Editing DarkMatter/VeraRubin (section)

===Princeton IAS===
[[File:Rood1983postcard combined.png|right|thumb|150px|Postcard from Herbert Rood (1983)]]Also, in late May of 1983, I received a postcard requesting reprints of my work from Dr. Herbert Rood (Princeton's Institute for Advanced Study).  The letter that I wrote to him in response (dated 3 June 1983) contains the following text:
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<font color="purple">"Dear Herbert: &nbsp;Your recent request for reprints of my work on the non-Newtonian Force Law came as a bit of a shock.  I was, until then, unaware that Vera had mentioned my work in her article &#8212; in fact, that issue of ''Scientific American'' only arrived to subscribers here at LSU the day that your request for reprints appeared in my mailbox."</font>
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Shortly thereafter I received a letter (dated 17 June 1983) from Dr. [https://en.wikipedia.org/wiki/John_N._Bahcall John N. Bahcall] (also, Princeton's IAS) that began as follows &hellip;
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<font color="darkgreen">"Dear Joel: &nbsp; Herb Rood showed me an abstract that you had written in which you consider some of the Solar system consequences of modifying the Newtonian force law."</font>
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-- John N. Bahcall
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Bahcall then asked whether or not I had considered how the standard mathematical expression of the virial theorem would be generalized in the context of my proposed non-Newtonian gravitational attraction.  He derived what he considered to be the appropriate additional term that would be required, then applied the result to the case of "rich clusters" of galaxies.  His conclusion was that my proposed modification of Newton's Law <font color="darkgreen">"&hellip; would overestimate the missing mass [in rich clusters] by a factor of 30"</font> relative to what is observed.  His reference regarding the relevant observational measurements was [https://en.wikipedia.org/wiki/Neta_Bahcall Neta Bahcall's] article in [https://www.annualreviews.org/doi/10.1146/annurev.aa.15.090177.002445 Annual Review of Astronomy and Astrophysics (1977, Vol. 15, pp. 505 - 540)].

I wrote back to John Bahcall, stating that I agreed with his derived correction to the virial theorem but that my interpretation of the published observational results &#8212; as found for example in Neta Bahcall's review article &#8212; was different from his.  It looked to me as though the modified virial theorem expression nicely explains the mass-to-light ratio measurements in rich clusters.  After studying my response, Dr. Bahcall wrote back:
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<font color="darkgreen">"&hellip; Thank you for your interesting letter on the r<sup>-1</sup> force.  You are indeed right that the mass to light ratio is typically 300 for rich clusters (I misquoted Neta's article).  Thus there is no inconsistency with the virial equation I derived, provided one takes [a scale length] a &sim; 10 kpc &hellip; Very intriguing."</font>
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-- John N. Bahcall
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Over the subsequent couple of decades, John and Neta Bahcall visited LSU several times.  As it turns out, John had graduated from high school in Shreveport, Louisiana, and he had a brother who lived in Baton Rouge.