First, I want to thank you for reading my article. Your comment on needing integration not only shows your understanding, but exposes why I most closely identify with Michael Faraday. I am not familiar with writing integrations but have done so semi-manually and by using other tools to verify the trends I describe.
In agreement with your observation, the trend is established by summing the solutions to the equation at a plurality of equidistant R values. Proper integration would directly plot that trend based on G and M values used, and there is likely the ability to simplify further. I look forward to anyone with a better calculus skillset to try and “James Maxwell” this theory 😁.
From looking at the equations in the Robert Gentry paper you referenced, I believe he leveraged the same geometrical consideration in his equations and included that same integration. I suspect the biggest difference in our approaches is that I am referencing the change at the observer’s point with an expanding horizon (not expanding space, but expanding sphere of influence/observation over time) whereas he seemed to envision the system from an originating horizon inwards. In either case, the rule of squares adds to the emanating surface as R expands while reducing the power of that surface at that distance. That has to be one of the most elegant way to use exponents to describe a straight line, especially for a lab provable scenario!
I do believe that my approach has measurable evidence and application, and have attempted to explore so in the following article. Recognizing that time dilation, even in a non-expanding space context, will have some influence on ‘c’ propagation, I also explore briefly the possibility of adding that to the integration. Please note I used an assistant for the math, so it needs to be scrutinized.
I understand that I can be wordy, some of my descriptions may be unconventional, and I also strive to be apologetic. That being said, this article may better summarize my theory with a virtual QnA that may better illustrate some of the more difficult to convey aspects.
I look forward to your thoughts. Thank you for taking an interest in my efforts!