## Merkurs Periheldrehung

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### Merkurs Periheldrehung

Dieser Beitrag ist ein Unterkapitel von nbody.yukterez.net und schwarzschild.yukterez.net

1) Newton (von der Wechselwirkung mit den anderen Planeten stammender Anteil)

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`(* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)(* ||| Mathematica Syntax || yukterez.net || n Body Newtonian Mass & Charge Simulator ||| *)(* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)ClearAll["Global`*"]; ClearAll["Local`*"];Needs["DifferentialEquations`NDSolveProblems`"];Needs["DifferentialEquations`NDSolveUtilities`"];Amp = 1; kg = 1; m = 1; sek = 1; km = 1000 m; (* SI Einheiten *) mt1 = {"StiffnessSwitching", Method-> {"ExplicitRungeKutta", Automatic}};mt2 = {"ImplicitRungeKutta", "DifferenceOrder"-> 20};mt3 = {"EquationSimplification"-> "Residual"};mt0 = Automatic;mta = mt2;wp  = MachinePrecision; (* Zeitrahmen *)T1   = (1697-2019) yr;T2   = (1848-2019) yr;T0   = Min[T1, T2]-50 yr;(* Konstanten *) G   = 667384/10^16 m^3/kg/sek^2;ε0  = 8854187817*^-21 Amp^2 sek^4/kg/m^3;c   = 299792458 m/sek;Au  = 149597870700 m;dy  = 24*3600 sek;yr  = 36525*dy/100;                                               (* Ephemeriden vom 19.02.2019, 0:00:00 TDB *)(* Sonne *)m1  = +1.988435*^30 kg;q1  = +77 Amp sek;x1x = -1.147196570503204*^-03 Au;y1y = +7.515074431920434*^-03 Au;z1z = -4.730273651193038*^-05 Au;v1x = -8.107931162902937*^-06 Au/dy;v1y = +1.520849732928662*^-06 Au/dy;v1z = +2.095554598567427*^-07 Au/dy; (* Merkur *)m2  = +3.30104*^23 kg;q2  = +0 Amp sek; x2x = +2.493682187528474*^-01 Au;y2y = +2.060848667278006*^-01 Au;z2z = -6.803162776737710*^-03 Au;v2x = -2.301828852252654*^-02 Au/dy;v2y = +2.326003199133993*^-02 Au/dy;v2z = +4.011640539083395*^-03 Au/dy; (* Venus *)m3  = +4.86732*^24 kg;q3  = +0 Amp sek; x3x = -5.604572600267276*^-01 Au;y3y = -4.500554270408416*^-01 Au;z3z = +2.595073246894732*^-02 Au;v3x = +1.265689462094818*^-02 Au/dy;v3y = -1.574829638876520*^-02 Au/dy;v3z = -9.467652690844731*^-04 Au/dy; (* Erde + Mond *)m4  = +5.9721986*^24 kg+7.3459*^22 kg;q4  = +0 Amp sek;x4x = -8.552072163834489*^-01 Au;y4y = +5.049715021822364*^-01 Au;z4z = -6.849877545851131*^-05 Au;v4x = -8.942912568116291*^-03 Au/dy;v4y = -1.492365678503182*^-02 Au/dy;v4z = +2.741178622694643*^-07 Au/dy; (* Mars *)m5  = +6.41693*^23 kg;q5  = +0 Amp sek; x5x = +5.580724605736193*^-01 Au;y5y = +1.416261572201534*^+00 Au;z5z = +1.574925082740965*^-02 Au;v5x = -1.248544019487808*^-02 Au/dy;v5y = +6.355083417008326*^-03 Au/dy;v5z = +4.394992947386628*^-04 Au/dy; (* Jupiter *)m6  = +1.89813*^27 kg;q6  = +0 Amp sek; x6x = -1.795821860926694*^+00 Au;y6y = -5.016469167174772*^+00 Au;z6z = +6.097587180308248*^-02 Au; v6x = +7.014525824256318*^-03 Au/dy;v6y = -2.183010990796764*^-03 Au/dy;v6z = -1.478090774743338*^-04 Au/dy;(* Saturn *)m7  = +5.68319*^26 kg;q7  = +0 Amp sek;x7x = +2.211165351380597*^+00 Au;y7y = -9.803846216723874*^+00 Au;z7z = +8.244475037063657*^-02 Au;v7x = +5.133965065556525*^-03 Au/dy;v7y = +1.210333590471664*^-03 Au/dy;v7z = -2.255855621236429*^-04 Au/dy;(* Uranus *)m8  = +8.68103*^25 kg;q8  = +0 Amp sek;x8x = +1.691367572961052*^+01 Au;y8y = +1.040615964042521*^+01 Au;z8z = -1.804702052122950*^-01 Au;v8x = -2.089933372733080*^-03 Au/dy;v8y = +3.166549064213605*^-03 Au/dy;v8z = +3.884093561739733*^-05 Au/dy;(* Neptun *)m9  = +1.02413*^26 kg;q9  = +0 Amp sek;x9x = +2.901867480863295*^+01 Au;y9y = -7.331260396521146*^+00 Au;z9z = -5.177914737734761*^-01 Au;v9x = +7.476131405747911*^-04 Au/dy;v9y = +3.062101642790218*^-03 Au/dy;v9z = -8.000840096853115*^-05 Au/dy;(* Pluto + Charon *)m0  = +1.303*^22 kg+1.586*^21 kg;q0  = +0 Amp sek;x0x = +1.202894612500549*^+01 Au;y0y = -3.151878221568063*^+01 Au;z0z = -1.067812248721266*^-01 Au;v0x = +3.004427922255182*^-03 Au/dy;v0y = +4.501898344345873*^-04 Au/dy;v0z = -9.299030165680609*^-04 Au/dy; (* Differentialgleichung *) nds=NDSolve[{ x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t], x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t], x3'[t] == vx3[t], y3'[t] == vy3[t], z3'[t] == vz3[t], x4'[t] == vx4[t], y4'[t] == vy4[t], z4'[t] == vz4[t], x5'[t] == vx5[t], y5'[t] == vy5[t], z5'[t] == vz5[t], x6'[t] == vx6[t], y6'[t] == vy6[t], z6'[t] == vz6[t], x7'[t] == vx7[t], y7'[t] == vy7[t], z7'[t] == vz7[t], x8'[t] == vx8[t], y8'[t] == vy8[t], z8'[t] == vz8[t], x9'[t] == vx9[t], y9'[t] == vy9[t], z9'[t] == vz9[t], x0'[t] == vx0[t], y0'[t] == vy0[t], z0'[t] == vz0[t],  vx1'[t] ==(G m2 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+(G m3 (x3[t]-x1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+(G m4 (x4[t]-x1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+(G m5 (x5[t]-x1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+(G m6 (x6[t]-x1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+(G m7 (x7[t]-x1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+(G m8 (x8[t]-x1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+(G m9 (x9[t]-x1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+(G m0 (x0[t]-x1[t]))/Sqrt[((x0[t]-x1[t])^2+(y0[t]-y1[t])^2+(z0[t]-z1[t])^2)^3]+If[q1 == 0, 0, (-q1*q2/(4π ε0 )/m1 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+(-q1*q3/(4π ε0 )/m1 (x3[t]-x1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+(-q1*q4/(4π ε0 )/m1 (x4[t]-x1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+(-q1*q5/(4π ε0 )/m1 (x5[t]-x1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+(-q1*q6/(4π ε0 )/m1 (x6[t]-x1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+(-q1*q7/(4π ε0 )/m1 (x7[t]-x1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+(-q1*q8/(4π ε0 )/m1 (x8[t]-x1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+(-q1*q9/(4π ε0 )/m1 (x9[t]-x1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+(-q1*q0/(4π ε0 )/m1 (x0[t]-x1[t]))/Sqrt[((x0[t]-x1[t])^2+(y0[t]-y1[t])^2+(z0[t]-z1[t])^2)^3]],  vy1'[t] ==(G m2 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+(G m3 (y3[t]-y1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+(G m4 (y4[t]-y1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+(G m5 (y5[t]-y1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+(G m6 (y6[t]-y1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+(G m7 (y7[t]-y1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+(G m8 (y8[t]-y1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+(G m9 (y9[t]-y1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+(G m0 (y0[t]-y1[t]))/Sqrt[((x0[t]-x1[t])^2+(y0[t]-y1[t])^2+(z0[t]-z1[t])^2)^3]+If[q1 == 0, 0, (-q1*q2/(4π ε0 )/m1 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+(-q1*q3/(4π ε0 )/m1 (y3[t]-y1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+(-q1*q4/(4π ε0 )/m1 (y4[t]-y1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+(-q1*q5/(4π ε0 )/m1 (y5[t]-y1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+(-q1*q6/(4π ε0 )/m1 (y6[t]-y1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+(-q1*q7/(4π ε0 )/m1 (y7[t]-y1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+(-q1*q8/(4π ε0 )/m1 (y8[t]-y1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+(-q1*q9/(4π ε0 )/m1 (y9[t]-y1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+(-q1*q0/(4π ε0 )/m1 (y0[t]-y1[t]))/Sqrt[((x0[t]-x1[t])^2+(y0[t]-y1[t])^2+(z0[t]-z1[t])^2)^3]],  vz1'[t] ==(G m2 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+(G m3 (z3[t]-z1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+(G m4 (z4[t]-z1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+(G m5 (z5[t]-z1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+(G m6 (z6[t]-z1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+(G m7 (z7[t]-z1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+(G m8 (z8[t]-z1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+(G m9 (z9[t]-z1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+(G m0 (z0[t]-z1[t]))/Sqrt[((x0[t]-x1[t])^2+(y0[t]-y1[t])^2+(z0[t]-z1[t])^2)^3]+If[q1 == 0, 0, (-q1*q2/(4π ε0 )/m1 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+(-q1*q3/(4π ε0 )/m1 (z3[t]-z1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+(-q1*q4/(4π ε0 )/m1 (z4[t]-z1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+(-q1*q5/(4π ε0 )/m1 (z5[t]-z1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+(-q1*q6/(4π ε0 )/m1 (z6[t]-z1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+(-q1*q7/(4π ε0 )/m1 (z7[t]-z1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+(-q1*q8/(4π ε0 )/m1 (z8[t]-z1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+(-q1*q9/(4π ε0 )/m1 (z9[t]-z1[t]))/Sqrt[((x9[t]-x1[t])^2+(y9[t]-y1[t])^2+(z9[t]-z1[t])^2)^3]+(-q1*q0/(4π ε0 )/m1 (z0[t]-z1[t]))/Sqrt[((x0[t]-x1[t])^2+(y0[t]-y1[t])^2+(z0[t]-z1[t])^2)^3]],  vx2'[t] ==(G m1 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+(G m3 (x3[t]-x2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+(G m4 (x4[t]-x2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+(G m5 (x5[t]-x2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+(G m6 (x6[t]-x2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+(G m7 (x7[t]-x2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+(G m8 (x8[t]-x2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+(G m9 (x9[t]-x2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+(G m0 (x0[t]-x2[t]))/Sqrt[((x0[t]-x2[t])^2+(y0[t]-y2[t])^2+(z0[t]-z2[t])^2)^3]+If[q2 == 0, 0, (-q2*q1/(4π ε0 )/m2 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+(-q2*q3/(4π ε0 )/m2 (x3[t]-x2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+(-q2*q4/(4π ε0 )/m2 (x4[t]-x2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+(-q2*q5/(4π ε0 )/m2 (x5[t]-x2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+(-q2*q6/(4π ε0 )/m2 (x6[t]-x2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+(-q2*q7/(4π ε0 )/m2 (x7[t]-x2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+(-q2*q8/(4π ε0 )/m2 (x8[t]-x2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+(-q2*q9/(4π ε0 )/m2 (x9[t]-x2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+(-q2*q0/(4π ε0 )/m2 (x0[t]-x2[t]))/Sqrt[((x0[t]-x2[t])^2+(y0[t]-y2[t])^2+(z0[t]-z2[t])^2)^3]],  vy2'[t] ==(G m1 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+(G m3 (y3[t]-y2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+(G m4 (y4[t]-y2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+(G m5 (y5[t]-y2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+(G m6 (y6[t]-y2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+(G m7 (y7[t]-y2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+(G m8 (y8[t]-y2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+(G