Gravity & Charge, 9 Body Simulator

Feb 19th, 2019 (edited)
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1. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
2. (* ||| Mathematica Syntax || yukterez.net || 9 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 = 50 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. (* Uranus *)
132.
133. m8 = +8.68103*^25 kg;
134. q8 = +0 Amp sek;
135.
136. x8x = +1.691367572961052*^+01 Au;
137. y8y = +1.040615964042521*^+01 Au;
138. z8z = -1.804702052122950*^-01 Au;
139.
140. v8x = -2.089933372733080*^-03 Au/dy;
141. v8y = +3.166549064213605*^-03 Au/dy;
142. v8z = +3.884093561739733*^-05 Au/dy;
143.
144. (* Neptun *)
145.
146. m9 = +1.02413*^26 kg;
147. q9 = +0 Amp sek;
148.
149. x9x = +2.901867480863295*^+01 Au;
150. y9y = -7.331260396521146*^+00 Au;
151. z9z = -5.177914737734761*^-01 Au;
152.
153. v9x = +7.476131405747911*^-04 Au/dy;
154. v9y = +3.062101642790218*^-03 Au/dy;
155. v9z = -8.000840096853115*^-05 Au/dy;
156.
157. (* Differentialgleichung *)
158.
159. nds=NDSolve[{
160.
161. x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t],
162. x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t],
163. x3'[t] == vx3[t], y3'[t] == vy3[t], z3'[t] == vz3[t],
164. x4'[t] == vx4[t], y4'[t] == vy4[t], z4'[t] == vz4[t],
165. x5'[t] == vx5[t], y5'[t] == vy5[t], z5'[t] == vz5[t],
166. x6'[t] == vx6[t], y6'[t] == vy6[t], z6'[t] == vz6[t],
167. x7'[t] == vx7[t], y7'[t] == vy7[t], z7'[t] == vz7[t],
168. x8'[t] == vx8[t], y8'[t] == vy8[t], z8'[t] == vz8[t],
169. x9'[t] == vx9[t], y9'[t] == vy9[t], z9'[t] == vz9[t],
170.
171. vx1'[t] ==
172. (G m2 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
173. (G m3 (x3[t]-x1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
174. (G m4 (x4[t]-x1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
175. (G m5 (x5[t]-x1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
176. (G m6 (x6[t]-x1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
177. (G m7 (x7[t]-x1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
178. (G m8 (x8[t]-x1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
179. (G m9 (x9[t]-x1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+
180. If[q1 == 0, 0,
181. (-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]+
182. (-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]+
183. (-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]+
184. (-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]+
185. (-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]+
186. (-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]+
187. (-q1*q8/(4Pi ε0 )/m1 (x8[t]-x1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
188. (-q1*q9/(4Pi ε0 )/m1 (x9[t]-x1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]]+
189. Λ*c^2*x1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
190.
191. vy1'[t] ==
192. (G m2 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
193. (G m3 (y3[t]-y1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
194. (G m4 (y4[t]-y1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
195. (G m5 (y5[t]-y1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
196. (G m6 (y6[t]-y1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
197. (G m7 (y7[t]-y1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
198. (G m8 (y8[t]-y1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
199. (G m9 (y9[t]-y1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+
200. If[q1 == 0, 0,
201. (-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]+
202. (-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]+
203. (-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]+
204. (-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]+
205. (-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]+
206. (-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]+
207. (-q1*q8/(4Pi ε0 )/m1 (y8[t]-y1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
208. (-q1*q9/(4Pi ε0 )/m1 (y9[t]-y1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]]+
209. Λ*c^2*y1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
210.
211. vz1'[t] ==
212. (G m2 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
213. (G m3 (z3[t]-z1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
214. (G m4 (z4[t]-z1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
215. (G m5 (z5[t]-z1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
216. (G m6 (z6[t]-z1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
217. (G m7 (z7[t]-z1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
218. (G m8 (z8[t]-z1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
219. (G m9 (z9[t]-z1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+
220. If[q1 == 0, 0,
221. (-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]+
222. (-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]+
223. (-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]+
224. (-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]+
225. (-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]+
226. (-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]+
227. (-q1*q8/(4Pi ε0 )/m1 (z8[t]-z1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
228. (-q1*q9/(4Pi ε0 )/m1 (z9[t]-z1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]]+
229. Λ*c^2*z1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
230.
