Yukterez

Gravity & Charge, 7 Body Simulator

Feb 20th, 2019 (edited)
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  1. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  2. (* ||| Mathematica Syntax || yukterez.net || 7 Body Newtonian Mass & Charge Simulator ||| *)
  3. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  4.  
  5. ClearAll["Global`*"]; ClearAll["Local`*"];
  6. Needs["DifferentialEquations`NDSolveProblems`"];
  7. Needs["DifferentialEquations`NDSolveUtilities`"];
  8.  
  9. Amp = 1; kg = 1; m = 1; sek = 1; km = 1000 m; (* SI Einheiten *)
  10.  
  11. mt1 = {"StiffnessSwitching", Method-> {"ExplicitRungeKutta", Automatic}};
  12. mt2 = {"ImplicitRungeKutta", "DifferenceOrder"-> 20};
  13. mt3 = {"EquationSimplification"-> "Residual"};
  14. mt0 = Automatic;
  15. mta = mt2;
  16. wp = MachinePrecision;
  17.  
  18. (* Plot Optionen *)
  19.  
  20. Tmax = 40 yr;
  21. tMax = Min[Tmax, plunge];
  22. trail = 10 yr;
  23. point = 0.015;
  24. thk = 0.004;
  25. plotrange = 12 Au {{-1, +1}, {-1, +1}, {-1, +1}};
  26. viewpoint = {40, 30, 20};
  27. imagesize = 430;
  28. startpos = 0;
  29.  
  30. (* Konstanten *)
  31.  
  32. G = 667384/10^16 m^3/kg/sek^2;
  33. Λ = 11056*^-56/m^2;
  34. ε0 = 8854187817*^-21 Amp^2 sek^4/kg/m^3;
  35. c = 299792458 m/sek;
  36. Au = 149597870700 m;
  37. dy = 24*3600 sek;
  38. yr = 36525*dy/100;
  39. (* Ephemeriden vom 19.02.2019, 0:00:00 TDB *)
  40. (* Sonne *)
  41.  
  42. m1 = +1.988435*^30 kg;
  43. q1 = +77 Amp sek;
  44.  
  45. x1x = -1.147196570503204*^-03 Au;
  46. y1y = +7.515074431920434*^-03 Au;
  47. z1z = -4.730273651193038*^-05 Au;
  48.  
  49. v1x = -8.107931162902937*^-06 Au/dy;
  50. v1y = +1.520849732928662*^-06 Au/dy;
  51. v1z = +2.095554598567427*^-07 Au/dy;
  52.  
  53. (* Merkur *)
  54.  
  55. m2 = +3.30104*^23 kg;
  56. q2 = +0 Amp sek;
  57.  
  58. x2x = +2.493682187528474*^-01 Au;
  59. y2y = +2.060848667278006*^-01 Au;
  60. z2z = -6.803162776737710*^-03 Au;
  61.  
  62. v2x = -2.301828852252654*^-02 Au/dy;
  63. v2y = +2.326003199133993*^-02 Au/dy;
  64. v2z = +4.011640539083395*^-03 Au/dy;
  65.  
  66. (* Venus *)
  67.  
  68. m3 = +4.86732*^24 kg;
  69. q3 = +0 Amp sek;
  70.  
  71. x3x = -5.604572600267276*^-01 Au;
  72. y3y = -4.500554270408416*^-01 Au;
  73. z3z = +2.595073246894732*^-02 Au;
  74.  
  75. v3x = +1.265689462094818*^-02 Au/dy;
  76. v3y = -1.574829638876520*^-02 Au/dy;
  77. v3z = -9.467652690844731*^-04 Au/dy;
  78.  
  79. (* Erde + Mond *)
  80.  
  81. m4 = +5.9721986*^24 kg+7.3459*^22 kg;
  82. q4 = +0 Amp sek;
  83.  
  84. x4x = -8.552072163834489*^-01 Au;
  85. y4y = +5.049715021822364*^-01 Au;
  86. z4z = -6.849877545851131*^-05 Au;
  87.  
  88. v4x = -8.942912568116291*^-03 Au/dy;
  89. v4y = -1.492365678503182*^-02 Au/dy;
  90. v4z = +2.741178622694643*^-07 Au/dy;
  91.  
  92. (* Mars *)
  93.  
  94. m5 = +6.41693*^23 kg;
  95. q5 = +0 Amp sek;
  96.  
  97. x5x = +5.580724605736193*^-01 Au;
  98. y5y = +1.416261572201534*^+00 Au;
  99. z5z = +1.574925082740965*^-02 Au;
  100.  
