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v:ext="edit" data="1"/> </o:shapelayout></xml><![endif]--> </head> <body lang=RU link=blue vlink=purple style='tab-interval:35.4pt'> <div class=WordSection1> <h1 style='margin:0cm;margin-bottom:.0001pt;mso-add-space:auto'><span style='font-size:11.0pt;color:black;font-weight:normal'><a href="http://sergf.ru/hs.htm"><span style='color:purple'>0</span><span class=apple-converted-space><span style='color:purple;mso-ansi-language:EN-GB'> </span></span><span style='color:purple'>@CAA:><</span><span class=apple-converted-space><span style='color:purple;mso-ansi-language:EN-GB'> </span></span><span style='color:purple'>O7K:5</span></a></span><span lang=EN-GB style='font-size:11.0pt;color:black;mso-ansi-language:EN-GB; font-weight:normal'><o:p></o:p></span></h1> <h1 style='margin:0cm;margin-bottom:.0001pt;mso-add-space:auto'><span lang=EN-GB style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-GB'><o:p>&nbsp;</o:p></span></h1> <h1><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'>Characteristic speed<o:p></o:p></span></h1> <div id=bodyContent> <div id=siteSub> <p class=MsoNormal><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'><a href="https://en.wikiversity.org/wiki/Characteristic_speed">From <span class=SpellE>Wikiversity</span></a><o:p></o:p></span></p> </div> <div id=mw-content-text> <p><b><span lang=EN style='mso-ansi-language:EN'>Characteristic speed</span></b><span lang=EN style='mso-ansi-language:EN'> is a physical quantity characterizing the average speed of motion of the particles inside a single body or a particle system at rest. The ratio of the characteristic speeds of similar objects allows us to find the coefficient of similarity in speeds between different levels of matter in <a href="http://sergf.ru/bvmen.htm">Infinite Hierarchical Nesting of Matter</a>.</span><span lang=EN style='mso-ascii-font-family:"Times New Roman"; mso-ascii-theme-font:major-bidi;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-hansi-font-family:"Times New Roman";mso-hansi-theme-font:major-bidi; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi; mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:HE'> </span><span lang=EN style='mso-ansi-language:EN'>For the nucleon form of matter the characteristic speed does not exceed the speed of light.<o:p></o:p></span></p> <div id=toc> <div id=toctitle> <h2><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'>Contents<o:p></o:p></span></h2> </div> <ul type=disc> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l0 level1 lfo1;tab-stops:list 36.0pt'><span class=tocnumber><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'>1</span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'> <span class=toctext>Definition</span><o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l0 level1 lfo1;tab-stops:list 36.0pt'><span class=tocnumber><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'>2</span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'> <span class=toctext>Connection with the escape velocity</span><o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l0 level1 lfo1;tab-stops:list 36.0pt'><span class=tocnumber><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'>3</span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'> <span class=toctext>Application</span><o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l0 level1 lfo1;tab-stops:list 36.0pt'><span class=tocnumber><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'>4</span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'> <span class=toctext>References</span><o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l0 level1 lfo1;tab-stops:list 36.0pt'><span class=tocnumber><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'>5</span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'> <span class=toctext>External links</span><o:p></o:p></span></li> </ul> </div> <h2 align=center style='text-align:center'><span id=Definition><span class=mw-headline><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'>Definition</span></span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN'><o:p></o:p></span></h2> <p><span lang=EN style='mso-ansi-language:EN'>The characteristic speed is estimated by the formula:</span><span lang=EN style='mso-ansi-language:EN-GB'> </span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span></span><span style='mso-no-proof:yes'><img border=0 width=99 height=51 id="_x0000_i1087" src="hsen_files/aab7b5fbd6dded96a4a2fbeb173b7577.png" alt="C_x = \sqrt { \frac {|E|}{M} },"></span><span lang=EN style='mso-ansi-language: EN'><o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>where </span><span style='mso-no-proof:yes'><img border=0 width=23 height=20 id="_x0000_i1086" src="hsen_files/cbdcf0e203060323ebcd0079f280f4b8.png" alt="|E|"></span><span style='mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'> </span></span><span lang=EN style='mso-ansi-language:EN'>denotes the absolute value of the total energy of the body (particle system), </span><span style='mso-no-proof:yes'><img border=0 width=21 height=14 id="_x0000_i1085" src="hsen_files/69691c7bdcc3ce6d5d8a1361f22d04ac.png" alt=" M "></span><span style='mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'> </span></span><span lang=EN style='mso-ansi-language:EN'>is the body mass.