231. vx2'[t] ==
232. (G m1 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
233. (G m3 (x3[t]-x2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
234. (G m4 (x4[t]-x2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
235. (G m5 (x5[t]-x2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
236. (G m6 (x6[t]-x2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
237. (G m7 (x7[t]-x2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
238. (G m8 (x8[t]-x2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
239. (G m9 (x9[t]-x2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+
240. If[q2 == 0, 0,
241. (-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]+
242. (-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]+
243. (-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]+
244. (-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]+
245. (-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]+
246. (-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]+
247. (-q2*q8/(4Pi ε0 )/m2 (x8[t]-x2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
248. (-q2*q9/(4Pi ε0 )/m2 (x9[t]-x2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]]+
249. Λ*c^2*x2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
250.
251. vy2'[t] ==
252. (G m1 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
253. (G m3 (y3[t]-y2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
254. (G m4 (y4[t]-y2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
255. (G m5 (y5[t]-y2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
256. (G m6 (y6[t]-y2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
257. (G m7 (y7[t]-y2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
258. (G m8 (y8[t]-y2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
259. (G m9 (y9[t]-y2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+
260. If[q2 == 0, 0,
261. (-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]+
262. (-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]+
263. (-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]+
264. (-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]+
265. (-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]+
266. (-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]+
267. (-q2*q8/(4Pi ε0 )/m2 (y8[t]-y2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
268. (-q2*q9/(4Pi ε0 )/m2 (y9[t]-y2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]]+
269. Λ*c^2*y2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
270.
271. vz2'[t] ==
272. (G m1 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
273. (G m3 (z3[t]-z2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
274. (G m4 (z4[t]-z2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
275. (G m5 (z5[t]-z2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
276. (G m6 (z6[t]-z2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
277. (G m7 (z7[t]-z2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
278. (G m8 (z8[t]-z2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
279. (G m9 (z9[t]-z2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+
280. If[q2 == 0, 0,
281. (-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]+
282. (-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]+
283. (-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]+
284. (-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]+
285. (-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]+
286. (-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]+
287. (-q2*q8/(4Pi ε0 )/m2 (z8[t]-z2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
288. (-q2*q9/(4Pi ε0 )/m2 (z9[t]-z2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]]+
289. Λ*c^2*z2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
290.
291. vx3'[t] ==
292. (G m1 (x1[t]-x3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
293. (G m2 (x2[t]-x3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
294. (G m4 (x4[t]-x3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
295. (G m5 (x5[t]-x3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
296. (G m6 (x6[t]-x3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
297. (G m7 (x7[t]-x3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
298. (G m8 (x8[t]-x3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
299. (G m9 (x9[t]-x3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+
300. If[q3 == 0, 0,
301. (-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]+
302. (-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]+
303. (-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]+
304. (-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]+
305. (-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]+
306. (-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]+
307. (-q3*q8/(4Pi ε0 )/m3 (x8[t]-x3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
308. (-q3*q9/(4Pi ε0 )/m3 (x9[t]-x3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]]+
309. Λ*c^2*x3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
310.
311. vy3'[t] ==
312. (G m1 (y1[t]-y3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
313. (G m2 (y2[t]-y3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
314. (G m4 (y4[t]-y3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
315. (G m5 (y5[t]-y3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
316. (G m6 (y6[t]-y3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
317. (G m7 (y7[t]-y3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
318. (G m8 (y8[t]-y3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
319. (G m9 (y9[t]-y3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+
320. If[q3 == 0, 0,
321. (-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]+
322. (-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]+
323. (-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]+
324. (-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]+
325. (-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]+
326. (-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]+
327. (-q3*q8/(4Pi ε0 )/m3 (y8[t]-y3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
328. (-q3*q9/(4Pi ε0 )/m3 (y9[t]-y3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]]+
329. Λ*c^2*y3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
330.
331. vz3'[t] ==
332. (G m1 (z1[t]-z3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
333. (G m2 (z2[t]-z3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
334. (G m4 (z4[t]-z3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
335. (G m5 (z5[t]-z3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
336. (G m6 (z6[t]-z3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
337. (G m7 (z7[t]-z3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
338. (G m8 (z8[t]-z3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
339. (G m9 (z9[t]-z3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+
340. If[q3 == 0, 0,
341. (-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]+
342. (-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]+
343. (-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]+
344. (-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]+
345. (-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]+
346. (-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]+
347. (-q3*q8/(4Pi ε0 )/m3 (z8[t]-z3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
348. (-q3*q9/(4Pi ε0 )/m3 (z9[t]-z3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]]+
349. Λ*c^2*z3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
350.
