Recent content by physics4all

  1. P

    I Universal Gravity without Shell Theorem

    Thank you! I was looking for something similar to this essay, although not that. Author(s) matched Newton’s pre-calculus geometry with Energy rather than. Force. There are some steps skipped and even though I think I understand where derivations are coming from, would not want to presume. Is...
  2. P

    I Universal Gravity without Shell Theorem

  3. P

    I Universal Gravity without Shell Theorem

    true th I'm not looking for somebody to review arithmetic:) I was doing something else, and certain things began to remind something. Somehow that expression, when Plugged into Newtonian Gravity matches (almost to tenth) "missing" matter and constant speed (or rather miniscule positive...
  4. P

    I Universal Gravity without Shell Theorem

    Well, fair is fair… will work on it. [Mentor Update -- OP has edited the first post above to use LaTeX now.]
  5. P

    I Universal Gravity without Shell Theorem

    Not to be rude… this is not the lesson. At least not until an error is pointed out. If my log transformations in 6.1-6.3 correct, would not take more then 15 mins to simplify. Or even plug in some numbers straight up and do simple math to confirm. Just don’t know personally...
  6. P

    I Universal Gravity without Shell Theorem

    This is exactly what I did. 6 iterations of Taylor series for natural logs is enough to confirm this long expression converges on form (3) as expected. Then I noticed at distances d very super large comparing to both s and r, all 3 log combinations begin to grow as power of e with ultimate...
  7. P

    I Universal Gravity without Shell Theorem

    I couldn't get Latex text to render. Sorry if text looks unreadable... [Mentor Update -- OP has updated the below text using LaTeX] Thus, for two perfect spheres with radiuses r and s, densities Pr and Ps, which are positioned in space at distance d between their respective centers, expression...
Back
Top