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>If we take into account that the mass energy equivalence is the principle of proportionality between energy and mass, then the square of the characteristic speed is the factor that connects these quantities in one formula: </span><span style='mso-no-proof:yes'><img border=0 width=99 height=23 id="_x0000_i1084" src="hsen_files/2961aea54f9f0295c90841345832f3df.png" alt=" |E| = M C^2_x ."></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>Due to its definition in terms of energy and mass, the characteristic speed can differ from the average speed of the system s particles, being found in other ways and depending on the mode of averaging.<o:p></o:p></span></p> <h2 align=center style='text-align:center'><span id="Connection_with_the_escape_velocity"><span class=mw-headline><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN'>Connection with the escape velocity</span></span></span><span lang=EN style='mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN'><o:p></o:p></span></h2> <p><span lang=EN style='mso-ansi-language:EN'>For a sufficiently large body of uniform density with the radius </span><span style='mso-no-proof:yes'><img border=0 width=15 height=14 id="_x0000_i1083" src="hsen_files/e1e1d3d40573127e9ee0480caf1283d6.png" alt=" R "></span><span lang=EN style='mso-ansi-language:EN'>, which is spherical under the action of gravitational force, the absolute value of the total energy, according to the virial theorem, is equal to the half of the absolute value of gravitational energy </span><span style='mso-no-proof:yes'><img border=0 width=30 height=21 id="_x0000_i1082" src="hsen_files/b3ca95dca0084e225e4f97a8bfb4ee52.png" alt="|E_g|"></span><span lang=EN style='mso-ansi-language:EN'>.<span style='mso-spacerun:yes'>  </span>It gives the following expression:<o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=249 height=51 id="_x0000_i1081" src="hsen_files/4170903a504f30910e1abc9f3e01d7bc.png" alt="C_x = \sqrt { \frac {|E_g |}{2M} }= \sqrt { \frac {k G M }{2R} }, \quad (1) "></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'><o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>where </span><span style='mso-no-proof:yes'><img border=0 width=14 height=14 id="_x0000_i1080" src="hsen_files/dfcf28d0734569a6a693bc8194de62bf.png" alt=" G "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>is the <a href="http://sergf.ru/gpoen.htm">gravitational constant</a>, </span><span style='mso-no-proof:yes'><img border=0 width=60 height=14 id="_x0000_i1079" src="hsen_files/73ab0929339204273405deaa580e173b.png" alt=" k=0.6 "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>for a uniform ball and increases when the density at the center of the ball is greater than the average density.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>Let us consider now the process, in which the matter from infinity with zero initial speed is transferred into some space region and is superimposed on each other, so that in the end the ball under consideration is formed. Suppose </span><span style='mso-no-proof: yes'><img border=0 width=9 height=9 id="_x0000_i1078" src="hsen_files/c030b67be5c19d838f2c01d54ef53e07.png" alt="~ r "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>is the current radius of the ball in its growth, </span><span style='mso-no-proof: yes'><img border=0 width=131 height=43 id="_x0000_i1077" src="hsen_files/41e7bc0a04841a7c94b631266fdd5aa5.png" alt=" M(r) = \frac {4 \pi \rho_0 r^3 }{3} "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>is the mass of the growing ball as a function of the current radius, </span><span style='mso-no-proof:yes'><img border=0 width=17 height=13 id="_x0000_i1076" src="hsen_files/d4278ba0b22eefeee3dfd3e7d5212720.png" alt=" ~\rho_0 "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>is the mass density. The work </span><span style='mso-no-proof:yes'><img border=0 width=25 height=14 id="_x0000_i1075" src="hsen_files/d52c8bd4eac4151115c9c335b9d8c96d.png" alt="~ dA "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>done on the transfer of the layer with the mass </span><span style='mso-no-proof:yes'><img border=0 width=133 height=22 id="_x0000_i1074" src="hsen_files/6295e051e92799117020f4c988521d46.png" alt=" ~d M = 4 \pi \rho_0 r^2 dr "></span><span lang=EN-GB style='mso-ansi-language: EN-GB'><span style='mso-spacerun:yes'>  </span></span><span lang=EN style='mso-ansi-language:EN'>from infinity to the growing ball is equal to the work of the gravitational force or to the product of mass and gravitational potential of the ball s surface:<o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=502 height=44 id="_x0000_i1073" src="hsen_files/dc83a9addca0a838a5d745a6daf21866.png" alt=" dA = \frac {G M(r) dM }{r} , \quad A = \frac {16 \pi^2 G }{3} \int_{0}^{R} \rho_0^2 r^4 \, dr = \frac {k G M^2 }{R}. \quad (2) "></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'><o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>Therefore, the work </span><span style='mso-no-proof:yes'><img border=0 width=15 height=14 id="_x0000_i1072" src="hsen_files/7fc56270e7a70fa81a5935b72eacbe29.png" alt=" A "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>is equal by its absolute value to the doubled total energy </span><span style='mso-no-proof:yes'><img border=0 width=23 height=20 id="_x0000_i1071" src="hsen_files/cbdcf0e203060323ebcd0079f280f4b8.png" alt="|E|"></span><span lang=EN-GB style='mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'>  </span></span><span lang=EN style='mso-ansi-language: EN'>and the gravitational energy </span><span style='mso-no-proof:yes'><img border=0 width=30 height=21 id="_x0000_i1070" src="hsen_files/b3ca95dca0084e225e4f97a8bfb4ee52.png" alt="|E_g|"></span><span lang=EN style='mso-ansi-language:EN'>,<span style='mso-spacerun:yes'>  </span>so that the characteristic speed equals: </span><span style='mso-no-proof: yes'><img border=0 width=104 height=51 id="_x0000_i1069" src="hsen_files/b90a40a813b33a7f50afcef4b0c83a54.png" alt="C_x = \sqrt { \frac { A }{ 2M }} ."></span><span lang=EN-GB style='mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'>  </span></span><span lang=EN style='mso-ansi-language:EN'>On the other hand, the product of the mass </span><span style='mso-no-proof:yes'><img border=0 width=31 height=14 id="_x0000_i1068" src="hsen_files/ba8bbeb315889843b03e21c8017f73db.png" alt=" d M "></span><span lang=EN-GB style='mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'>  </span></span><span lang=EN style='mso-ansi-language: EN'>and the gravitational potential is equal to the kinetic energy of falling of this mass on the ball with the current mass </span><span style='mso-no-proof: yes'><img border=0 width=44 height=21 id="_x0000_i1067" src="hsen_files/e8736f17bf6b5a38cbfe658e2a985193.png" alt=" M(r) "></span><span lang=EN style='mso-ansi-language:EN'>.<span style='mso-spacerun:yes'>  </span>This gives:<o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=479 height=44 id="_x0000_i1066" src="hsen_files/8825ee4e848497f660b3e424b6b49a3b.png" alt=" dA = \frac { dM v^2_3(r)}{2}, \quad \frac {G M(r) }{r} = \frac { v^2_3(r)}{2}, \quad A = \int_{0}^{R} \frac { v^2_3(r)}{2} \, dM. "></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'><o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>In view of (1) we also obtain:<o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=415 height=44 id="_x0000_i1065" src="hsen_files/fd44c1e4cb02dfbe2842c93b056e9ee8.png" alt="2C^2_x = \frac {k G M }{R} = \frac {A}{M}= \frac {1}{M} \int_{0}^{R} \frac { v^2_3(r)}{2} \, dM = \frac {1}{2} \overline{v^2_3(r)} ,"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'><o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span lang=EN style='mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=125 height=41 id="_x0000_i1064" src="hsen_files/8100d92176a7cdb0237c427e3a033762.png" alt="C_x =\frac {1}{2} \sqrt {\overline{v^2_3(r)} },"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN'><o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>where </span><span style='mso-no-proof:yes'><img border=0 width=43 height=24 id="_x0000_i1063" src="hsen_files/4743c26f0d7da6d5c8f41f4c65f46adc.png" alt=" \overline{v^2_3(r)} "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>indicates the averaged over the ball s volume square of the speed. We will take into account now that the speed </span><span style='mso-no-proof:yes'><img border=0 width=40 height=21 id="_x0000_i1062" src="hsen_files/66728048a77b2982a8fb1f708a4c0dfe.png" alt=" ~v_3(r) "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>actually is the third escape velocity, required to remove some mass to infinity from the surface of the ball with the current radius </span><span style='mso-no-proof:yes'><img border=0 width=9 height=9 id="_x0000_i1061" src="hsen_files/c030b67be5c19d838f2c01d54ef53e07.png" alt="~ r "></span><span lang=EN style='mso-ansi-language:EN'>in the process of the ball s growth. Then the characteristic speed of the ball in general represents half of the square root of the mean square of the third escape velocity, averaged over the entire volume of the ball.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>The characteristic feature of the gravitational field inside the uniform ball is that the field is directed radially towards the center of the ball. Besides, at the arbitrary current radius </span><span style='mso-no-proof:yes'><img border=0 width=9 height=9 id="_x0000_i1060" src="hsen_files/c030b67be5c19d838f2c01d54ef53e07.png" alt="~ r "></span><span lang=EN style='mso-ansi-language:EN'>the field depends only on the mass inside of this radius, but not on the mass of the outer shell. Consequently, if there were no outer shell and it did not impede the motion of a test body, the gravitational acceleration of the test body would equal the centripetal acceleration, so that the body would rotate around the mass </span><span style='mso-no-proof:yes'><img border=0 width=44 height=21 