351. vx4'[t] ==
352. (G m1 (x1[t]-x4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
353. (G m2 (x2[t]-x4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
354. (G m3 (x3[t]-x4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
355. (G m5 (x5[t]-x4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
356. (G m6 (x6[t]-x4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
357. (G m7 (x7[t]-x4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
358. (G m8 (x8[t]-x4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
359. (G m9 (x9[t]-x4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+
360. If[q4 == 0, 0,
361. (-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]+
362. (-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]+
363. (-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]+
364. (-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]+
365. (-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]+
366. (-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]+
367. (-q4*q8/(4Pi ε0 )/m4 (x8[t]-x4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
368. (-q4*q9/(4Pi ε0 )/m4 (x9[t]-x4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]]+
369. Λ*c^2*x4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
370.
371. vy4'[t] ==
372. (G m1 (y1[t]-y4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
373. (G m2 (y2[t]-y4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
374. (G m3 (y3[t]-y4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
375. (G m5 (y5[t]-y4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
376. (G m6 (y6[t]-y4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
377. (G m7 (y7[t]-y4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
378. (G m8 (y8[t]-y4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
379. (G m9 (y9[t]-y4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+
380. If[q4 == 0, 0,
381. (-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]+
382. (-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]+
383. (-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]+
384. (-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]+
385. (-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]+
386. (-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]+
387. (-q4*q8/(4Pi ε0 )/m4 (y8[t]-y4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
388. (-q4*q9/(4Pi ε0 )/m4 (y9[t]-y4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]]+
389. Λ*c^2*y4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
390.
391. vz4'[t] ==
392. (G m1 (z1[t]-z4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
393. (G m2 (z2[t]-z4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
394. (G m3 (z3[t]-z4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
395. (G m5 (z5[t]-z4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
396. (G m6 (z6[t]-z4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
397. (G m7 (z7[t]-z4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
398. (G m8 (z8[t]-z4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
399. (G m9 (z9[t]-z4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+
400. If[q4 == 0, 0,
401. (-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]+
402. (-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]+
403. (-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]+
404. (-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]+
405. (-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]+
406. (-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]+
407. (-q4*q8/(4Pi ε0 )/m4 (z8[t]-z4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
408. (-q4*q9/(4Pi ε0 )/m4 (z9[t]-z4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]]+
409. Λ*c^2*z4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
410.
411. vx5'[t] ==
412. (G m1 (x1[t]-x5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
413. (G m2 (x2[t]-x5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
414. (G m3 (x3[t]-x5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
415. (G m4 (x4[t]-x5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
416. (G m6 (x6[t]-x5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
417. (G m7 (x7[t]-x5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
418. (G m8 (x8[t]-x5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
419. (G m9 (x9[t]-x5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+
420. If[q5 == 0, 0,
421. (-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]+
422. (-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]+
423. (-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]+
424. (-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]+
425. (-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]+
426. (-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]+
427. (-q5*q8/(4Pi ε0 )/m5 (x8[t]-x5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
428. (-q5*q9/(4Pi ε0 )/m5 (x9[t]-x5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]]+
429. Λ*c^2*x5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
430.
431. vy5'[t] ==
432. (G m1 (y1[t]-y5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
433. (G m2 (y2[t]-y5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
434. (G m3 (y3[t]-y5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
435. (G m4 (y4[t]-y5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
436. (G m6 (y6[t]-y5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
437. (G m7 (y7[t]-y5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
438. (G m8 (y8[t]-y5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
439. (G m9 (y9[t]-y5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+
440. If[q5 == 0, 0,
441. (-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]+
442. (-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]+
443. (-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]+
444. (-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]+
445. (-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]+
446. (-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]+
447. (-q5*q8/(4Pi ε0 )/m5 (y8[t]-y5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
448. (-q5*q9/(4Pi ε0 )/m5 (y9[t]-y5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]]+
449. Λ*c^2*y5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
450.
451. vz5'[t] ==
452. (G m1 (z1[t]-z5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
453. (G m2 (z2[t]-z5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
454. (G m3 (z3[t]-z5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
455. (G m4 (z4[t]-z5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
456. (G m6 (z6[t]-z5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
457. (G m7 (z7[t]-z5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
458. (G m8 (z8[t]-z5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
459. (G m9 (z9[t]-z5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+
460. If[q5 == 0, 0,
461. (-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]+
462. (-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]+
463. (-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]+
464. (-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]+
465. (-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]+
466. (-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]+
467. (-q5*q8/(4Pi ε0 )/m5 (z8[t]-z5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
468. (-q5*q9/(4Pi ε0 )/m5 (z9[t]-z5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]]+
469. Λ*c^2*z5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
470.