  101. v5x = -1.248544019487808*^-02 Au/dy;
  102. v5y = +6.355083417008326*^-03 Au/dy;
  103. v5z = +4.394992947386628*^-04 Au/dy;
  104.  
  105. (* Jupiter *)
  106.  
  107. m6 = +1.89813*^27 kg;
  108. q6 = +0 Amp sek;
  109.  
  110. x6x = -1.795821860926694*^+00 Au;
  111. y6y = -5.016469167174772*^+00 Au;
  112. z6z = +6.097587180308248*^-02 Au;
  113.  
  114. v6x = +7.014525824256318*^-03 Au/dy;
  115. v6y = -2.183010990796764*^-03 Au/dy;
  116. v6z = -1.478090774743338*^-04 Au/dy;
  117.  
  118. (* Saturn *)
  119.  
  120. m7 = +5.68319*^26 kg;
  121. q7 = +0 Amp sek;
  122.  
  123. x7x = +2.211165351380597*^+00 Au;
  124. y7y = -9.803846216723874*^+00 Au;
  125. z7z = +8.244475037063657*^-02 Au;
  126.  
  127. v7x = +5.133965065556525*^-03 Au/dy;
  128. v7y = +1.210333590471664*^-03 Au/dy;
  129. v7z = -2.255855621236429*^-04 Au/dy;
  130.  
  131. (* Pluto + Charon *)
  132.  
  133. m0 = +1.303*^22 kg+1.586*^21 kg;
  134. q0 = +0 Amp sek;
  135.  
  136. x0x = +1.202894612500549*^+01 Au;
  137. y0y = -3.151878221568063*^+01 Au;
  138. z0z = -1.067812248721266*^-01 Au;
  139.  
  140. v0x = +3.004427922255182*^-03 Au/dy;
  141. v0y = +4.501898344345873*^-04 Au/dy;
  142. v0z = -9.299030165680609*^-04 Au/dy;
  143.  
  144. (* Differentialgleichung *)
  145.  
  146. nds=NDSolve[{
  147.  
  148. x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t],
  149. x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t],
  150. x3'[t] == vx3[t], y3'[t] == vy3[t], z3'[t] == vz3[t],
  151. x4'[t] == vx4[t], y4'[t] == vy4[t], z4'[t] == vz4[t],
  152. x5'[t] == vx5[t], y5'[t] == vy5[t], z5'[t] == vz5[t],
  153. x6'[t] == vx6[t], y6'[t] == vy6[t], z6'[t] == vz6[t],
  154. x7'[t] == vx7[t], y7'[t] == vy7[t], z7'[t] == vz7[t],
  155.  
  156. vx1'[t] ==
  157. (G m2 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  158. (G m3 (x3[t]-x1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  159. (G m4 (x4[t]-x1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  160. (G m5 (x5[t]-x1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  161. (G m6 (x6[t]-x1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  162. (G m7 (x7[t]-x1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  163. If[q1 == 0, 0,
  164. (-q1*q2/(4Pi ε0 )/m1 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  165. (-q1*q3/(4Pi ε0 )/m1 (x3[t]-x1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  166. (-q1*q4/(4Pi ε0 )/m1 (x4[t]-x1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  167. (-q1*q5/(4Pi ε0 )/m1 (x5[t]-x1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  168. (-q1*q6/(4Pi ε0 )/m1 (x6[t]-x1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  169. (-q1*q7/(4Pi ε0 )/m1 (x7[t]-x1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]]+
  170. Λ*c^2*x1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  171.  
  172. vy1'[t] ==
  173. (G m2 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  174. (G m3 (y3[t]-y1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  175. (G m4 (y4[t]-y1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  176. (G m5 (y5[t]-y1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  177. (G m6 (y6[t]-y1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  178. (G m7 (y7[t]-y1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  179. If[q1 == 0, 0,
  180. (-q1*q2/(4Pi ε0 )/m1 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  181. (-q1*q3/(4Pi ε0 )/m1 (y3[t]-y1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  182. (-q1*q4/(4Pi ε0 )/m1 (y4[t]-y1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  183. (-q1*q5/(4Pi ε0 )/m1 (y5[t]-y1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  184. (-q1*q6/(4Pi ε0 )/m1 (y6[t]-y1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  185. (-q1*q7/(4Pi ε0 )/m1 (y7[t]-y1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]]+
  186. Λ*c^2*y1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  187.  