id="_x0000_i1059" src="hsen_files/b3443346f81d2b5513600b39e27d37d7.png" alt="~ M(r) "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>under the action of gravitation:<o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=140 height=43 id="_x0000_i1058" src="hsen_files/72b2928e89d3dce67ef483c2dcf7b522.png" alt=" \frac{G M(r) }{r^2} = \frac{ v^2_1(r) }{r},"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN'><o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>where </span><span style='mso-no-proof:yes'><img border=0 width=40 height=21 id="_x0000_i1057" src="hsen_files/3904506cdb52ed947f1c02f5dcf13dee.png" alt="~ v_1(r) "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>is the orbital rotation speed of the test body, which is directly proportional to the radius </span><span style='mso-no-proof:yes'><img border=0 width=9 height=9 id="_x0000_i1056" src="hsen_files/c030b67be5c19d838f2c01d54ef53e07.png" alt="~ r "></span><span lang=EN style='mso-ansi-language:EN'>.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>In view of (2) we find:<o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=309 height=44 id="_x0000_i1055" src="hsen_files/52f315cc0972219066588dc7e944c0a4.png" alt=" A = \int_{0}^{R} \frac {G M(r) }{r} \, dM = \int_{0}^{R} v^2_1(r) \, dM , "></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'><o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span lang=EN style='mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=320 height=42 id="_x0000_i1054" src="hsen_files/c4e9d0249a487a781e96933bbdd7c102.png" alt="2C^2_x = \frac {A}{M}= \frac {1}{M} \int_{0}^{R} v^2_1(r) \, dM = \overline{v^2_1(r)} ,"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'><o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span lang=EN style='mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=115 height=51 id="_x0000_i1053" src="hsen_files/85869349bb028fca872ab706501b7e61.png" alt=" C_x = \sqrt {\frac {\overline{v^2_1(r)}} {2} }."></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN'><o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>The speed </span><span style='mso-no-proof:yes'><img border=0 width=40 height=21 id="_x0000_i1052" src="hsen_files/3904506cdb52ed947f1c02f5dcf13dee.png" alt="~ v_1(r) "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>in its meaning is the first escape velocity as the orbital rotation speed on the current radius </span><span style='mso-no-proof:yes'><img border=0 width=9 height=9 id="_x0000_i1051" src="hsen_files/c030b67be5c19d838f2c01d54ef53e07.png" alt="~ r "></span><span lang=EN style='mso-ansi-language:EN'>inside the ball. Then the characteristic speed </span><span style='mso-no-proof:yes'><img border=0 width=21 height=17 id="_x0000_i1050" src="hsen_files/8ecda504afcdc094c9ec327097b30e3c.png" alt="~ C_x "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>of the ball in general is the square root of the squared first escape velocity, averaged over the volume of the ball, which is divided by </span><span style='mso-no-proof:yes'><img border=0 width=26 height=21 id="_x0000_i1049" src="hsen_files/c475af0fc6a341d865339933e251aba7.png" alt=" \sqrt 2"></span><span lang=EN style='mso-ansi-language:EN'>.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>If we take into account the escape velocities only on the ball s surface with </span><span style='mso-no-proof:yes'><img border=0 width=50 height=14 id="_x0000_i1048" src="hsen_files/6d9a7cc05ce3a94f3396e39e10aecdbc.png" alt="~ r =R "></span><span lang=EN style='mso-ansi-language:EN'>,<span style='mso-spacerun:yes'>  </span>then we can write for them:<o:p></o:p></span></p> <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=399 height=50 id="_x0000_i1047" src="hsen_files/26a8a266970acc52b4f2434e4b10b3e2.png" alt=" \frac{G M }{R} = \frac { v^2_3}{2} = v^2_1 = \frac {2 C^2_x }{k} , \quad C_x = \frac {v_3\sqrt k}{2} = \frac {v_1 \sqrt k}{\sqrt 2}."></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'><o:p></o:p></span></p> <h2 align=center style='text-align:center'><span id=Application><span class=mw-headline><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'>Application</span></span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN'><o:p></o:p></span></h2> <p><span lang=EN style='mso-ansi-language:EN'>In the theory of <a href="http://sergf.ru/bvmen.htm">Infinite Hierarchical Nesting of Matter</a>, the characteristic speeds of space objects particles fall into several distinct groups, corresponding to different classes. This allows us to almost definitely refer each object to one of the known classes according to the characteristic speed of its particles.