User contributions for Xxsrm

28 June 2024

• 17:4817:48, 28 June 2024 diff hist −1 Appendix/Ramblings/ToroidalCoordinates →Multipole Moment in Toroidal Coordinates current
• 17:4817:48, 28 June 2024 diff hist 0 N File:TorusIntegration.png No edit summary current
• 17:4617:46, 28 June 2024 diff hist 0 N File:TCoordsE.gif No edit summary current

14 December 2023

• 18:0018:00, 14 December 2023 diff hist +30 MediaWiki:Sidebar No edit summary

12 December 2023

• 16:3216:32, 12 December 2023 diff hist −13 Appendix/EquationTemplates →Other Equations with Assigned Templates current
• 16:2916:29, 12 December 2023 diff hist +554 N Template:Math/EQ TRApproximation Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Other_Equations_with_Assigned_Templates </td> <td align="right"> <math>\Phi_\mathrm{TR}(\varpi,z)</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math>-\biggl[ \frac{2GM}{\pi } \biggr]\frac{K(k)}{\sqrt{(\varpi+a)^2 + z^2}}</math> </td> </tr> <tr> <td align="center" colspan="4"> <math>\mathrm{where:}~~~k..." current
• 16:2716:27, 12 December 2023 diff hist +66 N Template:Math/EQ Polytrope03 Created page with "<math>\rho = \biggl[ \frac{H}{(n+1)K_\mathrm{n}} \biggr]^n </math>" current
• 16:2616:26, 12 December 2023 diff hist +45 N Template:Math/EQ Polytrope02 Created page with "<math>H = (n+1)K_\mathrm{n} \rho^{1/n}</math>" current
• 16:2516:25, 12 December 2023 diff hist +42 N Template:Math/EQ Polytrope01 Created page with "<math>P = K_\mathrm{n} \rho^{1+1/n}</math>" current
• 16:2416:24, 12 December 2023 diff hist +54 N Template:Math/EQ EOSideal02 Created page with "<math>P = (\gamma_\mathrm{g} - 1)\epsilon \rho </math>" current
• 16:2316:23, 12 December 2023 diff hist +24 N Template:Math/EQ EOSideal00 Created page with "<math>P = n_g k T</math>" current
• 16:2216:22, 12 December 2023 diff hist +675 N Template:Math/EQ CT99Axisymmetric Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Other_Equations_with_Assigned_Templates </td> <td align="right"> <math>\Phi(\varpi,z)\biggr|_\mathrm{axisym}</math> </td> <td align="center"> <math>=</math> </td> <td align="left"> <math> - \frac{G}{\pi} \iint\limits_\mathrm{config} \biggl[ \frac{\mu}{(\varpi~ \varpi^')^{1 / 2}} \biggr] K(\mu) \rho(\varpi^', z^') 2\pi \varpi^'~ d\v..." current
• 16:1916:19, 12 December 2023 diff hist +760 N Template:Math/EQ RadialPulsation04 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math>0 = \frac{d^2x}{dr_0^2} + \frac{1}{r_0}\biggl[4 + \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{dx}{dr_0} + \biggl[ \biggl(3 - \frac{4}{\gamma_g}\biggr) \frac{d\ln P_0}{d\ln r_0} \biggr] \frac{x}{r_0^2} - \frac{1}{\Delta} \biggl[\frac{d\ln P_0}{d\ln r_0}\cdot \frac{\rho_c}{\rho_0} \biggl( \frac{\sigma_c..." current
• 16:1816:18, 12 December 2023 diff hist +437 N Template:Math/EQ RadialPulsation01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math> \frac{d^2x}{dr_0^2} + \biggl[\frac{4}{r_0} - \biggl(\frac{g_0 \rho_0}{P_0}\biggr) \biggr] \frac{dx}{dr_0} + \biggl(\frac{\rho_0}{\gamma_\mathrm{g} P_0} \biggr)\biggl[\omega^2 + (4 - 3\gamma_\mathrm{g})\frac{g_0}{r_0} \biggr] x = 0 </math> </td> </tr> </table>" current
• 15:4815:48, 12 December 2023 diff hist +350 N Template:Math/EQ SSradiationTransport01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{dT}{dr} = - \frac{ 3 }{ 4a_\mathrm{rad} c} \biggl(\frac{ \kappa \rho }{ T^3 }\biggr) \frac{ L_r }{ 4\pi r^2 }</math> </td> </tr> </table>" current
• 15:4715:47, 12 December 2023 diff hist +264 N Template:Math/EQ SSmassConservation01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{dM_r}{dr} = 4\pi r^2 \rho</math> </td> </tr> </table>" current