  188. vz1'[t] ==
  189. (G m2 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  190. (G m3 (z3[t]-z1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  191. (G m4 (z4[t]-z1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  192. (G m5 (z5[t]-z1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  193. (G m6 (z6[t]-z1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  194. (G m7 (z7[t]-z1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  195. If[q1 == 0, 0,
  196. (-q1*q2/(4Pi ε0 )/m1 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  197. (-q1*q3/(4Pi ε0 )/m1 (z3[t]-z1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  198. (-q1*q4/(4Pi ε0 )/m1 (z4[t]-z1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  199. (-q1*q5/(4Pi ε0 )/m1 (z5[t]-z1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  200. (-q1*q6/(4Pi ε0 )/m1 (z6[t]-z1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  201. (-q1*q7/(4Pi ε0 )/m1 (z7[t]-z1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]]+
  202. Λ*c^2*z1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  203.  
  204. vx2'[t] ==
  205. (G m1 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
  206. (G m3 (x3[t]-x2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  207. (G m4 (x4[t]-x2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  208. (G m5 (x5[t]-x2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  209. (G m6 (x6[t]-x2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  210. (G m7 (x7[t]-x2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  211. If[q2 == 0, 0,
  212. (-q2*q1/(4Pi ε0 )/m2 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
  213. (-q2*q3/(4Pi ε0 )/m2 (x3[t]-x2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  214. (-q2*q4/(4Pi ε0 )/m2 (x4[t]-x2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  215. (-q2*q5/(4Pi ε0 )/m2 (x5[t]-x2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  216. (-q2*q6/(4Pi ε0 )/m2 (x6[t]-x2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  217. (-q2*q7/(4Pi ε0 )/m2 (x7[t]-x2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]]+
  218. Λ*c^2*x2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  219.  
  220. vy2'[t] ==
  221. (G m1 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
  222. (G m3 (y3[t]-y2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  223. (G m4 (y4[t]-y2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  224. (G m5 (y5[t]-y2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  225. (G m6 (y6[t]-y2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  226. (G m7 (y7[t]-y2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  227. If[q2 == 0, 0,
  228. (-q2*q1/(4Pi ε0 )/m2 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
  229. (-q2*q3/(4Pi ε0 )/m2 (y3[t]-y2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  230. (-q2*q4/(4Pi ε0 )/m2 (y4[t]-y2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  231. (-q2*q5/(4Pi ε0 )/m2 (y5[t]-y2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  232. (-q2*q6/(4Pi ε0 )/m2 (y6[t]-y2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  233. (-q2*q7/(4Pi ε0 )/m2 (y7[t]-y2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]]+
  234. Λ*c^2*y2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  235.  
  236. vz2'[t] ==
  237. (G m1 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  238. (G m3 (z3[t]-z2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  239. (G m4 (z4[t]-z2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  240. (G m5 (z5[t]-z2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  241. (G m6 (z6[t]-z2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  242. (G m7 (z7[t]-z2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  243. If[q2 == 0, 0,
  244. (-q2*q1/(4Pi ε0 )/m2 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  245. (-q2*q3/(4Pi ε0 )/m2 (z3[t]-z2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  246. (-q2*q4/(4Pi ε0 )/m2 (z4[t]-z2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  247. (-q2*q5/(4Pi ε0 )/m2 (z5[t]-z2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  248. (-q2*q6/(4Pi ε0 )/m2 (z6[t]-z2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  249. (-q2*q7/(4Pi ε0 )/m2 (z7[t]-z2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]]+
  250. Λ*c^2*z2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  251.  
  252. vx3'[t] ==
  253. (G m1 (x1[t]-x3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  254. (G m2 (x2[t]-x3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  255. (G m4 (x4[t]-x3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  256. (G m5 (x5[t]-x3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  257. (G m6 (x6[t]-x3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  258. (G m7 (x7[t]-x3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  259. If[q3 == 0, 0,
  260. (-q3*q1/(4Pi ε0 )/m3 (x1[t]-x3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  261. (-q3*q2/(4Pi ε0 )/m3 (x2[t]-x3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  262. (-q3*q4/(4Pi ε0 )/m3 (x4[t]-x3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  263. (-q3*q5/(4Pi ε0 )/m3 (x5[t]-x3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  264. (-q3*q6/(4Pi ε0 )/m3 (x6[t]-x3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  265. (-q3*q7/(4Pi ε0 )/m3 (x7[t]-x3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]]+
  266. Λ*c^2*x3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
  267.  