471. vx6'[t] ==
472. (G m1 (x1[t]-x6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
473. (G m2 (x2[t]-x6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
474. (G m3 (x3[t]-x6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
475. (G m4 (x4[t]-x6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
476. (G m5 (x5[t]-x6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
477. (G m7 (x7[t]-x6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
478. (G m8 (x8[t]-x6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
479. (G m9 (x9[t]-x6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+
480. If[q6 == 0, 0,
481. (-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]+
482. (-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]+
483. (-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]+
484. (-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]+
485. (-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]+
486. (-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]+
487. (-q6*q8/(4Pi ε0 )/m6 (x8[t]-x6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
488. (-q6*q9/(4Pi ε0 )/m6 (x9[t]-x6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]]+
489. Λ*c^2*x6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
490.
491. vy6'[t] ==
492. (G m1 (y1[t]-y6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
493. (G m2 (y2[t]-y6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
494. (G m3 (y3[t]-y6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
495. (G m4 (y4[t]-y6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
496. (G m5 (y5[t]-y6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
497. (G m7 (y7[t]-y6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
498. (G m8 (y8[t]-y6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
499. (G m9 (y9[t]-y6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+
500. If[q6 == 0, 0,
501. (-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]+
502. (-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]+
503. (-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]+
504. (-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]+
505. (-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]+
506. (-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]+
507. (-q6*q8/(4Pi ε0 )/m6 (y8[t]-y6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
508. (-q6*q9/(4Pi ε0 )/m6 (y9[t]-y6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]]+
509. Λ*c^2*y6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
510.
511. vz6'[t] ==
512. (G m1 (z1[t]-z6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
513. (G m2 (z2[t]-z6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
514. (G m3 (z3[t]-z6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
515. (G m4 (z4[t]-z6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
516. (G m5 (z5[t]-z6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
517. (G m7 (z7[t]-z6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
518. (G m8 (z8[t]-z6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
519. (G m9 (z9[t]-z6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+
520. If[q6 == 0, 0,
521. (-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]+
522. (-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]+
523. (-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]+
524. (-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]+
525. (-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]+
526. (-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]+
527. (-q6*q8/(4Pi ε0 )/m6 (z8[t]-z6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
528. (-q6*q9/(4Pi ε0 )/m6 (z9[t]-z6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]]+
529. Λ*c^2*z6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
530.
531. vx7'[t] ==
532. (G m1 (x1[t]-x7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
533. (G m2 (x2[t]-x7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
534. (G m3 (x3[t]-x7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
535. (G m4 (x4[t]-x7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
536. (G m5 (x5[t]-x7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
537. (G m6 (x6[t]-x7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
538. (G m8 (x8[t]-x7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
539. (G m9 (x9[t]-x7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+
540. If[q7 == 0, 0,
541. (-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]+
542. (-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]+
543. (-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]+
544. (-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]+
545. (-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]+
546. (-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]+
547. (-q7*q8/(4Pi ε0 )/m7 (x8[t]-x7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
548. (-q7*q9/(4Pi ε0 )/m7 (x9[t]-x7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]]+
549. Λ*c^2*x7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
550.
551. vy7'[t] ==
552. (G m1 (y1[t]-y7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
553. (G m2 (y2[t]-y7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
554. (G m3 (y3[t]-y7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
555. (G m4 (y4[t]-y7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
556. (G m5 (y5[t]-y7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
557. (G m6 (y6[t]-y7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
558. (G m8 (y8[t]-y7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
559. (G m9 (y9[t]-y7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+
560. If[q7 == 0, 0,
561. (-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]+
562. (-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]+
563. (-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]+
564. (-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]+
565. (-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]+
566. (-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]+
567. (-q7*q8/(4Pi ε0 )/m7 (y8[t]-y7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
568. (-q7*q9/(4Pi ε0 )/m7 (y9[t]-y7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]]+
569. Λ*c^2*y7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
570.
571. vz7'[t] ==
572. (G m1 (z1[t]-z7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
573. (G m2 (z2[t]-z7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
574. (G m3 (z3[t]-z7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
575. (G m4 (z4[t]-z7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
576. (G m5 (z5[t]-z7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
577. (G m6 (z6[t]-z7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
578. (G m8 (z8[t]-z7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
579. (G m9 (z9[t]-z7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+
580. If[q7 == 0, 0,
581. (-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]+
582. (-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]+
583. (-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]+
584. (-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]+
585. (-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]+
586. (-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]+
587. (-q7*q8/(4Pi ε0 )/m7 (z8[t]-z7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
588. (-q7*q9/(4Pi ε0 )/m7 (z9[t]-z7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]]+
589. Λ*c^2*z7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
590.
