Hi, everyone. Our mutual friend Gopi has recently published some papers on the foundations of astronomy. Although we normally do not encourage much discussion about advanced physics or mathematics, I think these papers should be published and Simon will approve of our using CluesForum as a platform for a few select science works now and then, if just for critical awareness of their existence.

In this case, please allow me to republish a few papers of Gopi's in this thread, where his questions about Kepler's and Newton's problems are sharpened in specific critiques of logic and formulas.

I hope we can forgive an occasional name like Steiner or Mathis appearing, (the "offense" only because of potential controversy around names, not because of any particular critique of their work to discuss here) and just look to the thrust of the arguments being made about Kepler and Newton, which I trust could be instrumental in making a solid new foundation for astronomy and/or other scientific inquiries.

Thank you!

I think Gopi would be alright with my forwarding along a segment of his e-mail message to us as follows:

[... B]y going through Newton's proof carefully, we find that he did not derive the inverse-square law for planets, the law of gravity, and the laws of circular motion by mathematical necessity, but assumed it ad-hoc. I wanted to share this series of papers with you and the folks on this forum, and hope to see what you think of it:

1st paper: Replacing the Foundations of Astronomy provides an outline of the process, into which this research is embedded.

2nd paper: Identifies how Newton simply assumed the inverse-square law in planetary motion by cleverly disguising Kepler's third law.

3rd paper: Original form of Kepler's law, that he actually observed, and what was done to squeeze it to a linear system.

4th paper: The biggie showing gravity is insufficient, physically and mathematically, to sustain circular/elliptical motion. At most it provides one component of an infinite series.

I hope there is something here for all, and it is worth the digging. The first paper is written in a colloquial way, while the other three require good amount of algebra, and occasionally calculus. Having the Principia, even an e-copy, handy will also help. The last paper is the most relevant of all for the entire thread of research, where it shows that circular motion can only be seen in terms of forces if we include an infinite series of them. Picking up just acceleration due to gravity would be like picking up a grain of sand and calling it a beach.

Anyway happy reading, and hope some of it makes sense!