  268. vy3'[t] ==
  269. (G m1 (y1[t]-y3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  270. (G m2 (y2[t]-y3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  271. (G m4 (y4[t]-y3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  272. (G m5 (y5[t]-y3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  273. (G m6 (y6[t]-y3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  274. (G m7 (y7[t]-y3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  275. If[q3 == 0, 0,
  276. (-q3*q1/(4Pi ε0 )/m3 (y1[t]-y3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  277. (-q3*q2/(4Pi ε0 )/m3 (y2[t]-y3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  278. (-q3*q4/(4Pi ε0 )/m3 (y4[t]-y3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  279. (-q3*q5/(4Pi ε0 )/m3 (y5[t]-y3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  280. (-q3*q6/(4Pi ε0 )/m3 (y6[t]-y3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  281. (-q3*q7/(4Pi ε0 )/m3 (y7[t]-y3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]]+
  282. Λ*c^2*y3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
  283.  
  284. vz3'[t] ==
  285. (G m1 (z1[t]-z3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  286. (G m2 (z2[t]-z3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  287. (G m4 (z4[t]-z3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  288. (G m5 (z5[t]-z3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  289. (G m6 (z6[t]-z3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  290. (G m7 (z7[t]-z3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  291. If[q3 == 0, 0,
  292. (-q3*q1/(4Pi ε0 )/m3 (z1[t]-z3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  293. (-q3*q2/(4Pi ε0 )/m3 (z2[t]-z3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  294. (-q3*q4/(4Pi ε0 )/m3 (z4[t]-z3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  295. (-q3*q5/(4Pi ε0 )/m3 (z5[t]-z3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  296. (-q3*q6/(4Pi ε0 )/m3 (z6[t]-z3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  297. (-q3*q7/(4Pi ε0 )/m3 (z7[t]-z3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]]+
  298. Λ*c^2*z3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
  299.  
  300. vx4'[t] ==
  301. (G m1 (x1[t]-x4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  302. (G m2 (x2[t]-x4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  303. (G m3 (x3[t]-x4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  304. (G m5 (x5[t]-x4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  305. (G m6 (x6[t]-x4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  306. (G m7 (x7[t]-x4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  307. If[q4 == 0, 0,
  308. (-q4*q1/(4Pi ε0 )/m4 (x1[t]-x4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  309. (-q4*q2/(4Pi ε0 )/m4 (x2[t]-x4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  310. (-q4*q3/(4Pi ε0 )/m4 (x3[t]-x4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  311. (-q4*q5/(4Pi ε0 )/m4 (x5[t]-x4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  312. (-q4*q6/(4Pi ε0 )/m4 (x6[t]-x4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  313. (-q4*q7/(4Pi ε0 )/m4 (x7[t]-x4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]]+
  314. Λ*c^2*x4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
  315.  
  316. vy4'[t] ==
  317. (G m1 (y1[t]-y4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  318. (G m2 (y2[t]-y4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  319. (G m3 (y3[t]-y4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  320. (G m5 (y5[t]-y4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  321. (G m6 (y6[t]-y4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  322. (G m7 (y7[t]-y4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  323. If[q4 == 0, 0,
  324. (-q4*q1/(4Pi ε0 )/m4 (y1[t]-y4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  325. (-q4*q2/(4Pi ε0 )/m4 (y2[t]-y4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  326. (-q4*q3/(4Pi ε0 )/m4 (y3[t]-y4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  327. (-q4*q5/(4Pi ε0 )/m4 (y5[t]-y4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  328. (-q4*q6/(4Pi ε0 )/m4 (y6[t]-y4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  329. (-q4*q7/(4Pi ε0 )/m4 (y7[t]-y4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]]+
  330. Λ*c^2*y4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
  331.  
  332. vz4'[t] ==
  333. (G m1 (z1[t]-z4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  334. (G m2 (z2[t]-z4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  335. (G m3 (z3[t]-z4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  336. (G m5 (z5[t]-z4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  337. (G m6 (z6[t]-z4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  338. (G m7 (z7[t]-z4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  339. If[q4 == 0, 0,
  340. (-q4*q1/(4Pi ε0 )/m4 (z1[t]-z4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  341. (-q4*q2/(4Pi ε0 )/m4 (z2[t]-z4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  342. (-q4*q3/(4Pi ε0 )/m4 (z3[t]-z4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  343. (-q4*q5/(4Pi ε0 )/m4 (z5[t]-z4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  344. (-q4*q6/(4Pi ε0 )/m4 (z6[t]-z4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  345. (-q4*q7/(4Pi ε0 )/m4 (z7[t]-z4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]]+
  346. Λ*c^2*z4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
  347.  
