Editing Appendix/Ramblings/DarkMatterMusings (section)

=Musings Regarding Dark Matter and Dark Energy=

[<font color="red">Joel E. Tohline recollection on 3/8/2015</font>]  It was during my first year (July 1978 - June 1979) as a J. Willard Gibbs Instructor in the Astronomy Department at Yale University that I started wondering whether the nearly ubiquitous display of "flat rotation curves" in disk galaxies might be explained, not via the dark matter hypothesis, but by invoking a <math>1/r</math> force-law for gravity at large distances.  My reasoning was simple:
<ol>
<li>I was uncomfortable with the "dark matter" hypothesis, which smelled to me like the story of aether, all over again.</li>
<li>If Isaac Newton had been handed Vera Rubin's observations &#8212; which showed that orbital velocities were approximately constant with distance &#8212; instead of Kepler's observations &#8212; which showed that orbital velocities behaved as <math>v \propto r^{-1/2}</math> &#8212; he likely would have hypothesized that the gravitational acceleration due to a central point mass is proportional to <math>r^{-1}</math> instead of <math>r^{-2}</math>.</li>
</ol>
While I put quite a lot of thought into this idea in the late '70s and early '80s &#8212; and I still give it some thought from time to time because I consider the astrophysics community's fundamental understanding of "dark matter" and now, too, "dark energy" to be weak &#8212; I produced only two publications on the topic, neither of which was in a refereed archival journal:
<ul>
<li>[http://adsabs.harvard.edu/abs/1983IAUS..100..205T ''Stabilizing a Cold Disk with a <math>1/r</math> Force Law.'']</li>
<li>[https://www.phys.lsu.edu/faculty/tohline/vita/Tohline.C5.pdf ''Does Gravity Exhibit a <math>1/r</math> force on the Scale of Galaxies?'']</li>
</ul>

From time to time, I plan to post here some of the research notes that I have generated on this topic over the years, as well as recollections of discussions of the topic that I have had with professional colleagues.  I begin by posting a scanned copy of one of my most cherished possessions from my time at Yale.

<ul>
<li>[https://www.phys.lsu.edu/faculty/tohline/TinsleyNotes1978.pdf Notes from Beatrice Tinsley] showing that she, too, had given some thought to the implications of a <math>1/r</math> force-law for gravity in 1978.</li>
<li>[[DarkMatter/VeraRubin|Early interactions with Vera Rubin]].</li>
<li>[[DarkMatter/UniformSphere|Attraction associated with a uniform-density sphere]] &#8212; my derivation in the early '80s, with the kind assistance of LSU Professor Attipat K. Rajagopal.</li>
<li>[[DarkMatter/CK2015|Remarks on Christodoulou &amp; Kazanas (2015)]].</li>
<li>[[Appendix/Ramblings/StrongNuclearForce|Radial Dependence of the Strong Nuclear Force]]</li>
</ul>

[<font color="red">Joel E. Tohline on 24 October 2022</font>] Today I stumbled on the following interesting paper:
<ul>
  <li>
[https://www.raa-journal.org/issues/all/2014/v14n10/202203/P020220325476789616599.pdf C. Lu, Z.-W. Li, S.-F. Yuan, Z. Wan, S.-H. Qin, K. Zhu, &amp; Y. Xie (2014), Research in Astronomy and Astrophysics, Vol. 14, No. 10, pp. 1301 - 1306]: &nbsp; ''Preliminary Limits on a Logarithmic Correction to the Newtonian Gravitational Potential in Binary Pulsars''.  They "estimate the upper limit of the <b>Tohline-Kuhn-Kruglyak</b> parameter &lambda; &hellip;"  They, in turn, refer to the following &hellip;
    <ul>
      <li>[https://ui.adsabs.harvard.edu/abs/1977AN....298...65M/abstract J. P. M&uuml;cket &amp; H.-J. Treder (1977, Astronomische Nachrichten, Vol. 298, Issue 2, p. 65)] <-- First to consider ''The Perihelion Advance according to a Post-Newtonian Gravitational Law with Logarithmic Correction Term'' in the context of planets.</li>
      <li>[https://ui.adsabs.harvard.edu/abs/2012PhR...513....1C/abstract T. Clifton, P. G. Ferreira, A. Padilla, &amp; C. Skordis (2012, Physics Reports, Vol. 513, Issue 1, pp. 1 - 189)] <-- recent review titled, ''Modified Gravity and Cosmology''.</li>
    </ul>
  </li>
</ul>