https://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&feed=atom&action=historyUser:Tohline/DarkMatter/VeraRubin - Revision history2024-03-28T18:40:12ZRevision history for this page on the wikiMediaWiki 1.36.2https://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22180&oldid=prevTohline: /* Princeton IAS */2021-07-02T21:13:21Z<p><span dir="auto"><span class="autocomment">Princeton IAS</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Princeton IAS===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Princeton IAS===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Also in <del style="font-weight: bold; text-decoration: none;">early June </del>of 1983, I received a <del style="font-weight: bold; text-decoration: none;">request for </del>reprints of my work from Dr. Herbert Rood (Princeton's Institute for Advanced Study). <del style="font-weight: bold; text-decoration: none;">I do not now have a copy of his request, but the </del>letter that I wrote to him in response (dated 3 June 1983) contains the following text:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[File:Rood1983postcard combined.png|right|thumb|150px|Postcard from Herbert Rood (1983)]]</ins>Also<ins style="font-weight: bold; text-decoration: none;">, </ins>in <ins style="font-weight: bold; text-decoration: none;">late May </ins>of 1983, I received a <ins style="font-weight: bold; text-decoration: none;">postcard requesting </ins>reprints of my work from Dr. Herbert Rood (Princeton's Institute for Advanced Study). <ins style="font-weight: bold; text-decoration: none;">The </ins>letter that I wrote to him in response (dated 3 June 1983) contains the following text:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22177&oldid=prevTohline: /* Early Interactions with Vera Rubin */2021-06-29T18:51:42Z<p><span dir="auto"><span class="autocomment">Early Interactions with Vera Rubin</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Early Interactions with Vera Rubin=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Early Interactions with Vera Rubin=</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><font color="red">Note from Joel E. Tohline:</font>&nbsp; <del style="font-weight: bold; text-decoration: none;">Whether </del>she knew it <del style="font-weight: bold; text-decoration: none;">or not</del>, [https://en.wikipedia.org/wiki/Vera_Rubin Dr. Vera C. Rubin] was a significant influence on my astronomy career. What follows are some highlights of my early professional interactions with her.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><font color="red">Note from Joel E. Tohline:</font>&nbsp; <ins style="font-weight: bold; text-decoration: none;">I doubt that </ins>she knew it, <ins style="font-weight: bold; text-decoration: none;">but </ins>[https://en.wikipedia.org/wiki/Vera_Rubin Dr. Vera C. Rubin] was a significant influence on my astronomy career. What follows are some highlights of my early professional interactions with her.</div></td></tr>
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</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22176&oldid=prevTohline: /* Early Interactions with Vera Rubin */2021-06-29T18:49:58Z<p><span dir="auto"><span class="autocomment">Early Interactions with Vera Rubin</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Early Interactions with Vera Rubin=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Early Interactions with Vera Rubin=</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><font color="red">Note from Joel E. Tohline:</font>&nbsp; Whether she knew it or not, [https://en.wikipedia.org/wiki/Vera_Rubin Dr. Vera C. Rubin] was a significant influence on my <del style="font-weight: bold; text-decoration: none;">early </del>astronomy career. What follows are some highlights of my early professional interactions with her.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><font color="red">Note from Joel E. Tohline:</font>&nbsp; Whether she knew it or not, [https://en.wikipedia.org/wiki/Vera_Rubin Dr. Vera C. Rubin] was a significant influence on my astronomy career. What follows are some highlights of my early professional interactions with her.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
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</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22175&oldid=prevTohline: /* Exchange of Letters with Jim Felten (1984) … and Beyond */2021-06-28T23:01:11Z<p><span dir="auto"><span class="autocomment">Exchange of Letters with Jim Felten (1984) … and Beyond</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the spring of 1985, I received a package of documents from Dr. Michael Disney (Cardiff, Wales). In addition to a wonderfully worded cover letter, the package contained a couple of thick draft articles in which he explored in a number of different directions what the implications would be of a modification to Newton's Law of the type I was proposing. He had not previously seen my work on this topic, but his thoughts were so in tune with my own that I was sure he had read my mind! It was wonderful to have heard from such a kindred spirit; his (draft) writings were like poetry, to me. Toward the end of the decade, at the invitation of Mike Disney and his astronomy colleagues at University College, Cardiff, I spent ten very enjoyable and intellectually stimulating days visiting Wales.