I need to make a short but crucial correction. I’m human (so they say), and subject to the same force of habit as everybody else. I’ve been wrong about the curvature of the potential energy field. It curves as 1/x, not 1/x². If the force of gravity follows an inverse square law, then the curvature that causes it must be the simple inverse. Duh. Why did it take me this long to notice? I had to start running the numbers to see that I kept coming up with an inverse cube force to see the problem. Now, all my diagrams are wrong.
Symmetry at work: The classical gravitational force (inverse square) is the derivative of the curvature (inverse) of the potential energy field. The gravitational potential is the integral of the force. That means the classical gravitational potential is the curvature of the potential energy field is the simple inverse.
To see the near and far field formulas for the gravitational attraction and gravitational potential to a stationary particle, you have to see the original post on Substack. Stupid Blogger doesn't have LaTex support.
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