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>Partitioning of space objects into classes can be done with the help of the similarity coefficients, since between the objects there is <a href="http://sergf.ru/pumen.htm">similarity of matter levels</a>, and for the stars there is <a href="http://sergf.ru/dpsen.htm">discreteness of stellar parameters</a>. If we assume that the coefficient of similarity in velocities is equal to </span><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype><v:shape id=" 8AC=>:_x0020_83" o:spid="_x0000_i1046" type="#_x0000_t75" alt="S_0=7.338\cdot 10^{-4}" style='width:106.5pt;height:15.75pt;visibility:visible; mso-wrap-style:square'> <v:imagedata src="hsen.files/image001.png" o:title="cdot 10^{-4}"/> </v:shape><![endif]--><![if !vml]><img border=0 width=142 height=21 src="hsen.files/image001.png" alt="S_0=7.338\cdot 10^{-4}" v:shapes=" 8AC=>:_x0020_83"><![endif]></span><span lang=EN-GB style='font-size:9.0pt;font-family:"Arial",sans-serif;color:#252525; background:white;mso-ansi-language:EN-GB'>,</span><span lang=EN-GB style='mso-ansi-language:EN-GB;mso-no-proof:yes'> </span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>then at the stellar level we have seven characteristic speeds for different classes of objects: <sup id="cite_ref-1">[1]</sup><o:p></o:p></span></p> <ol start=1 type=1> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l2 level1 lfo2;tab-stops:list 36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=106 height=18 id="_x0000_i1045" src="hsen_files/97473dfc059519503259b508f9510e67.png" alt="C_1= 299792"></span><span lang=EN style='mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s.<o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l2 level1 lfo2;tab-stops:list 36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=96 height=17 id="_x0000_i1044" src="hsen_files/32ce1020a4d4d3cf525d81faac59f3af.png" alt="C_2= 70780"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s.<o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l2 level1 lfo2;tab-stops:list 36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=96 height=17 id="_x0000_i1043" src="hsen_files/e32436ecc477dec78e3eb23b543000a5.png" alt="C_3= 16710"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s.<o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l2 level1 lfo2;tab-stops:list 36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=86 height=17 id="_x0000_i1042" src="hsen_files/0ba99ad6afaea9dc6ed86dfef3050cf8.png" alt="C_4= 3945"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s.<o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l2 level1 lfo2;tab-stops:list 36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=76 height=17 id="_x0000_i1041" src="hsen_files/e218de145cccb4016c38394b0af82ee6.png" alt="C_5= 930"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s.<o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l2 level1 lfo2;tab-stops:list 36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=124 height=17 id="_x0000_i1040" src="hsen_files/81528eb276dd5608972fca438faea71b.png" alt="C_6 = C_s = 220"></span><span lang=EN style='mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s.<o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l2 level1 lfo2;tab-stops:list 36.0pt'><span style='mso-fareast-font-family: "Times New Roman";mso-no-proof:yes'><img border=0 width=66 height=17 id="_x0000_i1039" src="hsen_files/ddb5bfdc5c020f0d27f7c8a4e85b41f9.png" alt="C_7 = 52"></span><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s.<o:p></o:p></span></li> </ol> <p><span lang=EN style='mso-ansi-language:EN'>The speed </span><span style='mso-no-proof:yes'><img border=0 width=19 height=18 id="_x0000_i1038" src="hsen_files/9824b26a51714309aa4afd370035ce53.png" alt="C_1"></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>is equal to the speed of light, and it is assumed that this is the speed of the particles inside the proton, according to the <a href="http://sergf.ru/smpen.htm">substantial proton model</a>, and of the particles within the hypothetical black holes.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>In the speed range from </span><span style='mso-no-proof:yes'><img border=0 width=20 height=17 id="_x0000_i1037" src="hsen_files/01fe9cac15c05ddb569271027aa28cdf.png" alt="C_3"></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>to </span><span style='mso-no-proof:yes'><img border=0 width=20 height=17 id="_x0000_i1036" src="hsen_files/932d0ec79260e01afd1dd960c7bc69bb.png" alt="C_2"></span><span style='mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'> </span></span><span lang=EN style='mso-ansi-language: EN'>the neutron stars are located, the range from </span><span style='mso-no-proof:yes'><img border=0 width=20 height=17 id="_x0000_i1035" src="hsen_files/39b9c3f22c8d1f146931d8372e8790ed.png" alt="C_5"></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>to </span><span style='mso-no-proof:yes'><img border=0 width=20 height=17 id="_x0000_i1034" src="hsen_files/ce27d75165fe3c1bd5998413085b3309.png" alt="C_4"></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>includes white dwarfs, and the speeds of particles of the main sequence stars are greater than the stellar speed </span><span style='mso-no-proof:yes'><img border=0 width=124 height=17 id="_x0000_i1033" src="hsen_files/81528eb276dd5608972fca438faea71b.png" alt="C_6 = C_s= 220"></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s, but less than the speed </span><span style='mso-no-proof:yes'><img border=0 width=76 height=17 id="_x0000_i1032" src="hsen_files/e218de145cccb4016c38394b0af82ee6.png" alt="C_5= 930"></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'> </span>km/s. The characteristic speeds of planets are not higher than </span><span style='mso-no-proof:yes'><img border=0 width=66 height=17 id="_x0000_i1031" src="hsen_files/ddb5bfdc5c020f0d27f7c8a4e85b41f9.png" alt="C_7= 52"></span><span style='mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'> </span></span><span lang=EN style='mso-ansi-language:EN'>km/s, otherwise such a planet should be considered a stellar object.