<div dir="ltr"><span style="color:rgb(80,0,80);font-size:12.8px">Hello Carl.</span><div><font color="#500050"><span style="font-size:12.8px"><br></span></font></div><div><span style="font-size:12.8px">

<span style="color:rgb(80,0,80);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Your remarks about the Lagrangian points are interesting.<br></span>

<br class="gmail-m_2957806811975009105gmail-Apple-interchange-newline"><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">In fact Tufail Ab</span><font color="#000000"><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">bas</span><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"> </span><font style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">and I tried to connect the concept of Lagrangian point with "a-sol".  </font></font><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">This a-sol is nothing but  </span><font color="#00ff00" style="color:rgb(80,0,80);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">proposed</font><span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"> </span><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">as most probabilistic orbit in our solar system at a Radial Distance of about 8,8+11 meter away from the sun, which is analogous to Bohr Orbit of Hydrogen Atom. 

<span style="color:rgb(34,34,34);font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">That is also the Distan</span><font color="#000000"><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">ce to the Sun </span><font style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">that fall<span> </span></font><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">between</span><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"> </span><font style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">Jupiter and Saturn</font><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">.</span>  

<span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">However, yet we could not calculate to find any connection between "Lagrangian" and "a-sol Distance".</span></font></span></span></div><div><font color="#000000" style="font-size:12.8px"><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">

</span>

<span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">Our paper  (</span><a href="https://drive.google.com/open?id=1Ro3PuiVIZGB2KXMjWsuB2S4BqYosfjWE" style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255)" target="_blank">Wave function of solar system</a><span style="font-family:arial,sans-serif;font-size:12.8px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"> </span></font><span style="text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline"><font color="#000000" style="font-family:arial,sans-serif;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-style:normal;font-size:12.8px">) mentions this Distance in equation 2.3.</font><br>

<span style="font-family:arial,sans-serif;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-style:normal;font-size:12.8px;color:rgb(34,34,34);text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">We stated:</span>

<br>

<font color="#0000ff" style="font-family:arial,sans-serif;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px"><i><span style="font-size:12.8px;font-family:arial,sans-serif;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">" </span><span id="gmail-m_2957806811975009105gmail-m_-5233118774843731186gmail-m_-7764718197052524576m_1144433829443188617m_2249526239956194123m_7610173625816147063gmail-docs-internal-guid-301c6dd2-b93d-09de-5469-3878dc44e191" style="font-size:12.8px;font-family:arial,sans-serif;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><p dir="ltr" style="line-height:1.2;margin-top:0pt;margin-bottom:0pt;display:inline"><span style="font-family:"Times New Roman";font-size:12pt;vertical-align:baseline;white-space:pre-wrap;background-color:transparent">Bohr radius of Hydrogen is the most probabilistic radius of the electron, derived by formula </span><span style="font-family:"Times New Roman";font-size:12pt;font-weight:700;vertical-align:baseline;white-space:pre-wrap;background-color:transparent">a</span><span style="font-family:"Times New Roman";font-size:7.2pt;font-weight:700;vertical-align:sub;white-space:pre-wrap;background-color:transparent">0 </span><span style="font-family:"Times New Roman";font-size:12pt;font-weight:700;vertical-align:baseline;white-space:pre-wrap;background-color:transparent">= r</span><span style="font-family:"Times New Roman";font-size:7.2pt;font-weight:700;vertical-align:sub;white-space:pre-wrap;background-color:transparent">e</span><span style="font-family:"Times New Roman";font-size:12pt;font-weight:700;vertical-align:baseline;white-space:pre-wrap;background-color:transparent">/α</span><span style="font-family:"Times New Roman";font-size:7.2pt;font-weight:700;vertical-align:super;white-space:pre-wrap;background-color:transparent">2 </span><span style="font-family:"Times New Roman";font-size:12pt;font-weight:700;vertical-align:baseline;white-space:pre-wrap;background-color:transparent">.</span><span style="font-family:"Times New Roman";font-size:12pt;vertical-align:baseline;white-space:pre-wrap;background-color:transparent"> Using the same definition we shall define </span><span style="font-family:"Times New Roman";font-size:12pt;font-weight:700;vertical-align:baseline;white-space:pre-wrap;background-color:transparent">a</span><span style="font-family:"Times New Roman";font-size:7.2pt;font-weight:700;vertical-align:sub;white-space:pre-wrap;background-color:transparent">sol</span><span style="font-family:"Times New Roman";font-size:12pt;vertical-align:baseline;white-space:pre-wrap;background-color:transparent"> as per equation 2.3."</span></p></span>