591. vx8'[t] ==
592. (G m1 (x1[t]-x8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
593. (G m2 (x2[t]-x8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
594. (G m3 (x3[t]-x8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
595. (G m4 (x4[t]-x8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
596. (G m5 (x5[t]-x8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
597. (G m6 (x6[t]-x8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
598. (G m7 (x7[t]-x8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
599. (G m9 (x9[t]-x8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+
600. If[q8 == 0, 0,
601. (-q8*q1/(4Pi ε0 )/m8 (x1[t]-x8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
602. (-q8*q2/(4Pi ε0 )/m8 (x2[t]-x8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
603. (-q8*q3/(4Pi ε0 )/m8 (x3[t]-x8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
604. (-q8*q4/(4Pi ε0 )/m8 (x4[t]-x8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
605. (-q8*q5/(4Pi ε0 )/m8 (x5[t]-x8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
606. (-q8*q6/(4Pi ε0 )/m8 (x6[t]-x8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
607. (-q8*q7/(4Pi ε0 )/m8 (x7[t]-x8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
608. (-q8*q9/(4Pi ε0 )/m8 (x9[t]-x8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]]+
609. Λ*c^2*x8[t]^2/Sqrt[x8[t]^2+y8[t]^2+z8[t]^2],
610.
611. vy8'[t] ==
612. (G m1 (y1[t]-y8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
613. (G m2 (y2[t]-y8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
614. (G m3 (y3[t]-y8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
615. (G m4 (y4[t]-y8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
616. (G m5 (y5[t]-y8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
617. (G m6 (y6[t]-y8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
618. (G m7 (y7[t]-y8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
619. (G m9 (y9[t]-y8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+
620. If[q8 == 0, 0,
621. (-q8*q1/(4Pi ε0 )/m8 (y1[t]-y8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
622. (-q8*q2/(4Pi ε0 )/m8 (y2[t]-y8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
623. (-q8*q3/(4Pi ε0 )/m8 (y3[t]-y8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
624. (-q8*q4/(4Pi ε0 )/m8 (y4[t]-y8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
625. (-q8*q5/(4Pi ε0 )/m8 (y5[t]-y8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
626. (-q8*q6/(4Pi ε0 )/m8 (y6[t]-y8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
627. (-q8*q7/(4Pi ε0 )/m8 (y7[t]-y8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
628. (-q8*q9/(4Pi ε0 )/m8 (y9[t]-y8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]]+
629. Λ*c^2*y8[t]^2/Sqrt[x8[t]^2+y8[t]^2+z8[t]^2],
630.
631. vz8'[t] ==
632. (G m1 (z1[t]-z8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
633. (G m2 (z2[t]-z8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
634. (G m3 (z3[t]-z8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
635. (G m4 (z4[t]-z8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
636. (G m5 (z5[t]-z8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
637. (G m6 (z6[t]-z8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
638. (G m7 (z7[t]-z8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
639. (G m9 (z9[t]-z8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+
640. If[q8 == 0, 0,
641. (-q8*q1/(4Pi ε0 )/m8 (z1[t]-z8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
642. (-q8*q2/(4Pi ε0 )/m8 (z2[t]-z8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
643. (-q8*q3/(4Pi ε0 )/m8 (z3[t]-z8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
644. (-q8*q4/(4Pi ε0 )/m8 (z4[t]-z8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
645. (-q8*q5/(4Pi ε0 )/m8 (z5[t]-z8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
646. (-q8*q6/(4Pi ε0 )/m8 (z6[t]-z8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
647. (-q8*q7/(4Pi ε0 )/m8 (z7[t]-z8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
648. (-q8*q9/(4Pi ε0 )/m8 (z9[t]-z8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]]+
649. Λ*c^2*z8[t]^2/Sqrt[x8[t]^2+y8[t]^2+z8[t]^2],
650.
651. vx9'[t] ==
652. (G m1 (x1[t]-x9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+
653. (G m2 (x2[t]-x9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+
654. (G m3 (x3[t]-x9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+
655. (G m4 (x4[t]-x9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+
656. (G m5 (x5[t]-x9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+
657. (G m6 (x6[t]-x9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+
658. (G m7 (x7[t]-x9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+
659. (G m8 (x8[t]-x9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+
660. If[q9 == 0, 0,
661. (-q9*q1/(4Pi ε0 )/m9 (x1[t]-x9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+
662. (-q9*q2/(4Pi ε0 )/m9 (x2[t]-x9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+
663. (-q9*q3/(4Pi ε0 )/m9 (x3[t]-x9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+
664. (-q9*q4/(4Pi ε0 )/m9 (x4[t]-x9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+
665. (-q9*q5/(4Pi ε0 )/m9 (x5[t]-x9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+
666. (-q9*q6/(4Pi ε0 )/m9 (x6[t]-x9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+
667. (-q9*q7/(4Pi ε0 )/m9 (x7[t]-x9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+
668. (-q9*q8/(4Pi ε0 )/m9 (x8[t]-x9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]]+
669. Λ*c^2*x9[t]^2/Sqrt[x9[t]^2+y9[t]^2+z9[t]^2],
670.