  348. vx5'[t] ==
  349. (G m1 (x1[t]-x5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  350. (G m2 (x2[t]-x5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  351. (G m3 (x3[t]-x5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  352. (G m4 (x4[t]-x5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  353. (G m6 (x6[t]-x5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  354. (G m7 (x7[t]-x5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  355. If[q5 == 0, 0,
  356. (-q5*q1/(4Pi ε0 )/m5 (x1[t]-x5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  357. (-q5*q2/(4Pi ε0 )/m5 (x2[t]-x5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  358. (-q5*q3/(4Pi ε0 )/m5 (x3[t]-x5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  359. (-q5*q4/(4Pi ε0 )/m5 (x4[t]-x5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  360. (-q5*q6/(4Pi ε0 )/m5 (x6[t]-x5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  361. (-q5*q7/(4Pi ε0 )/m5 (x7[t]-x5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]]+
  362. Λ*c^2*x5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
  363.  
  364. vy5'[t] ==
  365. (G m1 (y1[t]-y5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  366. (G m2 (y2[t]-y5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  367. (G m3 (y3[t]-y5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  368. (G m4 (y4[t]-y5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  369. (G m6 (y6[t]-y5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  370. (G m7 (y7[t]-y5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  371. If[q5 == 0, 0,
  372. (-q5*q1/(4Pi ε0 )/m5 (y1[t]-y5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  373. (-q5*q2/(4Pi ε0 )/m5 (y2[t]-y5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  374. (-q5*q3/(4Pi ε0 )/m5 (y3[t]-y5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  375. (-q5*q4/(4Pi ε0 )/m5 (y4[t]-y5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  376. (-q5*q6/(4Pi ε0 )/m5 (y6[t]-y5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  377. (-q5*q7/(4Pi ε0 )/m5 (y7[t]-y5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]]+
  378. Λ*c^2*y5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
  379.  
  380. vz5'[t] ==
  381. (G m1 (z1[t]-z5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  382. (G m2 (z2[t]-z5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  383. (G m3 (z3[t]-z5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  384. (G m4 (z4[t]-z5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  385. (G m6 (z6[t]-z5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  386. (G m7 (z7[t]-z5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  387. If[q5 == 0, 0,
  388. (-q5*q1/(4Pi ε0 )/m5 (z1[t]-z5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  389. (-q5*q2/(4Pi ε0 )/m5 (z2[t]-z5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  390. (-q5*q3/(4Pi ε0 )/m5 (z3[t]-z5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  391. (-q5*q4/(4Pi ε0 )/m5 (z4[t]-z5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  392. (-q5*q6/(4Pi ε0 )/m5 (z6[t]-z5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  393. (-q5*q7/(4Pi ε0 )/m5 (z7[t]-z5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]]+
  394. Λ*c^2*z5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
  395.  
  396. vx6'[t] ==
  397. (G m1 (x1[t]-x6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  398. (G m2 (x2[t]-x6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  399. (G m3 (x3[t]-x6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  400. (G m4 (x4[t]-x6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  401. (G m5 (x5[t]-x6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  402. (G m7 (x7[t]-x6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  403. If[q6 == 0, 0,
  404. (-q6*q1/(4Pi ε0 )/m6 (x1[t]-x6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  405. (-q6*q2/(4Pi ε0 )/m6 (x2[t]-x6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  406. (-q6*q3/(4Pi ε0 )/m6 (x3[t]-x6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  407. (-q6*q4/(4Pi ε0 )/m6 (x4[t]-x6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  408. (-q6*q5/(4Pi ε0 )/m6 (x5[t]-x6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  409. (-q6*q7/(4Pi ε0 )/m6 (x7[t]-x6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]]+
  410. Λ*c^2*x6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
  411.  
  412. vy6'[t] ==
  413. (G m1 (y1[t]-y6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  414. (G m2 (y2[t]-y6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  415. (G m3 (y3[t]-y6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  416. (G m4 (y4[t]-y6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  417. (G m5 (y5[t]-y6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  418. (G m7 (y7[t]-y6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  419. If[q6 == 0, 0,
  420. (-q6*q1/(4Pi ε0 )/m6 (y1[t]-y6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  421. (-q6*q2/(4Pi ε0 )/m6 (y2[t]-y6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  422. (-q6*q3/(4Pi ε0 )/m6 (y3[t]-y6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  423. (-q6*q4/(4Pi ε0 )/m6 (y4[t]-y6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  424. (-q6*q5/(4Pi ε0 )/m6 (y5[t]-y6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  425. (-q6*q7/(4Pi ε0 )/m6 (y7[t]-y6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]]+
  426. Λ*c^2*y6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
  427.  