• 15:4615:46, 12 December 2023 diff hist +286 N Template:Math/EQ SSenergyConservation01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{dL_r}{dr} = 4\pi r^2 \rho \epsilon_\mathrm{nuc}</math> </td> </tr> </table>" current
• 15:4415:44, 12 December 2023 diff hist +562 N Template:Math/EQ ZTFG01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right" width="35%"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="left"> <font><math>P_\mathrm{deg} = A_\mathrm{F} F(\chi) </math></font> </td> </tr> <tr> <td align="center" colspan="2"> where:  <math>F(\chi) \equiv \chi(2\chi^2 - 3)(\chi^2 + 1)^{1/2} + 3\sinh^{-1}\chi</math> </td> </tr> <tr> <td align="right" colspan="1"> and:    </td> <td align="left"..." current
• 15:4315:43, 12 December 2023 diff hist +343 N Template:Math/EQ PressureTotal01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="center"> <math>p_\mathrm{total} = \biggl(\frac{\mu_e m_p}{\bar{\mu} m_u} \biggr) 8 \chi^3 \frac{T}{T_e} + F(\chi) + \frac{8\pi^4}{15} \biggl( \frac{T}{T_e} \biggr)^4</math> </td> </tr> </table>" current
• 15:4315:43, 12 December 2023 diff hist +239 N Template:Math/EQ EOSradiation01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="center"> <math>P_\mathrm{rad} = \frac{1}{3} a_\mathrm{rad} T^4</math> </td> </tr> </table>" current
• 15:4215:42, 12 December 2023 diff hist +238 N Template:Math/EQ EOSideal0A Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Equations_of_State </td> <td align="center"> <math>P_\mathrm{gas} = \frac{\Re}{\bar{\mu}} \rho T</math> </td> </tr> </table>" current
• 15:3915:39, 12 December 2023 diff hist +27,268 N Appendix/EquationTemplates Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =50px<font size="+2" color="black">Key Equations</font>= Each of the equations displayed in the Tables, below, encapsulates a physical concept that is fundamental to our understanding of — and, hence our discussion of — the '''structure, stability, and dynamics of self-gravitating fluids.''' The pervasiveness of these physical concepts throughout astrophysics is reflected in the fact t..."
• 15:3515:35, 12 December 2023 diff hist +52 N Template:Math/MP PolytropicIndex Created page with "<span title="Polytropic index"><math>n</math></span>" current
• 15:3515:35, 12 December 2023 diff hist +66 N Template:Math/MP PolytropicConstant Created page with "<span title="Polytropic constant"><math>K_\mathrm{n}</math></span>" current
• 15:3415:34, 12 December 2023 diff hist +65 N Template:Math/MP MeanMolecularWeight Created page with "<span title="Mean molecular weight"><math>\bar{\mu}</math></span>" current
• 15:3315:33, 12 December 2023 diff hist +69 N Template:Math/MP ElectronMolecularWeight Created page with "<span title="Molecular weight of electrons"><math>\mu_e</math></span>" current
• 15:3215:32, 12 December 2023 diff hist +93 N Template:Math/MP AdiabaticIndex Created page with "<span title="Adiabatic index = Ratio of specific heats"><math>\gamma_\mathrm{g}</math></span>" current
• 15:3015:30, 12 December 2023 diff hist +51 N Template:Math/VAR SpecificVolume01 Created page with "<span title="Specific volume"><math>V</math></span>" current
• 15:3015:30, 12 December 2023 diff hist +69 N Template:Math/VAR NumberDensity01 Created page with "<span title="Number density of gas particles"><math>n_g</math></span>" current
• 15:2815:28, 12 December 2023 diff hist +44 N Template:Math/VAR Enthalpy01 Created page with "<span title="Enthalpy"><math>H</math></span>" current
• 15:2615:26, 12 December 2023 diff hist +99 N Template:Math/C ThompsonCrossSection Created page with "<span title="Thompson cross-section: 0.6652458E-24 square-centimeters"><math>\sigma_T</math></span>" current
• 15:2515:25, 12 December 2023 diff hist +70 N Template:Math/C SpeedOfLight Created page with "<span title="Speed of light:2.99792458E+10 cm/s"><math>c</math></span>" current