671. vy9'[t] ==
672. (G m1 (y1[t]-y9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+
673. (G m2 (y2[t]-y9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+
674. (G m3 (y3[t]-y9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+
675. (G m4 (y4[t]-y9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+
676. (G m5 (y5[t]-y9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+
677. (G m6 (y6[t]-y9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+
678. (G m7 (y7[t]-y9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+
679. (G m8 (y8[t]-y9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+
680. If[q9 == 0, 0,
681. (-q9*q1/(4Pi ε0 )/m9 (y1[t]-y9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+
682. (-q9*q2/(4Pi ε0 )/m9 (y2[t]-y9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+
683. (-q9*q3/(4Pi ε0 )/m9 (y3[t]-y9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+
684. (-q9*q4/(4Pi ε0 )/m9 (y4[t]-y9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+
685. (-q9*q5/(4Pi ε0 )/m9 (y5[t]-y9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+
686. (-q9*q6/(4Pi ε0 )/m9 (y6[t]-y9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+
687. (-q9*q7/(4Pi ε0 )/m9 (y7[t]-y9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+
688. (-q9*q8/(4Pi ε0 )/m9 (y8[t]-y9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]]+
689. Λ*c^2*y9[t]^2/Sqrt[x9[t]^2+y9[t]^2+z9[t]^2],
690.
691. vz9'[t] ==
692. (G m1 (z1[t]-z9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+
693. (G m2 (z2[t]-z9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+
694. (G m3 (z3[t]-z9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+
695. (G m4 (z4[t]-z9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+
696. (G m5 (z5[t]-z9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+
697. (G m6 (z6[t]-z9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+
698. (G m7 (z7[t]-z9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+
699. (G m8 (z8[t]-z9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+
700. If[q9 == 0, 0,
701. (-q9*q1/(4Pi ε0 )/m9 (z1[t]-z9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+
702. (-q9*q2/(4Pi ε0 )/m9 (z2[t]-z9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+
703. (-q9*q3/(4Pi ε0 )/m9 (z3[t]-z9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+
704. (-q9*q4/(4Pi ε0 )/m9 (z4[t]-z9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+
705. (-q9*q5/(4Pi ε0 )/m9 (z5[t]-z9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+
706. (-q9*q6/(4Pi ε0 )/m9 (z6[t]-z9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+
707. (-q9*q7/(4Pi ε0 )/m9 (z7[t]-z9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+
708. (-q9*q8/(4Pi ε0 )/m9 (z8[t]-z9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]]+
709. Λ*c^2*z9[t]^2/Sqrt[x9[t]^2+y9[t]^2+z9[t]^2],
710.
711. x1[0] == x1x, y1[0] == y1y, z1[0] == z1z,
712. x2[0] == x2x, y2[0] == y2y, z2[0] == z2z,
713. x3[0] == x3x, y3[0] == y3y, z3[0] == z3z,
714. x4[0] == x4x, y4[0] == y4y, z4[0] == z4z,
715. x5[0] == x5x, y5[0] == y5y, z5[0] == z5z,
716. x6[0] == x6x, y6[0] == y6y, z6[0] == z6z,
717. x7[0] == x7x, y7[0] == y7y, z7[0] == z7z,
718. x8[0] == x8x, y8[0] == y8y, z8[0] == z8z,
719. x9[0] == x9x, y9[0] == y9y, z9[0] == z9z,
720.
721. vx1[0] == v1x, vy1[0] == v1y, vz1[0] == v1z,
722. vx2[0] == v2x, vy2[0] == v2y, vz2[0] == v2z,
723. vx3[0] == v3x, vy3[0] == v3y, vz3[0] == v3z,
724. vx4[0] == v4x, vy4[0] == v4y, vz4[0] == v4z,
725. vx5[0] == v5x, vy5[0] == v5y, vz5[0] == v5z,
726. vx6[0] == v6x, vy6[0] == v6y, vz6[0] == v6z,
727. vx7[0] == v7x, vy7[0] == v7y, vz7[0] == v7z,
728. vx8[0] == v8x, vy8[0] == v8y, vz8[0] == v8z,
729. vx9[0] == v9x, vy9[0] == v9y, vz9[0] == v9z},
730.