  428. vz6'[t] ==
  429. (G m1 (z1[t]-z6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  430. (G m2 (z2[t]-z6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  431. (G m3 (z3[t]-z6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  432. (G m4 (z4[t]-z6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  433. (G m5 (z5[t]-z6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  434. (G m7 (z7[t]-z6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  435. If[q6 == 0, 0,
  436. (-q6*q1/(4Pi ε0 )/m6 (z1[t]-z6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  437. (-q6*q2/(4Pi ε0 )/m6 (z2[t]-z6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  438. (-q6*q3/(4Pi ε0 )/m6 (z3[t]-z6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  439. (-q6*q4/(4Pi ε0 )/m6 (z4[t]-z6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  440. (-q6*q5/(4Pi ε0 )/m6 (z5[t]-z6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  441. (-q6*q7/(4Pi ε0 )/m6 (z7[t]-z6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]]+
  442. Λ*c^2*z6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
  443.  
  444. vx7'[t] ==
  445. (G m1 (x1[t]-x7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  446. (G m2 (x2[t]-x7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  447. (G m3 (x3[t]-x7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  448. (G m4 (x4[t]-x7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  449. (G m5 (x5[t]-x7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  450. (G m6 (x6[t]-x7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  451. If[q7 == 0, 0,
  452. (-q7*q1/(4Pi ε0 )/m7 (x1[t]-x7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  453. (-q7*q2/(4Pi ε0 )/m7 (x2[t]-x7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  454. (-q7*q3/(4Pi ε0 )/m7 (x3[t]-x7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  455. (-q7*q4/(4Pi ε0 )/m7 (x4[t]-x7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  456. (-q7*q5/(4Pi ε0 )/m7 (x5[t]-x7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  457. (-q7*q6/(4Pi ε0 )/m7 (x6[t]-x7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]]+
  458. Λ*c^2*x7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
  459.  
  460. vy7'[t] ==
  461. (G m1 (y1[t]-y7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  462. (G m2 (y2[t]-y7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  463. (G m3 (y3[t]-y7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  464. (G m4 (y4[t]-y7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  465. (G m5 (y5[t]-y7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  466. (G m6 (y6[t]-y7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  467. If[q7 == 0, 0,
  468. (-q7*q1/(4Pi ε0 )/m7 (y1[t]-y7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  469. (-q7*q2/(4Pi ε0 )/m7 (y2[t]-y7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  470. (-q7*q3/(4Pi ε0 )/m7 (y3[t]-y7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  471. (-q7*q4/(4Pi ε0 )/m7 (y4[t]-y7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  472. (-q7*q5/(4Pi ε0 )/m7 (y5[t]-y7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  473. (-q7*q6/(4Pi ε0 )/m7 (y6[t]-y7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]]+
  474. Λ*c^2*y7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
  475.  
  476. vz7'[t] ==
  477. (G m1 (z1[t]-z7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  478. (G m2 (z2[t]-z7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  479. (G m3 (z3[t]-z7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  480. (G m4 (z4[t]-z7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  481. (G m5 (z5[t]-z7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  482. (G m6 (z6[t]-z7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  483. If[q7 == 0, 0,
  484. (-q7*q1/(4Pi ε0 )/m7 (z1[t]-z7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  485. (-q7*q2/(4Pi ε0 )/m7 (z2[t]-z7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  486. (-q7*q3/(4Pi ε0 )/m7 (z3[t]-z7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  487. (-q7*q4/(4Pi ε0 )/m7 (z4[t]-z7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  488. (-q7*q5/(4Pi ε0 )/m7 (z5[t]-z7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  489. (-q7*q6/(4Pi ε0 )/m7 (z6[t]-z7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]]+
  490. Λ*c^2*z7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
  491.  
  492. x1[0] == x1x, y1[0] == y1y, z1[0] == z1z,
  493. x2[0] == x2x, y2[0] == y2y, z2[0] == z2z,
  494. x3[0] == x3x, y3[0] == y3y, z3[0] == z3z,
  495. x4[0] == x4x, y4[0] == y4y, z4[0] == z4z,
  496. x5[0] == x5x, y5[0] == y5y, z5[0] == z5z,
  497. x6[0] == x6x, y6[0] == y6y, z6[0] == z6z,
  498. x7[0] == x7x, y7[0] == y7y, z7[0] == z7z,
  499.  