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>For comparison, the characteristic speed of the Earth is 4.3 km/s, the characteristic speed of Jupiter is 23 km/s, the characteristic speed of the Sun is about 495 km/s.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>The characteristic speed of a main sequence star can be expressed in terms of the stellar speed: </span><span style='mso-no-proof:yes'><img border=0 width=131 height=21 id="_x0000_i1030" src="hsen_files/5424fa1bf87712da733df7750c1d21e4.png" alt=" C_m = C_s (A/Z), "></span><span lang=EN style='mso-ansi-language:EN'><o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>where </span><span style='mso-no-proof:yes'><img border=0 width=15 height=14 id="_x0000_i1029" src="hsen_files/7fc56270e7a70fa81a5935b72eacbe29.png" alt=" A "></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>and </span><span style='mso-no-proof:yes'><img border=0 width=14 height=14 id="_x0000_i1028" src="hsen_files/21c2e59531c8710156d34a3c30ac81d5.png" alt=" Z "></span><span lang=EN-GB style='mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'>  </span></span><span lang=EN style='mso-ansi-language: EN'>are the mass and charge numbers, corresponding to the star from the point of view of similarity between atoms and stars. In turn, the stellar speed is determined through the speed of light and the coefficient of similarity in velocities: </span><span style='mso-no-proof:yes'><img border=0 width=73 height=17 id="_x0000_i1027" src="hsen_files/d089e828e3d69a4d73e2a08ba925a7e6.png" alt=" C_s= c S_0 "></span><span lang=EN style='mso-ansi-language:EN'>. The stellar speed is one of the <a href="http://sergf.ru/scen.htm">stellar constants</a>, and it determines the characteristic speed of particles of the main sequence star with minimum mass.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'>Large stellar systems, such as galaxies, consist of a number of stars, moving at quite high speeds around the common center of inertia of one or another system. Therefore, the characteristic speed for a galaxy is the average speed of the stars motion. For a large number of galaxies, there are dependences of the speed of the stars motion on the distance to the galactic center, which after averaging show the rotation of certain parts of the galaxy. If we average the speeds of the stars motion over the entire volume of the galaxy, the resulting average value will be proportional to the characteristic speed of this galaxy. This is the consequence of the virial theorem, according to which </span><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";color:black;mso-ansi-language: EN-US'>the absolute value of total energy of a system of particles is equal to kinetic energy of the particles</span><span lang=EN style='mso-ansi-language: EN'>.<o:p></o:p></span></p> <p><span lang=EN style='mso-ansi-language:EN'><a href="http://sergf.ru/kpken.htm">Quantization of parameters of cosmic systems</a> is manifested at all levels of matter and it is a typical property of physical systems, which, after the exchange of energy (exchange of matter), return to their initial state. In this case, the characteristic speed of the system s particles can again achieve the previous equilibrium value. Some physical systems with degenerate relativistic objects (atoms, neutron stars) achieve a large degree of discreteness and stability, so that their characteristic speeds change very little. It is known, for example, that the degree of accuracy of the best atomic clocks coincides with the accuracy of repetition of pulses, coming from pulsars.<o:p></o:p></span></p> <p class=MsoNormal><span lang=EN style='mso-ansi-language:EN'>In the space objects, the characteristic speed allows us to estimate the kinetic energy of the particles motion and the internal temperature. From the point of view of the Le Sage's theory of gravitation, the gravitational energy of the body and the gravitation force are created by fluxes of gravitons, penetrating all bodies. <sup id="cite_ref-2">[2]</sup> <sup>[</sup></span><sup><span lang=EN-GB style='mso-ansi-language:EN-GB'>3</span></sup><sup><span lang=EN style='mso-ansi-language:EN'>]</span></sup><span lang=EN style='mso-ansi-language: EN'><span style='mso-spacerun:yes'>  </span>However, the fluxes of gravitons create not only the gravitational pressure, but also they transfer part of their energy to the particles, so that according to the virial theorem the internal kinetic (thermal) energy is not less than half of the absolute value of the body s gravitational energy. Thus the interior of </span><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";color:black; mso-ansi-language:EN-US'>an equilibrium space</span><span lang=EN style='mso-ansi-language:EN'> body cannot get colder than a certain value, which depends on its mass and size, while maintaining the constant characteristic speed of the body s particles.