</i></font><br>

<span style="font-family:arial,sans-serif;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-style:normal;font-size:12.8px;color:rgb(34,34,34);text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;float:none;display:inline">In Appendix C you find the value for the Radial Distance a</span><font size="1" style="font-family:arial,sans-serif;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-style:normal;color:rgb(34,34,34);text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial">sol</font><font style="font-family:arial,sans-serif;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-style:normal;color:rgb(34,34,34);text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;font-size:12.8px">  <span id="gmail-m_2957806811975009105gmail-m_-5233118774843731186gmail-m_-7764718197052524576m_1144433829443188617m_2249526239956194123m_7610173625816147063gmail-docs-internal-guid-301c6dd2-b947-42e8-9c9b-e2e44b5a9672" style="font-size:small"><div dir="ltr" style="display:inline"><span style="font-size:12.8px">(8.803E+11 meter) </span></div></span><br>

</font><br>

<span id="gmail-m_2957806811975009105gmail-m_-5233118774843731186gmail-m_-7764718197052524576m_1144433829443188617m_2249526239956194123m_7610173625816147063gmail-docs-internal-guid-301c6dd2-b947-42e8-9c9b-e2e44b5a9672" style="text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><div dir="ltr" style="font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;color:rgb(34,34,34)"><font face="arial, helvetica, sans-serif" style="">At this distance (8.803E+11 meter) away from the Sun  the Root Mean Square Velocity (VRMS) is exactly 12278 meter per second. Jupiter is orbiting at a velocity of about 13100 meter per second. The Lagrangian Point L2 from Jupiter has an orbiting  velocity of 12624 meter per second at a Radial Distance of: 8.32E+11 meter (derived from GM equals v^2 * Radial Distance).</font></div><div dir="ltr" style="font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;color:rgb(34,34,34)"><font face="arial, helvetica, sans-serif"><br></font></div><div><font face="arial, helvetica, sans-serif"><span style="font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px">If you are interested, you can find our calculations about the Lagrangian points at: </span><a href="https://drive.google.com/open?id=1Bjlqmzuiqx426egdh1yAXdYjBDaMcrcGh464Db_9_AU" target="_blank" style="font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;color:rgb(34,34,34)">https://drive.google.com/<wbr>open?id=<wbr>1Bjlqmzuiqx426egdh1yAXdYjBDaMc<wbr>rcGh464Db_9_AU </a><br>

</font><span style="text-align:start;text-indent:0px;background-color:rgb(255,255,255)"><font size="2"><font style=""><div class="gmail_quote" style=""><div dir="ltr" style=""><div style="font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px"><font color="#000000" face="arial, helvetica, sans-serif">Down Under the calculations you will find two graphs that express the relation between the Distance of the planet to the Sun with the Orbital Speed of the planet. In the graph you can see, that the 12278 point is the lowest point near the edge (it depends on how you stretch the image)</font></div><div style=""><font color="#000000" style=""><font style="font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px" face="arial, helvetica, sans-serif">I wonder: Is the Distance at L2 point of Jupiter the point that is the best possibility for mass to "hang on" in orbit around the sun?</font><br><br><font face="arial, sans-serif" size="3" style="font-family:arial,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px"><img src="cid:ii_jfwr72p61_162babe391d54f43" width="500" height="500" style="margin-right: 0px;"></font><br><br><a href="https://www.integrandoconhecimento.com/single-post/2016/07/13/%C3%89-assim-que-J%C3%BApiter-protege-a-Terra-contra-aster%C3%B3ides" style="font-family:Arial">https://www.integrandoconhecimento.com/single-post/2016/07/13/%C3%89-assim-que-J%C3%BApiter-protege-a-Terra-contra-aster%C3%B3ides</a><br></font></div></div></div></font></font></span>