  500. vx1[0] == v1x, vy1[0] == v1y, vz1[0] == v1z,
  501. vx2[0] == v2x, vy2[0] == v2y, vz2[0] == v2z,
  502. vx3[0] == v3x, vy3[0] == v3y, vz3[0] == v3z,
  503. vx4[0] == v4x, vy4[0] == v4y, vz4[0] == v4z,
  504. vx5[0] == v5x, vy5[0] == v5y, vz5[0] == v5z,
  505. vx6[0] == v6x, vy6[0] == v6y, vz6[0] == v6z,
  506. vx7[0] == v7x, vy7[0] == v7y, vz7[0] == v7z},
  507.  
  508. {x1, x2, x3, x4, x5, x6, x7, y1, y2, y3, y4, y5, y6, y7, z1, z2, z3, z4, z5, z6, z7,
  509. vx1, vx2, vx3, vx4, vx5, vx6, vx7, vy1, vy2, vy3, vy4, vy5, vy6, vy7, vz1, vz2, vz3, vz4, vz5, vz6, vz7},
  510.  
  511. {t, 0, Tmax},
  512.  
  513. WorkingPrecision-> wp,
  514. MaxSteps-> Infinity,
  515. Method-> mta,
  516. InterpolationOrder-> All,
  517. StepMonitor :> (laststep=plunge; plunge=t;
  518. stepsize=plunge-laststep;), Method->{"EventLocator",
  519. "Event" :> (If[stepsize<1*^-4, 0, 1])}];
  520.  
  521. (* Position, Geschwindigkeit *)
  522.  
  523. f2p[t_]={{x1[t], y1[t], z1[t]}, {x2[t], y2[t], z2[t]}, {x3[t], y3[t], z3[t]}, {x4[t], y4[t], z4[t]}, {x5[t], y5[t], z5[t]}, {x6[t], y6[t], z6[t]}, {x7[t], y7[t], z7[t]}}/.nds[[1]];
  524. f2v[t_]={{vx1[t], vy1[t], vz1[t]}, {vx2[t], vy2[t], vz2[t]}, {vx3[t], vy3[t], vz3[t]}, {vx4[t], vy4[t], vz4[t]}, {vx5[t], vy5[t], vz5[t]}, {vx6[t], vy6[t], vz6[t]}, {vx7[t], vy7[t], vz7[t]}}/.nds[[1]];
  525. swp[t_]=(m1 Evaluate[f2p[t][[1]]]+m2 Evaluate[f2p[t][[2]]]+m3 Evaluate[f2p[t][[3]]]+m4 Evaluate[f2p[t][[4]]]+m5 Evaluate[f2p[t][[5]]]+m6 Evaluate[f2p[t][[6]]]+m7 Evaluate[f2p[t][[7]]])/(m1+m2+m3+m4+m5+m6+m7);
  526.  
  527. (* Formatierung *)
  528.  
  529. s[text_]=Style[text, FontSize->11];
  530. sw[text_]=Style[text, White, FontSize->11];
  531. colorfunc[n_]=Function[{x, y, z, t},
  532. Hue[0, n, 0.5,
  533. If[Tmax<0, Max[Min[(+T+(-t+trail))/trail, 1], 0],
  534. Max[Min[(-T+(t+trail))/trail, 1], 0]]]];
  535.  
  536. (* Animation *)
  537.  
  538. Do[Print[Rasterize[
  539. Grid[{{
  540. Show[
  541.  
  542. If[T == 0, {},
  543.  
  544. ParametricPlot3D[Evaluate[f2p[t]],
  545. {t, Max[0, T-trail], T},
  546.  
  547. PlotStyle->{
  548. {Thickness[thk], Red},
  549. {Thickness[thk], Blue},
  550. {Thickness[thk], Green},
  551. {Thickness[thk], Magenta},
  552. {Thickness[thk], Cyan},
  553. {Thickness[thk], Orange},
  554. {Thickness[thk], Purple}},
  555.  
  556. PlotRange->plotrange, AspectRatio->1, MaxRecursion->15, Axes->True, ImageSize->imagesize]],
  557.  
  558. Graphics3D[
  559. If[startpos==1, {
  560. {PointSize[2point/3], Lighter[Red], Point[{x1x, y1y, z1z}]},
  561. {PointSize[2point/3], Lighter[Blue], Point[{x2x, y2y, z2z}]},
  562. {PointSize[2point/3], Lighter[Green], Point[{x3x, y3y, z3z}]},
  563. {PointSize[2point/3], Lighter[Magenta], Point[{x4x, y4y, z4z}]},
  564. {PointSize[2point/3], Lighter[Cyan], Point[{x5x, y5y, z5z}]},
  565. {PointSize[2point/3], Lighter[Orange], Point[{x6x, y6y, z6z}]},
  566. {PointSize[2point/3], Lighter[Purple], Point[{x7x, y7y, z7z}]}
  567. }, {}],
  568.  