</span><span lang=EN style='mso-ansi-language:EN-US'> </span><span lang=EN style='mso-ansi-language: EN'>The same follows from the solution of the equations of the <a href="http://sergf.ru/afen.htm">acceleration field</a> for a <a href="http://sergf.ru/roen.htm">relativistic uniform system</a>, in which the Lorentz factor, the kinetic energy and the stationary velocity distribution of particles inside the body are determined.</span><sup id="cite_ref-4"><span lang=EN-US style='mso-ansi-language:EN-US'> [4]</span></sup><span lang=EN-US style='mso-ansi-language:EN-US'> <sup id="cite_ref-5" original-title="">[5]<o:p></o:p></sup></span></p> <p><span lang=EN style='mso-ansi-language:EN'>The speeds</span><span lang=EN style='mso-ansi-language:EN-US'> </span><span lang=EN style='mso-ansi-language: EN'><span style='mso-spacerun:yes'> </span></span><span style='mso-no-proof: yes'><img border=0 width=21 height=17 id="_x0000_i1026" src="hsen_files/b8d9de3ddb68decd9ddbbac1e47dec08.png" alt="C_{x}"></span><span lang=EN style='mso-ansi-language:EN'><span style='mso-spacerun:yes'>  </span>are boundary for the maximum rotation speeds of the stars surfaces, as well as for the average motion speeds of the stars relative to those stellar systems, in which these stars were formed (the principle of local stellar speed).<o:p></o:p></span></p> <p class=MsoNormal><span lang=EN style='mso-ansi-language:EN'>In Infinite Hierarchical Nesting of Matter, analogs of nucleons at the level of stars are neutron stars, and the characteristic speed of nucleons is higher than that of stars, approximately 4.3 times. The inverse of this quantity is the coefficient of similarity in speeds<span style='mso-spacerun:yes'>  </span><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id=" 8AC=>:_x0020_21" o:spid="_x0000_i1025" type="#_x0000_t75" alt="{\displaystyle S=0.23}" style='width:78pt; height:19.5pt;visibility:visible;mso-wrap-style:square'> <v:imagedata src="hsen.files/image002.png" o:title="displaystyle S=0"/> </v:shape><![endif]--><![if !vml]><img border=0 width=104 height=26 src="hsen.files/image002.png" alt="{\displaystyle S=0.23}" v:shapes=" 8AC=>:_x0020_21"><![endif]></span><span style='mso-spacerun:yes'> </span>between these levels of matter. If a neutron star consists of nucleons, then nucleons consist of similar particles of the lowest level of matter, called <a href="http://sergf.ru/praen.htm">praons</a>, and praons in turn consist of graons. Between the levels of nucleons and praons and between the levels of praons and graons, it is also possible to estimate the similarity coefficients for speeds, which turn out to be close to unity. This is due to the fact that nucleons inside a neutron star have a Lorentz factor of about 1.04, but the praons inside the nucleon and the graons inside the praon have a Lorentz factor of about 1.9.</span><sup id="cite_ref-6"><span lang=EN-US style='mso-ansi-language:EN-US'>[6]</span></sup><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <h2 align=center style='text-align:center'><span class=mw-headline><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN'>References</span></span><span lang=EN-US style='mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN-US'><o:p></o:p></span></h2> <ol start=1 type=1> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l3 level1 lfo3;tab-stops:list 36.0pt' id="cite_note-1"><span class=reference-text><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'>Fedosin S.G. <a href="http://lccn.loc.gov/2009457349"><span class=SpellE>Fizika</span> <span class=SpellE>i</span> <span class=SpellE>filosofiia</span> <span class=SpellE>podobiia</span> <span class=SpellE>ot</span> <span class=SpellE>preonov</span> do <span class=SpellE>metagalaktik</span></a>, Perm, pages 544, 1999. ISBN 5-8131-0012-1.</span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN'><o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l3 level1 lfo3;tab-stops:list 36.0pt' id="cite_note-2"><span class=reference-text><span lang=EN style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN'>Fedosin S.G. <a href="http://sergf.ru/mgen.htm">Model of Gravitational Interaction in the Concept of Gravitons.</a> </span></span><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'>Journal of Vectorial Relativity, Vol. 4, No. 1, </span><span lang=EN-US style='mso-ansi-language:EN-US'>pp. 1-24</span><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'> (2009)</span><span class=reference-text><span lang=EN style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN'>.</span></span><span lang=EN style='color:black;mso-ansi-language:EN-US'> </span><span style='color:black'><a href="http://dx.doi.org/10.5281/zenodo.890886"><span lang=EN-US style='mso-ansi-language:EN-US'>http://dx.doi.org/10.5281/zenodo.890886</span></a></span><span lang=EN-US style='color:black;mso-ansi-language:EN-US'>.