731. {x1, x2, x3, x4, x5, x6, x7, x8, x9, y1, y2, y3, y4, y5, y6, y7, y8, y9, z1, z2, z3, z4, z5, z6, z7, z8, z9,
732. vx1, vx2, vx3, vx4, vx5, vx6, vx7, vx8, vx9, vy1, vy2, vy3, vy4, vy5, vy6, vy7, vy8, vy9, vz1, vz2, vz3, vz4, vz5, vz6, vz7, vz8, vz9},
733.
734. {t, 0, Tmax},
735.
736. WorkingPrecision-> wp,
737. MaxSteps-> Infinity,
738. Method-> mta,
739. InterpolationOrder-> All,
740. StepMonitor :> (laststep=plunge; plunge=t;
741. stepsize=plunge-laststep;), Method->{"EventLocator",
742. "Event" :> (If[stepsize<1*^-4, 0, 1])}];
743.
744. (* Position, Geschwindigkeit *)
745.
746. 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]}, {x8[t], y8[t], z8[t]}, {x9[t], y9[t], z9[t]}}/.nds[[1]];
747. 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]}, {vx8[t], vy8[t], vz8[t]}, {vx9[t], vy9[t], vz9[t]}}/.nds[[1]];
748. 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]]]+m8 Evaluate[f2p[t][[8]]]+m9 Evaluate[f2p[t][[9]]])/(m1+m2+m3+m4+m5+m6+m7+m8+m9);
749.
750. (* Formatierung *)
751.
752. s[text_]=Style[text, FontSize->11];
753. sw[text_]=Style[text, White, FontSize->11];
754. colorfunc[n_]=Function[{x, y, z, t},
755. Hue[0, n, 0.5,
756. If[Tmax<0, Max[Min[(+T+(-t+trail))/trail, 1], 0],
757. Max[Min[(-T+(t+trail))/trail, 1], 0]]]];
758.
759. (* Animation *)
760.
761. Do[Print[Rasterize[
762. Grid[{{
763. Show[
764.
765. If[T == 0, {},
766.
767. ParametricPlot3D[Evaluate[f2p[t]],
768. {t, Max[0, T-trail], T},
769.
770. PlotStyle->{
771. {Thickness[thk], Red},
772. {Thickness[thk], Blue},
773. {Thickness[thk], Green},
774. {Thickness[thk], Magenta},
775. {Thickness[thk], Cyan},
776. {Thickness[thk], Orange},
777. {Thickness[thk], Purple},
778. {Thickness[thk], Pink},
779. {Thickness[thk], Brown}},
780.
781. PlotRange->plotrange, AspectRatio->1, MaxRecursion->15, Axes->True, ImageSize->imagesize]],
782.
783. Graphics3D[
784. If[startpos==1, {
785. {PointSize[2point/3], Lighter[Red], Point[{x1x, y1y, z1z}]},
786. {PointSize[2point/3], Lighter[Blue], Point[{x2x, y2y, z2z}]},
787. {PointSize[2point/3], Lighter[Green], Point[{x3x, y3y, z3z}]},
788. {PointSize[2point/3], Lighter[Magenta], Point[{x4x, y4y, z4z}]},
789. {PointSize[2point/3], Lighter[Cyan], Point[{x5x, y5y, z5z}]},
790. {PointSize[2point/3], Lighter[Orange], Point[{x6x, y6y, z6z}]},
791. {PointSize[2point/3], Lighter[Purple], Point[{x7x, y7y, z7z}]},
792. {PointSize[2point/3], Lighter[Pink], Point[{x8x, y8y, z8z}]},
793. {PointSize[2point/3], Lighter[Brown], Point[{x9x, y9y, z9z}]}
794. }, {}],
795.
796. PlotRange->plotrange, AspectRatio->1, Axes->True, ImageSize->imagesize],
797.
798. Graphics3D[{PointSize[point], Red, Point[Evaluate[f2p[T]][[1]]]}],
799. Graphics3D[{PointSize[point], Blue, Point[Evaluate[f2p[T]][[2]]]}],
800. Graphics3D[{PointSize[point], Green, Point[Evaluate[f2p[T]][[3]]]}],
801. Graphics3D[{PointSize[point], Magenta, Point[Evaluate[f2p[T]][[4]]]}],
802. Graphics3D[{PointSize[point], Cyan, Point[Evaluate[f2p[T]][[5]]]}],
803. Graphics3D[{PointSize[point], Orange, Point[Evaluate[f2p[T]][[6]]]}],
804. Graphics3D[{PointSize[point], Purple, Point[Evaluate[f2p[T]][[7]]]}],
805. Graphics3D[{PointSize[point], Pink, Point[Evaluate[f2p[T]][[8]]]}],
806. Graphics3D[{PointSize[point], Brown, Point[Evaluate[f2p[T]][[9]]]}],
807.