  569. PlotRange->plotrange, AspectRatio->1, Axes->True, ImageSize->imagesize],
  570.  
  571. Graphics3D[{PointSize[point], Red, Point[Evaluate[f2p[T]][[1]]]}],
  572. Graphics3D[{PointSize[point], Blue, Point[Evaluate[f2p[T]][[2]]]}],
  573. Graphics3D[{PointSize[point], Green, Point[Evaluate[f2p[T]][[3]]]}],
  574. Graphics3D[{PointSize[point], Magenta, Point[Evaluate[f2p[T]][[4]]]}],
  575. Graphics3D[{PointSize[point], Cyan, Point[Evaluate[f2p[T]][[5]]]}],
  576. Graphics3D[{PointSize[point], Orange, Point[Evaluate[f2p[T]][[6]]]}],
  577. Graphics3D[{PointSize[point], Purple, Point[Evaluate[f2p[T]][[7]]]}],
  578.  
  579. ViewPoint->viewpoint]},
  580.  
  581. { },
  582. {s["t"->N[T]], sw[1/2]},
  583. { },
  584. {s["p1{x,y,z}"-> Evaluate[f2p[T][[1]]]], sw[1/2]},
  585. {s["v1{x,y,z}"-> Evaluate[f2v[T][[1]]]], sw[1/2]},
  586. {s["v1{total}"->{Evaluate[Chop@Norm[f2v[T][[1]]]]}], sw[1/2]},
  587. { },
  588. {s["p2{x,y,z}"-> Evaluate[f2p[T][[2]]]], sw[1/2]},
  589. {s["v2{x,y,z}"-> Evaluate[f2v[T][[2]]]], sw[1/2]},
  590. {s["v2{total}"->{Evaluate[Chop@Norm[f2v[T][[2]]]]}], sw[1/2]},
  591. { },
  592. {s["p3{x,y,z}"-> Evaluate[f2p[T][[3]]]], sw[1/2]},
  593. {s["v3{x,y,z}"-> Evaluate[f2v[T][[3]]]], sw[1/2]},
  594. {s["v3{total}"->{Evaluate[Chop@Norm[f2v[T][[3]]]]}], sw[1/2]},
  595. { },
  596. {s["p4{x,y,z}"-> Evaluate[f2p[T][[4]]]], sw[1/2]},
  597. {s["v4{x,y,z}"-> Evaluate[f2v[T][[4]]]], sw[1/2]},
  598. {s["v4{total}"->{Evaluate[Chop@Norm[f2v[T][[4]]]]}], sw[1/2]},
  599. { },
  600. {s["p5{x,y,z}"-> Evaluate[f2p[T][[5]]]], sw[1/2]},
  601. {s["v5{x,y,z}"-> Evaluate[f2v[T][[5]]]], sw[1/2]},
  602. {s["v5{total}"->{Evaluate[Chop@Norm[f2v[T][[5]]]]}], sw[1/2]},
  603. { },
  604. {s["p6{x,y,z}"-> Evaluate[f2p[T][[6]]]], sw[1/2]},
  605. {s["v6{x,y,z}"-> Evaluate[f2v[T][[6]]]], sw[1/2]},
  606. {s["v6{total}"->{Evaluate[Chop@Norm[f2v[T][[6]]]]}], sw[1/2]},
  607. { },
  608. {s["p7{x,y,z}"-> Evaluate[f2p[T][[7]]]], sw[1/2]},
  609. {s["v7{x,y,z}"-> Evaluate[f2v[T][[7]]]], sw[1/2]},
  610. {s["v7{total}"->{Evaluate[Chop@Norm[f2v[T][[7]]]]}], sw[1/2]},
  611. { },
  612. {s["ps{x,y,z}"-> swp[T]], sw[1/2]},
  613. {s["vs{x,y,z}"-> swp'[T]], sw[1/2]},
  614. {s["vs{total}"->{Chop@Norm[swp'[T]]}], sw[1/2]}
  615. }, Alignment->Left]]],
  616.  
  617. (* Zeitregler *)
  618.  
  619. {T, 0, tMax, tMax/5}]
  620.  
  621. (* Export als HTML Dokument *)
  622. (* Export["dateiname.html", EvaluationNotebook[], "GraphicsOutput" -> "PNG"] *)
  623. (* Export direkt als Bildsequenz *)
  624. (* ParallelDo[Export["dateiname" <> ToString[T] <> ".png", Rasterize[...] ], {T, 0, 10, 5}] *)
  625.  
  626.  
  627.  
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