m9 (y9[t]-y2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+(G m0 (y0[t]-y2[t]))/Sqrt[((x0[t]-x2[t])^2+(y0[t]-y2[t])^2+(z0[t]-z2[t])^2)^3]+If[q2 == 0, 0, (-q2*q1/(4π ε0 )/m2 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+(-q2*q3/(4π ε0 )/m2 (y3[t]-y2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+(-q2*q4/(4π ε0 )/m2 (y4[t]-y2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+(-q2*q5/(4π ε0 )/m2 (y5[t]-y2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+(-q2*q6/(4π ε0 )/m2 (y6[t]-y2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+(-q2*q7/(4π ε0 )/m2 (y7[t]-y2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+(-q2*q8/(4π ε0 )/m2 (y8[t]-y2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+(-q2*q9/(4π ε0 )/m2 (y9[t]-y2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+(-q2*q0/(4π ε0 )/m2 (y0[t]-y2[t]))/Sqrt[((x0[t]-x2[t])^2+(y0[t]-y2[t])^2+(z0[t]-z2[t])^2)^3]],  vz2'[t] ==(G m1 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+(G m3 (z3[t]-z2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+(G m4 (z4[t]-z2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+(G m5 (z5[t]-z2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+(G m6 (z6[t]-z2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+(G m7 (z7[t]-z2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+(G m8 (z8[t]-z2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+(G m9 (z9[t]-z2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+(G m0 (z0[t]-z2[t]))/Sqrt[((x0[t]-x2[t])^2+(y0[t]-y2[t])^2+(z0[t]-z2[t])^2)^3]+If[q2 == 0, 0, (-q2*q1/(4π ε0 )/m2 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+(-q2*q3/(4π ε0 )/m2 (z3[t]-z2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+(-q2*q4/(4π ε0 )/m2 (z4[t]-z2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+(-q2*q5/(4π ε0 )/m2 (z5[t]-z2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+(-q2*q6/(4π ε0 )/m2 (z6[t]-z2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+(-q2*q7/(4π ε0 )/m2 (z7[t]-z2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+(-q2*q8/(4π ε0 )/m2 (z8[t]-z2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+(-q2*q9/(4π ε0 )/m2 (z9[t]-z2[t]))/Sqrt[((x9[t]-x2[t])^2+(y9[t]-y2[t])^2+(z9[t]-z2[t])^2)^3]+(-q2*q0/(4π ε0 )/m2 (z0[t]-z2[t]))/Sqrt[((x0[t]-x2[t])^2+(y0[t]-y2[t])^2+(z0[t]-z2[t])^2)^3]],  vx3'[t] ==(G m1 (x1[t]-x3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+(G m2 (x2[t]-x3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+(G m4 (x4[t]-x3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+(G m5 (x5[t]-x3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+(G m6 (x6[t]-x3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+(G m7 (x7[t]-x3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+(G m8 (x8[t]-x3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+(G m9 (x9[t]-x3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+(G m0 (x0[t]-x3[t]))/Sqrt[((x0[t]-x3[t])^2+(y0[t]-y3[t])^2+(z0[t]-z3[t])^2)^3]+If[q3 == 0, 0, (-q3*q1/(4π ε0 )/m3 (x1[t]-x3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+(-q3*q2/(4π ε0 )/m3 (x2[t]-x3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+(-q3*q4/(4π ε0 )/m3 (x4[t]-x3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+(-q3*q5/(4π ε0 )/m3 (x5[t]-x3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+(-q3*q6/(4π ε0 )/m3 (x6[t]-x3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+(-q3*q7/(4π ε0 )/m3 (x7[t]-x3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+(-q3*q8/(4π ε0 )/m3 (x8[t]-x3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+(-q3*q9/(4π ε0 )/m3 (x9[t]-x3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+(-q3*q0/(4π ε0 )/m3 (x0[t]-x3[t]))/Sqrt[((x0[t]-x3[t])^2+(y0[t]-y3[t])^2+(z0[t]-z3[t])^2)^3]],  vy3'[t] ==(G m1 (y1[t]-y3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+(G m2 (y2[t]-y3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+(G m4 (y4[t]-y3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+(G m5 (y5[t]-y3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+(G m6 (y6[t]-y3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+(G m7 (y7[t]-y3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+(G m8 (y8[t]-y3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+(G m9 (y9[t]-y3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+(G m0 (y0[t]-y3[t]))/Sqrt[((x0[t]-x3[t])^2+(y0[t]-y3[t])^2+(z0[t]-z3[t])^2)^3]+If[q3 == 0, 0, (-q3*q1/(4π ε0 )/m3 (y1[t]-y3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+(-q3*q2/(4π ε0 )/m3 (y2[t]-y3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+(-q3*q4/(4π ε0 )/m3 (y4[t]-y3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+(-q3*q5/(4π ε0 )/m3 (y5[t]-y3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+(-q3*q6/(4π ε0 )/m3 (y6[t]-y3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+(-q3*q7/(4π ε0 )/m3 (y7[t]-y3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+(-q3*q8/(4π ε0 )/m3 (y8[t]-y3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+(-q3*q9/(4π ε0 )/m3 (y9[t]-y3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+(-q3*q0/(4π ε0 )/m3 (y0[t]-y3[t]))/Sqrt[((x0[t]-x3[t])^2+(y0[t]-y3[t])^2+(z0[t]-z3[t])^2)^3]],  vz3'[t] ==(G m1 (z1[t]-z3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+(G m2 (z2[t]-z3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+(G