that are routinely measured, well modeled and fairly easily tested for different kinds of instruments and systems. Some “quantum detectors” ought to be good gravitational detectors.
When the original Internet Foundation was cancelled, I took the domains and the task from Network Solutions. This is the 25th year. I am writing up my notes and recommending policies to agencies, corporations and groups. The global sensor networks use some of the more advanced sharing and collaboration methods.
Richard Collins, The Internet Foundation