</span><span class=reference-text><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></span></li> <li class=MsoNormal style='color:#252525;mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;mso-list:l3 level1 lfo3;tab-stops:list 36.0pt'><span lang=EN-GB style='background:white;mso-ansi-language:EN-GB'><span id="External_links">Fedosin S.G. </span><a href="http://vixra.org/abs/1503.0127"><span style='color:#663366;text-decoration:none;text-underline:none'>The graviton field as the source of mass and gravitational force in the modernized Le Sage s model.</span></a><span style='orphans: auto;widows: 1;-webkit-text-stroke-width: 0px; float:none;word-spacing:0px'>Physical Science International Journal, ISSN: 2348-0130, Vol. 8, Issue 4, </span></span><span lang=EN-US style='color:windowtext;background:white;mso-ansi-language:EN-US'>pp</span><span lang=EN-GB style='color:windowtext;background:white;mso-ansi-language: EN-GB'>. 1-18</span><span lang=EN-GB style='background:white;mso-ansi-language: EN-GB'> (2015). <a href="http://dx.doi.org/10.9734/PSIJ/2015/22197">http://dx.doi.org/10.9734/PSIJ/2015/22197</a> .<o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l3 level1 lfo3;tab-stops:list 36.0pt'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-US'><span id="External_links">Fedosin S.G. </span><a href="https://zenodo.org/record/1037246">The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept</a>. Continuum Mechanics and Thermodynamics, Vol. 29, Issue 2, pp. 361-371 (2017). <a href="https://dx.doi.org/10.1007/s00161-016-0536-8">https://dx.doi.org/10.1007/s00161-016-0536-8</a>.<o:p></o:p></span></li> <li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; mso-list:l3 level1 lfo3;tab-stops:list 36.0pt'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-US'>Fedosin S.G. <a href="http://em.rdcu.be/wf/click?upn=lMZy1lernSJ7apc5DgYM8f7AyOIJlVFO4uFv7zUQtzk-3D_DUeisO4Ue44lkDmCnrWVhK-2BAxKrUexyqlYtsmkyhvEp5zr527MDdThwbadScvhwZehXbanab8i5hqRa42b-2FKYwacOeM4LKDJeJuGA15M9FWvYOfBgfon7Bqg2f55NFYGJfVGaGhl0ghU-2BkIJ9Hz4M6SMBYS-2Fr-2FWWaj9eTxv23CKo9d8nFmYAbMtBBskFuW9fupsvIvN5eyv-2Fk-2BUc7hiS15rRISs1jpNnRQpDtk2OE9Hr6mYYe5Y-2B8lunO9GwVRw07Y1mdAqqtEZ-2BQjk5xUwPnA-3D-3D">The integral theorem of generalized virial in the relativistic uniform model</a>. Continuum Mechanics and Thermodynamics, Vol. 31, Issue 3, pp. 627-638 (2019). <a href="https://dx.doi.org/10.1007/s00161-018-0715-x">https://dx.doi.org/10.1007/s00161-018-0715-x</a>.<o:p></o:p></span></li> <li class=MsoNormal style='color:#252525;mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;mso-list:l3 level1 lfo3;tab-stops:list 36.0pt'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";color:windowtext; mso-ansi-language:EN-US'>Fedosin S.G. The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation. International Letters of Chemistry, Physics and Astronomy, Vol. 78, pp. 39-50 (2018). <a href="http://dx.doi.org/10.18052/www.scipress.com/ILCPA.78.39">http://dx.doi.org/10.18052/www.scipress.com/ILCPA.78.39</a>. </span><span lang=EN-US style='background:white;mso-ansi-language:EN-US'><o:p></o:p></span></li> </ol> <h2 align=center style='text-align:center'><span id="External_links"><span class=mw-headline><span lang=EN style='mso-fareast-font-family:"Times New Roman"; color:#252525;background:white;mso-ansi-language:EN'>External links</span></span></span><span lang=EN style='mso-fareast-font-family:"Times New Roman";color:#252525; background:white;mso-ansi-language:EN'><o:p></o:p></span></h2> <ul type=disc> <li class=MsoNormal style='color:#252525;mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;mso-list:l1 level1 lfo4;tab-stops:list 36.0pt'><span lang=EN style='mso-fareast-font-family:"Times New Roman";background:white; mso-ansi-language:EN'><a href="http://www.wikiznanie.ru/ru-wz/index.php/%D0%A5%D0%B0%D1%80%D0%B0%D0%BA%D1%82%D0%B5%D1%80%D0%BD%D0%B0%D1%8F_%D1%81%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82%D1%8C">Characteristic speed in Russian</a><o:p></o:p></span></li> </ul> <p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto; margin-left:36.0pt'><span lang=EN style='mso-fareast-font-family:"Times New Roman"; color:#252525;background:white;mso-ansi-language:EN'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal align=center style='mso-margin-top-alt:auto;mso-margin-bottom-alt: auto;margin-left:36.0pt;text-align:center'><span lang=FR-CA style='mso-fareast-font-family: "Times New Roman";color:black;background:white;mso-ansi-language:FR-CA'>Source: http://sergf.ru/hsen.htm</span><span lang=EN style='mso-fareast-font-family: "Times New Roman";color:#252525;background:white;mso-ansi-language:EN'><o:p></o:p></span></p> </div> <div> <p class=MsoNormal style='margin-top:12.0pt;margin-right:0cm;margin-bottom: 0cm;margin-left:17.85pt;margin-bottom:.0001pt'><span lang=EN-GB style='mso-fareast-font-family:"Times New Roman";color:black;background:white; mso-ansi-language:EN-GB'><a href="http://sergf.ru/wiki.htm"><span lang=EN-US style='color:purple;mso-ansi-language:EN-US'>On the list of pages</span></a><o:p></o:p></span></p> </div> </div> </div> </body> </html>