m4 (z4[t]-z3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+(G m5 (z5[t]-z3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+(G m6 (z6[t]-z3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+(G m7 (z7[t]-z3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+(G m8 (z8[t]-z3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+(G m9 (z9[t]-z3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+(G m0 (z0[t]-z3[t]))/Sqrt[((x0[t]-x3[t])^2+(y0[t]-y3[t])^2+(z0[t]-z3[t])^2)^3]+If[q3 == 0, 0, (-q3*q1/(4π ε0 )/m3 (z1[t]-z3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+(-q3*q2/(4π ε0 )/m3 (z2[t]-z3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+(-q3*q4/(4π ε0 )/m3 (z4[t]-z3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+(-q3*q5/(4π ε0 )/m3 (z5[t]-z3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+(-q3*q6/(4π ε0 )/m3 (z6[t]-z3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+(-q3*q7/(4π ε0 )/m3 (z7[t]-z3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+(-q3*q8/(4π ε0 )/m3 (z8[t]-z3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+(-q3*q9/(4π ε0 )/m3 (z9[t]-z3[t]))/Sqrt[((x9[t]-x3[t])^2+(y9[t]-y3[t])^2+(z9[t]-z3[t])^2)^3]+(-q3*q0/(4π ε0 )/m3 (z0[t]-z3[t]))/Sqrt[((x0[t]-x3[t])^2+(y0[t]-y3[t])^2+(z0[t]-z3[t])^2)^3]],  vx4'[t] ==(G m1 (x1[t]-x4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+(G m2 (x2[t]-x4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+(G m3 (x3[t]-x4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+(G m5 (x5[t]-x4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+(G m6 (x6[t]-x4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+(G m7 (x7[t]-x4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+(G m8 (x8[t]-x4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+(G m9 (x9[t]-x4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+(G m0 (x0[t]-x4[t]))/Sqrt[((x0[t]-x4[t])^2+(y0[t]-y4[t])^2+(z0[t]-z4[t])^2)^3]+If[q4 == 0, 0, (-q4*q1/(4π ε0 )/m4 (x1[t]-x4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+(-q4*q2/(4π ε0 )/m4 (x2[t]-x4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+(-q4*q3/(4π ε0 )/m4 (x3[t]-x4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+(-q4*q5/(4π ε0 )/m4 (x5[t]-x4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+(-q4*q6/(4π ε0 )/m4 (x6[t]-x4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+(-q4*q7/(4π ε0 )/m4 (x7[t]-x4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+(-q4*q8/(4π ε0 )/m4 (x8[t]-x4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+(-q4*q9/(4π ε0 )/m4 (x9[t]-x4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+(-q4*q0/(4π ε0 )/m4 (x0[t]-x4[t]))/Sqrt[((x0[t]-x4[t])^2+(y0[t]-y4[t])^2+(z0[t]-z4[t])^2)^3]],  vy4'[t] ==(G m1 (y1[t]-y4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+(G m2 (y2[t]-y4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+(G m3 (y3[t]-y4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+(G m5 (y5[t]-y4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+(G m6 (y6[t]-y4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+(G m7 (y7[t]-y4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+(G m8 (y8[t]-y4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+(G m9 (y9[t]-y4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+(G m0 (y0[t]-y4[t]))/Sqrt[((x0[t]-x4[t])^2+(y0[t]-y4[t])^2+(z0[t]-z4[t])^2)^3]+If[q4 == 0, 0, (-q4*q1/(4π ε0 )/m4 (y1[t]-y4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+(-q4*q2/(4π ε0 )/m4 (y2[t]-y4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+(-q4*q3/(4π ε0 )/m4 (y3[t]-y4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+(-q4*q5/(4π ε0 )/m4 (y5[t]-y4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+(-q4*q6/(4π ε0 )/m4 (y6[t]-y4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+(-q4*q7/(4π ε0 )/m4 (y7[t]-y4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+(-q4*q8/(4π ε0 )/m4 (y8[t]-y4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+(-q4*q9/(4π ε0 )/m4 (y9[t]-y4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+(-q4*q0/(4π ε0 )/m4 (y0[t]-y4[t]))/Sqrt[((x0[t]-x4[t])^2+(y0[t]-y4[t])^2+(z0[t]-z4[t])^2)^3]],  vz4'[t] ==(G m1 (z1[t]-z4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+(G m2 (z2[t]-z4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+(G m3 (z3[t]-z4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+(G m5 (z5[t]-z4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+(G m6 (z6[t]-z4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+(G m7 (z7[t]-z4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+(G m8 (z8[t]-z4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+(G m9 (z9[t]-z4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+(G m0 (z0[t]-z4[t]))/Sqrt[((x0[t]-x4[t])^2+(y0[t]-y4[t])^2+(z0[t]-z4[t])^2)^3]+If[q4 == 0, 0, (-q4*q1/(4π ε0 )/m4 (z1[t]-z4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+(-q4*q2/(4π ε0 )/m4 (z2[t]-z4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+(-q4*q3/(4π ε0 )/m4 (z3[t]-z4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+(-q4*q5/(4π ε0 )/m4 (z5[t]-z4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+(-q4*q6/(4π ε0 )/m4 (z6[t]-z4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+(-q4*q7/(4π ε0 )/m4 (z7[t]-z4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+(-q4*q8/(4π