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the spring of 1985, I received a package of documents from Dr. <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/Mike_Disney </ins>Michael Disney<ins style="font-weight: bold; text-decoration: none;">] </ins>(Cardiff, Wales). In addition to a wonderfully worded cover letter, the package contained a couple of thick draft articles in which he explored in a number of different directions what the implications would be of a modification to Newton's Law of the type I was proposing. He had not previously seen my work on this topic, but his thoughts were so in tune with my own that I was sure he had read my mind! It was wonderful to have heard from such a kindred spirit; his (draft) writings were like poetry, to me. Toward the end of the decade, at the invitation of Mike Disney and his astronomy colleagues at University College, Cardiff, I spent ten very enjoyable and intellectually stimulating days visiting Wales.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <li></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In early 1986, Jeff Kuhn (Princeton, at the time) sent me a preprint of the paper he had written in collaboration with Kruglyak; he had heard of my work from Milgrom. A brief exchange of letters followed. An acknowledgement of my effort to examine the stability of cold stellar disks appears in their published paper [https://ui.adsabs.harvard.edu/abs/1987ApJ...313....1K/abstract (ApJ, 313, 1)].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In early 1986, <ins style="font-weight: bold; text-decoration: none;">[https://www.ifa.hawaii.edu/users/kuhn/kuhn2.html </ins>Jeff Kuhn<ins style="font-weight: bold; text-decoration: none;">] </ins>(Princeton, at the time) sent me a preprint of the paper he had written in collaboration with Kruglyak; he had heard of my work from Milgrom. A brief exchange of letters followed. An acknowledgement of my effort to examine the stability of cold stellar disks appears in their published paper [https://ui.adsabs.harvard.edu/abs/1987ApJ...313....1K/abstract (ApJ, 313, 1)].</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </li></div></td></tr>
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</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22174&oldid=prevTohline: /* Princeton IAS */2021-06-28T22:54:34Z<p><span dir="auto"><span class="autocomment">Princeton IAS</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></td></tr></table></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></td></tr></table></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Shortly thereafter I received a letter (dated 17 June 1983) from Dr. John N. Bahcall (also, Princeton's IAS) that began as follows &hellip;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Shortly thereafter I received a letter (dated 17 June 1983) from Dr. <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/John_N._Bahcall </ins>John N. Bahcall<ins style="font-weight: bold; text-decoration: none;">] </ins>(also, Princeton's IAS) that began as follows &hellip;</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>-- John N. Bahcall</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>-- John N. Bahcall</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></td></tr></table></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></td></tr></table></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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://www.annualreviews.org/doi/10.1146/annurev.aa.15.090177.002445 <del style="font-weight: bold; text-decoration: none;">Neta Bahcall's article in </del>Annual Review of Astronomy and Astrophysics (1977, Vol. 15, pp. 505 - 540)].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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 <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/Neta_Bahcall Neta Bahcall's] article in </ins>[https://www.annualreviews.org/doi/10.1146/annurev.aa.15.090177.002445 Annual Review of Astronomy and Astrophysics (1977, Vol. 15, pp. 505 - 540)].</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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:</div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22173&oldid=prevTohline: /* Primack at UC, Santa Cruz */2021-06-28T22:45:28Z<p><span dir="auto"><span class="autocomment">Primack at UC, Santa Cruz</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Primack at UC, Santa Cruz===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Primack at UC, Santa Cruz===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>That same month (June 1983) I received a (hand-written) letter from Dr. Joel Primack (a physicist at UC, Santa Cruz) containing the following text:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>That same month (June 1983) I received a (hand-written) letter from Dr. <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/Joel_Primack </ins>Joel Primack<ins style="font-weight: bold; text-decoration: none;">] </ins>(a physicist at UC, Santa Cruz) containing the following text:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><font color="darkgreen">"I'm working on a review of dark matter for Annual Reviews (with Sandy Faber, George Blumenthal and Doug Lin) and would very much appreciate it if you would send me a copy of your paper on gravity weakening with distance as an explanation of constant rotation curves, referred to in <b>Vera Rubin's recent ''Scientific American'' article</b>&hellip; Please also send a copy to George Blumenthal at UC Santa Cruz. Thanks very much!"