808. ViewPoint->viewpoint]},
809.
810. { },
811. {s["t"->N[T]], sw[1/2]},
812. { },
813. {s["p1{x,y,z}"-> Evaluate[f2p[T][[1]]]], sw[1/2]},
814. {s["v1{x,y,z}"-> Evaluate[f2v[T][[1]]]], sw[1/2]},
815. {s["v1{total}"->{Evaluate[Chop@Norm[f2v[T][[1]]]]}], sw[1/2]},
816. { },
817. {s["p2{x,y,z}"-> Evaluate[f2p[T][[2]]]], sw[1/2]},
818. {s["v2{x,y,z}"-> Evaluate[f2v[T][[2]]]], sw[1/2]},
819. {s["v2{total}"->{Evaluate[Chop@Norm[f2v[T][[2]]]]}], sw[1/2]},
820. { },
821. {s["p3{x,y,z}"-> Evaluate[f2p[T][[3]]]], sw[1/2]},
822. {s["v3{x,y,z}"-> Evaluate[f2v[T][[3]]]], sw[1/2]},
823. {s["v3{total}"->{Evaluate[Chop@Norm[f2v[T][[3]]]]}], sw[1/2]},
824. { },
825. {s["p4{x,y,z}"-> Evaluate[f2p[T][[4]]]], sw[1/2]},
826. {s["v4{x,y,z}"-> Evaluate[f2v[T][[4]]]], sw[1/2]},
827. {s["v4{total}"->{Evaluate[Chop@Norm[f2v[T][[4]]]]}], sw[1/2]},
828. { },
829. {s["p5{x,y,z}"-> Evaluate[f2p[T][[5]]]], sw[1/2]},
830. {s["v5{x,y,z}"-> Evaluate[f2v[T][[5]]]], sw[1/2]},
831. {s["v5{total}"->{Evaluate[Chop@Norm[f2v[T][[5]]]]}], sw[1/2]},
832. { },
833. {s["p6{x,y,z}"-> Evaluate[f2p[T][[6]]]], sw[1/2]},
834. {s["v6{x,y,z}"-> Evaluate[f2v[T][[6]]]], sw[1/2]},
835. {s["v6{total}"->{Evaluate[Chop@Norm[f2v[T][[6]]]]}], sw[1/2]},
836. { },
837. {s["p7{x,y,z}"-> Evaluate[f2p[T][[7]]]], sw[1/2]},
838. {s["v7{x,y,z}"-> Evaluate[f2v[T][[7]]]], sw[1/2]},
839. {s["v7{total}"->{Evaluate[Chop@Norm[f2v[T][[7]]]]}], sw[1/2]},
840. { },
841. {s["p8{x,y,z}"-> Evaluate[f2p[T][[8]]]], sw[1/2]},
842. {s["v8{x,y,z}"-> Evaluate[f2v[T][[8]]]], sw[1/2]},
843. {s["v8{total}"->{Evaluate[Chop@Norm[f2v[T][[8]]]]}], sw[1/2]},
844. { },
845. {s["p9{x,y,z}"-> Evaluate[f2p[T][[9]]]], sw[1/2]},
846. {s["v9{x,y,z}"-> Evaluate[f2v[T][[9]]]], sw[1/2]},
847. {s["v9{total}"->{Evaluate[Chop@Norm[f2v[T][[9]]]]}], sw[1/2]},
848. { },
849. {s["ps{x,y,z}"-> swp[T]], sw[1/2]},
850. {s["vs{x,y,z}"-> swp'[T]], sw[1/2]},
851. {s["vs{total}"->{Chop@Norm[swp'[T]]}], sw[1/2]}
852. }, Alignment->Left]]],
853.
854. (* Zeitregler *)
855.
856. {T, 0, tMax, tMax/5}]
857.
858. (* Export als HTML Dokument *)
859. (* Export["dateiname.html", EvaluationNotebook[], "GraphicsOutput" -> "PNG"] *)
860. (* Export direkt als Bildsequenz *)
861. (* ParallelDo[Export["dateiname" <> ToString[T] <> ".png", Rasterize[...] ], {T, 0, 10, 5}] *)
862.
863.
864.
865.
866.
867.
868.
869.
870.
RAW Paste Data