ε0 )/m4 (z8[t]-z4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+(-q4*q9/(4π ε0 )/m4 (z9[t]-z4[t]))/Sqrt[((x9[t]-x4[t])^2+(y9[t]-y4[t])^2+(z9[t]-z4[t])^2)^3]+(-q4*q0/(4π ε0 )/m4 (z0[t]-z4[t]))/Sqrt[((x0[t]-x4[t])^2+(y0[t]-y4[t])^2+(z0[t]-z4[t])^2)^3]],  vx5'[t] ==(G m1 (x1[t]-x5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+(G m2 (x2[t]-x5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+(G m3 (x3[t]-x5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+(G m4 (x4[t]-x5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+(G m6 (x6[t]-x5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+(G m7 (x7[t]-x5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+(G m8 (x8[t]-x5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+(G m9 (x9[t]-x5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+(G m0 (x0[t]-x5[t]))/Sqrt[((x0[t]-x5[t])^2+(y0[t]-y5[t])^2+(z0[t]-z5[t])^2)^3]+If[q5 == 0, 0, (-q5*q1/(4π ε0 )/m5 (x1[t]-x5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+(-q5*q2/(4π ε0 )/m5 (x2[t]-x5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+(-q5*q3/(4π ε0 )/m5 (x3[t]-x5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+(-q5*q4/(4π ε0 )/m5 (x4[t]-x5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+(-q5*q6/(4π ε0 )/m5 (x6[t]-x5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+(-q5*q7/(4π ε0 )/m5 (x7[t]-x5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+(-q5*q8/(4π ε0 )/m5 (x8[t]-x5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+(-q5*q9/(4π ε0 )/m5 (x9[t]-x5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+(-q5*q0/(4π ε0 )/m5 (x0[t]-x5[t]))/Sqrt[((x0[t]-x5[t])^2+(y0[t]-y5[t])^2+(z0[t]-z5[t])^2)^3]],  vy5'[t] ==(G m1 (y1[t]-y5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+(G m2 (y2[t]-y5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+(G m3 (y3[t]-y5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+(G m4 (y4[t]-y5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+(G m6 (y6[t]-y5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+(G m7 (y7[t]-y5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+(G m8 (y8[t]-y5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+(G m9 (y9[t]-y5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+(G m0 (y0[t]-y5[t]))/Sqrt[((x0[t]-x5[t])^2+(y0[t]-y5[t])^2+(z0[t]-z5[t])^2)^3]+If[q5 == 0, 0, (-q5*q1/(4π ε0 )/m5 (y1[t]-y5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+(-q5*q2/(4π ε0 )/m5 (y2[t]-y5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+(-q5*q3/(4π ε0 )/m5 (y3[t]-y5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+(-q5*q4/(4π ε0 )/m5 (y4[t]-y5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+(-q5*q6/(4π ε0 )/m5 (y6[t]-y5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+(-q5*q7/(4π ε0 )/m5 (y7[t]-y5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+(-q5*q8/(4π ε0 )/m5 (y8[t]-y5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+(-q5*q9/(4π ε0 )/m5 (y9[t]-y5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+(-q5*q0/(4π ε0 )/m5 (y0[t]-y5[t]))/Sqrt[((x0[t]-x5[t])^2+(y0[t]-y5[t])^2+(z0[t]-z5[t])^2)^3]],  vz5'[t] ==(G m1 (z1[t]-z5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+(G m2 (z2[t]-z5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+(G m3 (z3[t]-z5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+(G m4 (z4[t]-z5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+(G m6 (z6[t]-z5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+(G m7 (z7[t]-z5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+(G m8 (z8[t]-z5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+(G m9 (z9[t]-z5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+(G m0 (z0[t]-z5[t]))/Sqrt[((x0[t]-x5[t])^2+(y0[t]-y5[t])^2+(z0[t]-z5[t])^2)^3]+If[q5 == 0, 0, (-q5*q1/(4π ε0 )/m5 (z1[t]-z5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+(-q5*q2/(4π ε0 )/m5 (z2[t]-z5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+(-q5*q3/(4π ε0 )/m5 (z3[t]-z5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+(-q5*q4/(4π ε0 )/m5 (z4[t]-z5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+(-q5*q6/(4π ε0 )/m5 (z6[t]-z5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+(-q5*q7/(4π ε0 )/m5 (z7[t]-z5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+(-q5*q8/(4π ε0 )/m5 (z8[t]-z5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+(-q5*q9/(4π ε0 )/m5 (z9[t]-z5[t]))/Sqrt[((x9[t]-x5[t])^2+(y9[t]-y5[t])^2+(z9[t]-z5[t])^2)^3]+(-q5*q0/(4π ε0 )/m5 (z0[t]-z5[t]))/Sqrt[((x0[t]-x5[t])^2+(y0[t]-y5[t])^2+(z0[t]-z5[t])^2)^3]], vx6'[t] ==(G m1 (x1[t]-x6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+(G m2 (x2[t]-x6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+(G m3 (x3[t]-x6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+(G m4 (x4[t]-x6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+(G m5 (x5[t]-x6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+(G m7 (x7[t]-x6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+(G m8 (x8[t]-x6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+(G m9 (x9[t]-x6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+(G m0 (x0[t]-x6[t]))/Sqrt[((x0[t]-x6[t])^2+(y0[t]-y6[t])^2+(z0[t]-z6[t])^2)^3]+If[q6 == 0, 0, (-q6*q1/(4π ε0 )/m6 (x1[t]-x6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+(-q6*q2/(4π ε0 )/m6 (x2[t]-x6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+(-q6*q3/(4π ε0 )/m6 (x3[t]-x6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+(-q6*q4/(4π ε0 )/m6 (x4[t]-x6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+(-q6*q5/(4π ε0 )/m6 (x5[t]-x6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+(-q6*q7/(4π ε0 )/m6 (x7[t]-x6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+(-q6*q8/(4π ε0 )/m6 (x8[t]-x6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+(-q6*q9/(4π ε0 )/m6 (x9[t]-x6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+(-q6*q0/(4π ε0 )/m6 (x0[t]-x6[t]))/Sqrt[((x0[t]-x6[t])^2+(y0[t]-y6[t])^2+(z0[t]-z6[t])^2)^3]],  vy6'[t] ==(G m1 (y1[t]-y6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+(G m2 (y2[t]-y6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+(G m3 (y3[t]-y6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+(G m4 (y4[t]-y6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+(G m5 (y5[t]-y6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+(G m7 (y7[t]-y6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+(G m8 (y8[t]-y6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+(G m9 (y9[t]-y6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+(G m0 (y0[t]-y6[t]))/Sqrt[((x0[t]-x6[t])^2+(y0[t]-y6[t])^2+(z0[t]-z6[t])^2)^3]+If[q6 == 0, 0, (-q6*q1/(4π ε0 )/m6 (y1[t]-y6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+(-q6*q2/(4π ε0 )/m6 (y2[t]-y6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+(-q6*q3/(4π ε0 )/m6 (y3[t]-y6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+(-q6*q4/(4π ε0 )/m6 (y4[t]-y6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+(-q6*q5/(4π ε0 )/m6 (y5[t]-y6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+(-q6*q7/(4π ε0 )/m6 (y7[t]-y6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+(-q6*q8/(4π ε0 )/m6 (y8[t]-y6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+(-q6*q9/(4π ε0 )/m6 (y9[t]-y6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+(-q6*q0/(4π ε0 )/m6 (y0[t]-y6[t]))/Sqrt[((x0[t]-x6[t])^2+(y0[t]-y6[t])^2+(z0[t]-z6[t])^2)^3]],  vz6'[t] ==(G m1 (z1[t]-z6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+(G m2 (z2[t]-z6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+(G m3 (z3[t]-z6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+(G m4 (z4[t]-z6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+(G m5 (z5[t]-z6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+(G m7 (z7[t]-z6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+(G m8 (z8[t]-z6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+(G m9 (z9[t]-z6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+(G m0 (z0[t]-z6[t]))/Sqrt[((x0[t]-x6[t])^2+(y0[t]-y6[t])^2+(z0[t]-z6[t])^2)^3]+If[q6 == 0, 0, (-q6*q1/(4π ε0 )/m6 (z1[t]-z6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+(-q6*q2/(4π ε0 )/m6 (z2[t]-z6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+(-q6*q3/(4π ε0 )/m6 (z3[t]-z6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+(-q6*q4/(4π ε0 )/m6 (z4[t]-z6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+(-q6*q5/(4π ε0 )/m6 (z5[t]-z6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+(-q6*q7/(4π ε0 )/m6 (z7[t]-z6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+(-q6*q8/(4π ε0 )/m6 (z8[t]-z6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+(-q6*q9/(4π ε0 )/m6 (z9[t]-z6[t]))/Sqrt[((x9[t]-x6[t])^2+(y9[t]-y6[t])^2+(z9[t]-z6[t])^2)^3]+(-q6*q0/(4π ε0 )/m6 (z0[t]-z6[t]))/Sqrt[((x0[t]-x6[t])^2+(y0[t]-y6[t])^2+(z0[t]-z6[t])^2)^3]], vx7'[t] ==(G m1 (x1[t]-x7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+(G m2 (x2[t]-x7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+(G m3 (x3[t]-x7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+(G m4 (x4[t]-x7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+(G m5 (x5[t]-x7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+(G m6 (x6[t]-x7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+(G m8 (x8[t]-x7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+(G m9 (x9[t]-x7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+(G m0 (x0[t]-x7[t]))/Sqrt[((x0[t]-x7[t])^2+(y0[t]-y7[t])^2+(z0[t]-z7[t])^2)^3]+If[q7 == 0, 0, (-q7*q1/(4π ε0 )/m7 (x1[t]-x7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+(-q7*q2/(4π ε0 )/m7 (x2[t]-x7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+(-q7*q3/(4π ε0 )/m7 (x3[t]-x7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+(-q7*q4/(4π ε0 )/m7 (x4[t]-x7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+(-q7*q5/(4π ε0 )/m7 (x5[t]-x7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+(-q7*q6/(4π ε0 )/m7 (x6[t]-x7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+(-q7*q8/(4π ε0 )/m7 (x8[t]-x7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+(-q7*q9/(4π ε0 )/m7 (x9[t]-x7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+(-q7*q0/(4π ε0 )/m7 (x0[t]-x7[t]))/Sqrt[((x0[t]-x7[t])^2+(y0[t]-y7[t])^2+(z0[t]-z7[t])^2)^3]],  vy7'[t] ==(G m1 (y1[t]-y7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+(G m2 (y2[t]-y7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+(G m3 (y3[t]-y7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+(G m4 (y4[t]-y7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+(G m5 (y5[t]-y7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+(G m6 (y6[t]-y7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+(G