<br>

<b id="gmail-m_2957806811975009105gmail-m_-5233118774843731186gmail-m_-7764718197052524576m_1144433829443188617m_2249526239956194123m_7610173625816147063gmail-docs-internal-guid-301c6dd2-b947-42e8-9c9b-e2e44b5a9672" style="font-family:arial,sans-serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-transform:none;white-space:normal;word-spacing:0px;font-size:12.8px;color:rgb(34,34,34);text-align:start;text-indent:0px;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial"><div><br></div><div>Best regards.</div><div>Ruud Loeffen.</div></b></div></span></span></div><div class="gmail_extra"><br><div class="gmail_quote">On Mon, Apr 9, 2018 at 5:06 AM,  <span dir="ltr"><<a href="mailto:cj@mb-soft.com" target="_blank">cj@mb-soft.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><u></u>





<div bgcolor="#ffffff">
<div><font size="2" face="Arial">I might have an idea for you guys.  About two 
hundred years ago, Laplace and Lagrange worked out the gravitational 
consequences of Newton's laws of gravitation.  It's really interesting 
stuff.  That was all "simple" (Euclidean) calculus, and one of the 
consequences that they figured out the Lagrange L4 and L5 points, both for 
Jupiter and for the Earth.  A company is even discussing building a HOTEL 
at the Earth's L4 point.</font></div>
<div><font size="2" face="Arial"></font> </div>
<div><font size="2" face="Arial">In any case, I think that if you duplicate the 
math of Lagrange and LaPlace, your understanding of gravitation may 
grow.</font></div>
<div><font size="2" face="Arial"></font> </div>
<div><font size="2" face="Arial">Further, there are some more advanced gravitational 
effects at both L4 and at L5, where the objects there follow very peculiar 
Lissajous orbits (in three dimensions).  I believe that math requires 
Riemannian Calculus to predict the orbits.  The Jupiter Trojans also move 
around in Lissajous orbits around each other.</font></div>
<div><font size="2" face="Arial"></font> </div>
<div><font size="2" face="Arial">In any case, I think these objects might provide 
for you a more thorough math of the gravitation.  Many years ago, I 
duplicated much of Lagrange's Calculus (all simplly based on Newton's equations) 
and I think I learned a lot from that "homework".  As of yet, I have not 
tried to do the math regarding the Lissajous orbits.</font></div>
<div><font size="2" face="Arial"></font> </div>
<div><font size="2" face="Arial">The Jupiter Trojans include thousands of asteroids 
in both groups.  Their Lissajous orbits are really complex, where they 
rarely hit each other, even in such tight orbits.  I don't think anybody 
knows yet WHY they don't collide more.  The Earth Trojans are pretty rare, 
mostly in our L4 and I think that only a couple small objects have been found in 
our L5 as of yet.</font></div><span class="gmail-m_2957806811975009105gmail-HOEnZb"><font color="#888888">
<div><font size="2" face="Arial"></font> </div>
<div><font size="2" face="Arial">Carl Johnson</font></div>
<div><span style="color:rgb(34,34,34)">______________________________</span><span style="color:rgb(34,34,34)"><wbr>_________________</span><br><font size="2" face="Arial"></font></div></font></span></div>
Physics mailing list<br>
<a href="mailto:Physics@tuks.nl" target="_blank">Physics@tuks.nl</a><br>
<a href="http://mail.tuks.nl/cgi-bin/mailman/listinfo/physics" rel="noreferrer" target="_blank">http://mail.tuks.nl/cgi-bin/ma<wbr>ilman/listinfo/physics</a><br>
<br></blockquote></div><br><div class="gmail-m_2957806811975009105gmail_signature"><div dir="ltr"><div><div dir="ltr"><div><br></div></div></div></div></div>
</div></div>