</font></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><font color="darkgreen">"I'm working on a review of dark matter for Annual Reviews (with Sandy Faber, George Blumenthal and Doug Lin) and would very much appreciate it if you would send me a copy of your paper on gravity weakening with distance as an explanation of constant rotation curves, referred to in <b>Vera Rubin's recent ''Scientific American'' article</b>&hellip; Please also send a copy to George Blumenthal at UC Santa Cruz. Thanks very much!"</font></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>-- Joel Primack</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>-- Joel Primack</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></td></tr></table></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></td></tr></table></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Receiving this request from Joel Primack was exciting for me on two fronts: (1) Having my work cited in a high-quality review article would significantly enhance its visibility. (2) I had only recently (1978) earned my doctoral degree in astronomy from UC, Santa Cruz and had completed courses taught by both Sandy Faber and George Blumenthal, so I knew them well and was happy to hear that they had become aware of research endeavors that I was pursuing beyond the focus of my dissertation research.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Receiving this request from Joel Primack was exciting for me on two fronts: (1) Having my work cited in a high-quality review article would significantly enhance its visibility. (2) I had only recently (1978) earned my doctoral degree in astronomy from UC, Santa Cruz and had completed courses taught by both <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/Sandra_Faber </ins>Sandy Faber<ins style="font-weight: bold; text-decoration: none;">] </ins>and <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/George_Blumenthal </ins>George Blumenthal<ins style="font-weight: bold; text-decoration: none;">]</ins>, so I knew them well and was happy to hear that they had become aware of research endeavors that I was pursuing beyond the focus of my dissertation research.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Princeton IAS===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Princeton IAS===</div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22172&oldid=prevTohline: /* Neighborhood Meeting at Yale University (1979) */2021-06-28T22:39:41Z<p><span dir="auto"><span class="autocomment">Neighborhood Meeting at Yale University (1979)</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div align="center">'''Rotation:''' The Dynamical Structure of Galaxies<br />''(A Neighborhood Meeting at Yale University)''<br />Dates: 23 - 24 March 1979</div></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div align="center">'''Rotation:''' The Dynamical Structure of Galaxies<br />''(A Neighborhood Meeting at Yale University)''<br />Dates: 23 - 24 March 1979</div></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Dr. [https://en.wikipedia.org/wiki/Vera_Rubin Vera Rubin] agreed to be our opening speaker. It was an opportunity for the (> 90) attendees to hear and see &#8212; first hand from the expert &#8212; how significant the evidence was for flat rotation curves. Five speakers followed: Dr. [https://en.wikipedia.org/wiki/Jeremiah_P._Ostriker Jeremiah Ostriker] (Princeton), Dr. [https://en.wikipedia.org/wiki/Alar_Toomre Alar Toomre] (MIT), Dr. Kevin Prendergast (Columbia University), Dr. Paul Schechter (Harvard-Smithsonian CfA), and Dr. Richard Miller (Chicago).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Dr. [https://en.wikipedia.org/wiki/Vera_Rubin Vera Rubin] agreed to be our opening speaker. It was an opportunity for the (> 90) attendees to hear and see &#8212; first hand from the expert &#8212; how significant the evidence was for flat rotation curves. Five speakers followed: Dr. [https://en.wikipedia.org/wiki/Jeremiah_P._Ostriker Jeremiah Ostriker] (Princeton), Dr. [https://en.wikipedia.org/wiki/Alar_Toomre Alar Toomre] (MIT), Dr. <ins style="font-weight: bold; text-decoration: none;">[https://ui.adsabs.harvard.edu/abs/2005BAAS...37.1555S/abstract </ins>Kevin Prendergast<ins style="font-weight: bold; text-decoration: none;">] </ins>(Columbia University), Dr. <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/Paul_L._Schechter </ins>Paul Schechter<ins style="font-weight: bold; text-decoration: none;">] </ins>(Harvard-Smithsonian CfA), and Dr. <ins style="font-weight: bold; text-decoration: none;">[https://physicalsciences.uchicago.edu/news/article/richard-miller-obituary/ </ins>Richard Miller<ins style="font-weight: bold; text-decoration: none;">] </ins>(Chicago).