• 15:2515:25, 12 December 2023 diff hist +82 N Template:Math/C RadiationConstant Created page with "<span title="Radiation constant: 7.566E-15 cgs"><math>a_\mathrm{rad}</math></span>" current
• 15:2415:24, 12 December 2023 diff hist +73 N Template:Math/C ProtonMass Created page with "<span title="Mass of the proton: 1.6726216E-24 g"><math>m_p</math></span>" current
• 15:2315:23, 12 December 2023 diff hist +68 N Template:Math/C PlanckConstant Created page with "<span title="Planck constant:6.626069E-27 cgs"><math>h</math></span>" current
• 15:2215:22, 12 December 2023 diff hist +75 N Template:Math/C GasConstant Created page with "<span title="Gas constant: 8.3145E+07 erg/(K mole)"><math>\Re</math></span>" current
• 15:2115:21, 12 December 2023 diff hist +104 N Template:Math/C FineStructureConstant Created page with "<span title="Fine structure constant: 7.29735E-3 (dimensionless)"><math>\alpha_\mathrm{fs}</math></span>" current
• 15:2115:21, 12 December 2023 diff hist +91 N Template:Math/C FermiPressure Created page with "<span title="Characteristic Fermi pressure: 6.002E+22 cgs"><math>A_\mathrm{F}</math></span>" current
• 15:2015:20, 12 December 2023 diff hist +88 N Template:Math/C FermiDensity Created page with "<span title="Characteristic Fermi density: ~ 1E+06 cgs"><math>B_\mathrm{F}</math></span>" current
• 15:1915:19, 12 December 2023 diff hist +112 N Template:Math/C ElectronTemperature Created page with "<span title="Temperature associated with rest-mass energy of the electron: 5.9381E+09 K"><math>T_e</math></span>" current
• 15:1815:18, 12 December 2023 diff hist +74 N Template:Math/C ElectronMass Created page with "<span title="Mass of the electron: 9.109382E-28 g"><math>m_e</math></span>" current
• 15:1715:17, 12 December 2023 diff hist +75 N Template:Math/C ElectronCharge Created page with "<span title="Charge on an electron: 4.803203E-10 cgs"><math>e</math></span>" current
• 15:1515:15, 12 December 2023 diff hist +88 N Template:Math/C BoltzmannConstant Created page with "<span title="Boltzmann constant: 1.38065E-16 erg/K (per particle)"><math>k</math></span>" current
• 15:1415:14, 12 December 2023 diff hist +88 N Template:Math/C AvogadroConstant Created page with "<span title="Avogadro constant: 6.022141E+23 particles per mole"><math>N_A</math></span>" current
• 15:1215:12, 12 December 2023 diff hist +70 N Template:Math/C AtomicMassUnit Created page with "<span title="Atomic Mass Unit: 1.660539E-24 g"><math>m_u</math></span>" current
• 15:0915:09, 12 December 2023 diff hist +14,662 N Appendix/VariablesTemplates Created page with "=Variables Templates= ==Physical Constants== <div align="center"> <table border=3 cellpadding=5 cellspacing=1 width="95%" bordercolor="darkblue"> <tr> <td colspan=4> To insert the symbol associated with a given physical variable or constant into the text of any Wiki document, type ...<br /><center> {{ Math/<i><font color="red">Template_Name</font></i> }}</center> </td> </tr> <tr> <th width="8%"> <font color="red">Symbol</font> </th> <th> <..." current
• 15:0415:04, 12 December 2023 diff hist +301 MediaWiki:Sidebar No edit summary
• 15:0415:04, 12 December 2023 diff hist −4 MediaWiki:Sidebar No edit summary
• 15:0315:03, 12 December 2023 diff hist +12 MediaWiki:Sidebar No edit summary
• 15:0115:01, 12 December 2023 diff hist +269 N MediaWiki:Sidebar Created page with " * navigation ** mainpage|mainpage-description ** recentchanges-url|recentchanges ** randompage-url|randompage ** helppage|help-mediawiki ** H_BookTiledMenu|Tiled Menu * Appendices ** Appendix/VariablesTemplates|Variables & Parameters * SEARCH * TOOLBOX * LANGUAGES"