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Tohline Visits CIW:DTM (1980)==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Tohline Visits CIW:DTM (1980)==</div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22171&oldid=prevTohline: /* Neighborhood Meeting at Yale University (1979) */2021-06-28T22:31:26Z<p><span dir="auto"><span class="autocomment">Neighborhood Meeting at Yale University (1979)</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div align="center">'''Rotation:''' The Dynamical Structure of Galaxies<br />''(A Neighborhood Meeting at Yale University)''<br />Dates: 23 - 24 March 1979</div></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><div align="center">'''Rotation:''' The Dynamical Structure of Galaxies<br />''(A Neighborhood Meeting at Yale University)''<br />Dates: 23 - 24 March 1979</div></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Dr. Vera Rubin agreed to be our opening speaker. It was an opportunity for the (> 90) attendees to hear and see &#8212; first hand from the expert &#8212; how significant the evidence was for flat rotation curves. Five speakers followed: Dr. Jeremiah Ostriker (Princeton), Dr. Alar Toomre (MIT), Dr. Kevin Prendergast (Columbia University), Dr. Paul Schechter (Harvard-Smithsonian CfA), and Dr. Richard Miller (Chicago).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Dr. <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/Vera_Rubin </ins>Vera Rubin<ins style="font-weight: bold; text-decoration: none;">] </ins>agreed to be our opening speaker. It was an opportunity for the (> 90) attendees to hear and see &#8212; first hand from the expert &#8212; how significant the evidence was for flat rotation curves. Five speakers followed: Dr. <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/Jeremiah_P._Ostriker </ins>Jeremiah Ostriker<ins style="font-weight: bold; text-decoration: none;">] </ins>(Princeton), Dr. <ins style="font-weight: bold; text-decoration: none;">[https://en.wikipedia.org/wiki/Alar_Toomre </ins>Alar Toomre<ins style="font-weight: bold; text-decoration: none;">] </ins>(MIT), Dr. Kevin Prendergast (Columbia University), Dr. Paul Schechter (Harvard-Smithsonian CfA), and Dr. Richard Miller (Chicago).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Tohline Visits CIW:DTM (1980)==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Tohline Visits CIW:DTM (1980)==</div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22170&oldid=prevTohline: /* Princeton IAS */2021-06-28T22:25:41Z<p><span dir="auto"><span class="autocomment">Princeton IAS</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>-- John N. Bahcall</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>-- John N. Bahcall</div></td></tr>
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<tr><td colspan="2"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">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.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Exchange of Letters with Jim Felten (1984) &hellip; and Beyond==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Exchange of Letters with Jim Felten (1984) &hellip; and Beyond==</div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/DarkMatter/VeraRubin&diff=22169&oldid=prevTohline: /* Princeton IAS */2021-06-28T22:21:11Z<p><span dir="auto"><span class="autocomment">Princeton IAS</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:21, 28 June 2021</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td></tr>
<tr><td colspan="2"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></td></tr></ins></div></td></tr>
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<tr><td colspan="2"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">-- John N. Bahcall</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></td></tr></table></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></td></tr></table></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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://www.annualreviews.org/doi/10.1146/annurev.aa.15.090177.002445 Neta Bahcall's article in Annual Review of Astronomy and Astrophysics (1977, Vol. 15, pp. 505 - 540)].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>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://www.annualreviews.org/doi/10.1146/annurev.aa.15.090177.002445 Neta Bahcall's article in Annual Review of Astronomy and Astrophysics (1977, Vol. 15, pp. 505 - 540)].</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><table border="0" align="center" width="60%"><tr><td align="left"></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><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></div></td></tr>
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</table>Tohline