m8 (y8[t]-y7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+(G m9 (y9[t]-y7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+(G m0 (y0[t]-y7[t]))/Sqrt[((x0[t]-x7[t])^2+(y0[t]-y7[t])^2+(z0[t]-z7[t])^2)^3]+If[q7 == 0, 0, (-q7*q1/(4π ε0 )/m7 (y1[t]-y7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+(-q7*q2/(4π ε0 )/m7 (y2[t]-y7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+(-q7*q3/(4π ε0 )/m7 (y3[t]-y7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+(-q7*q4/(4π ε0 )/m7 (y4[t]-y7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+(-q7*q5/(4π ε0 )/m7 (y5[t]-y7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+(-q7*q6/(4π ε0 )/m7 (y6[t]-y7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+(-q7*q8/(4π ε0 )/m7 (y8[t]-y7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+(-q7*q9/(4π ε0 )/m7 (y9[t]-y7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+(-q7*q0/(4π ε0 )/m7 (y0[t]-y7[t]))/Sqrt[((x0[t]-x7[t])^2+(y0[t]-y7[t])^2+(z0[t]-z7[t])^2)^3]],  vz7'[t] ==(G m1 (z1[t]-z7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+(G m2 (z2[t]-z7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+(G m3 (z3[t]-z7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+(G m4 (z4[t]-z7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+(G m5 (z5[t]-z7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+(G m6 (z6[t]-z7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+(G m8 (z8[t]-z7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+(G m9 (z9[t]-z7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+(G m0 (z0[t]-z7[t]))/Sqrt[((x0[t]-x7[t])^2+(y0[t]-y7[t])^2+(z0[t]-z7[t])^2)^3]+If[q7 == 0, 0, (-q7*q1/(4π ε0 )/m7 (z1[t]-z7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+(-q7*q2/(4π ε0 )/m7 (z2[t]-z7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+(-q7*q3/(4π ε0 )/m7 (z3[t]-z7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+(-q7*q4/(4π ε0 )/m7 (z4[t]-z7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+(-q7*q5/(4π ε0 )/m7 (z5[t]-z7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+(-q7*q6/(4π ε0 )/m7 (z6[t]-z7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+(-q7*q8/(4π ε0 )/m7 (z8[t]-z7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+(-q7*q9/(4π ε0 )/m7 (z9[t]-z7[t]))/Sqrt[((x9[t]-x7[t])^2+(y9[t]-y7[t])^2+(z9[t]-z7[t])^2)^3]+(-q7*q0/(4π ε0 )/m7 (z0[t]-z7[t]))/Sqrt[((x0[t]-x7[t])^2+(y0[t]-y7[t])^2+(z0[t]-z7[t])^2)^3]], vx8'[t] ==(G m1 (x1[t]-x8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+(G m2 (x2[t]-x8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+(G m3 (x3[t]-x8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+(G m4 (x4[t]-x8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+(G m5 (x5[t]-x8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+(G m6 (x6[t]-x8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+(G m7 (x7[t]-x8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+(G m9 (x9[t]-x8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+(G m0 (x0[t]-x8[t]))/Sqrt[((x0[t]-x8[t])^2+(y0[t]-y8[t])^2+(z0[t]-z8[t])^2)^3]+If[q8 == 0, 0, (-q8*q1/(4π ε0 )/m8 (x1[t]-x8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+(-q8*q2/(4π ε0 )/m8 (x2[t]-x8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+(-q8*q3/(4π ε0 )/m8 (x3[t]-x8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+(-q8*q4/(4π ε0 )/m8 (x4[t]-x8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+(-q8*q5/(4π ε0 )/m8 (x5[t]-x8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+(-q8*q6/(4π ε0 )/m8 (x6[t]-x8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+(-q8*q7/(4π ε0 )/m8 (x7[t]-x8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+(-q8*q9/(4π ε0 )/m8 (x9[t]-x8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+(-q8*q0/(4π ε0 )/m8 (x0[t]-x8[t]))/Sqrt[((x0[t]-x8[t])^2+(y0[t]-y8[t])^2+(z0[t]-z8[t])^2)^3]],  vy8'[t] ==(G m1 (y1[t]-y8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+(G m2 (y2[t]-y8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+(G m3 (y3[t]-y8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+(G m4 (y4[t]-y8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+(G m5 (y5[t]-y8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+(G m6 (y6[t]-y8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+(G m7 (y7[t]-y8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+(G m9 (y9[t]-y8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+(G m0 (y0[t]-y8[t]))/Sqrt[((x0[t]-x8[t])^2+(y0[t]-y8[t])^2+(z0[t]-z8[t])^2)^3]+If[q8 == 0, 0, (-q8*q1/(4π ε0 )/m8 (y1[t]-y8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+(-q8*q2/(4π ε0 )/m8 (y2[t]-y8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+(-q8*q3/(4π ε0 )/m8 (y3[t]-y8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+(-q8*q4/(4π ε0 )/m8 (y4[t]-y8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+(-q8*q5/(4π ε0 )/m8 (y5[t]-y8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+(-q8*q6/(4π ε0 )/m8 (y6[t]-y8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+(-q8*q7/(4π ε0 )/m8 (y7[t]-y8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+(-q8*q9/(4π ε0 )/m8 (y9[t]-y8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+(-q8*q0/(4π ε0 )/m8 (y0[t]-y8[t]))/Sqrt[((x0[t]-x8[t])^2+(y0[t]-y8[t])^2+(z0[t]-z8[t])^2)^3]],  vz8'[t] ==(G m1 (z1[t]-z8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+(G m2 (z2[t]-z8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+(G m3 (z3[t]-z8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+(G m4 (z4[t]-z8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+(G m5 (z5[t]-z8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+(G m6 (z6[t]-z8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+(G m7 (z7[t]-z8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+(G m9 (z9[t]-z8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+(G m0 (z0[t]-z8[t]))/Sqrt[((x0[t]-x8[t])^2+(y0[t]-y8[t])^2+(z0[t]-z8[t])^2)^3]+If[q8 == 0, 0, (-q8*q1/(4π ε0 )/m8 (z1[t]-z8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+(-q8*q2/(4π ε0 )/m8 (z2[t]-z8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+(-q8*q3/(4π ε0 )/m8 (z3[t]-z8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+(-q8*q4/(4π ε0 )/m8 (z4[t]-z8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+(-q8*q5/(4π ε0 )/m8 (z5[t]-z8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+(-q8*q6/(4π ε0 )/m8 (z6[t]-z8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+(-q8*q7/(4π ε0 )/m8 (z7[t]-z8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+(-q8*q9/(4π ε0 )/m8 (z9[t]-z8[t]))/Sqrt[((x9[t]-x8[t])^2+(y9[t]-y8[t])^2+(z9[t]-z8[t])^2)^3]+(-q8*q0/(4π ε0 )/m8 (z0[t]-z8[t]))/Sqrt[((x0[t]-x8[t])^2+(y0[t]-y8[t])^2+(z0[t]-z8[t])^2)^3]], vx9'[t] ==(G m1 (x1[t]-x9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+(G m2 (x2[t]-x9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+(G m3 (x3[t]-x9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+(G m4 (x4[t]-x9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+(G m5 (x5[t]-x9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+(G m6 (x6[t]-x9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+(G m7 (x7[t]-x9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+(G m8 (x8[t]-x9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+(G m0 (x0[t]-x9[t]))/Sqrt[((x0[t]-x9[t])^2+(y0[t]-y9[t])^2+(z0[t]-z9[t])^2)^3]+If[q9 == 0, 0, (-q9*q1/(4π ε0 )/m9 (x1[t]-x9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+(-q9*q2/(4π ε0 )/m9 (x2[t]-x9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+(-q9*q3/(4π ε0 )/m9 (x3[t]-x9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+(-q9*q4/(4π ε0 )/m9 (x4[t]-x9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+(-q9*q5/(4π ε0 )/m9 (x5[t]-x9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+(-q9*q6/(4π ε0 )/m9 (x6[t]-x9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+(-q9*q7/(4π ε0 )/m9 (x7[t]-x9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+(-q9*q8/(4π ε0 )/m9 (x8[t]-x9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+(-q9*q0/(4π ε0 )/m9 (x0[t]-x9[t]))/Sqrt[((x0[t]-x9[t])^2+(y0[t]-y9[t])^2+(z0[t]-z9[t])^2)^3]],  vy9'[t] ==(G m1 (y1[t]-y9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+(G m2 (y2[t]-y9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+(G m3 (y3[t]-y9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+(G m4 (y4[t]-y9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+(G m5 (y5[t]-y9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+(G m6 (y6[t]-y9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+(G m7 (y7[t]-y9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+(G m8 (y8[t]-y9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+(G m0 (y0[t]-y9[t]))/Sqrt[((x0[t]-x9[t])^2+(y0[t]-y9[t])^2+(z0[t]-z9[t])^2)^3]+If[q9 == 0, 0, (-q9*q1/(4π ε0 )/m9 (y1[t]-y9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+(-q9*q2/(4π ε0 )/m9 (y2[t]-y9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+(-q9*q3/(4π ε0 )/m9 (y3[t]-y9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+(-q9*q4/(4π ε0 )/m9 (y4[t]-y9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+(-q9*q5/(4π ε0 )/m9 (y5[t]-y9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+(-q9*q6/(4π ε0 )/m9 (y6[t]-y9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+(-q9*q7/(4π ε0 )/m9 (y7[t]-y9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+(-q9*q8/(4π ε0 )/m9 (y8[t]-y9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+(-q9*q0/(4π ε0 )/m9 (y0[t]-y9[t]))/Sqrt[((x0[t]-x9[t])^2+(y0[t]-y9[t])^2+(z0[t]-z9[t])^2)^3]],  vz9'[t] ==(G m1 (z1[t]-z9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+(G m2 (z2[t]-z9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+(G m3 (z3[t]-z9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+(G m4 (z4[t]-z9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+(G m5 (z5[t]-z9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+(G m6 (z6[t]-z9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+(G m7 (z7[t]-z9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+(G m8 (z8[t]-z9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+(G m0 (z0[t]-z9[t]))/Sqrt[((x0[t]-x9[t])^2+(y0[t]-y9[t])^2+(z0[t]-z9[t])^2)^3]+If[q9 == 0, 0, (-q9*q1/(4π ε0 )/m9 (z1[t]-z9[t]))/Sqrt[((x1[t]-x9[t])^2+(y1[t]-y9[t])^2+(z1[t]-z9[t])^2)^3]+(-q9*q2/(4π ε0 )/m9 (z2[t]-z9[t]))/Sqrt[((x2[t]-x9[t])^2+(y2[t]-y9[t])^2+(z2[t]-z9[t])^2)^3]+(-q9*q3/(4π ε0 )/m9 (z3[t]-z9[t]))/Sqrt[((x3[t]-x9[t])^2+(y3[t]-y9[t])^2+(z3[t]-z9[t])^2)^3]+(-q9*q4/(4π ε0 )/m9 (z4[t]-z9[t]))/Sqrt[((x4[t]-x9[t])^2+(y4[t]-y9[t])^2+(z4[t]-z9[t])^2)^3]+(-q9*q5/(4π ε0 )/m9 (z5[t]-z9[t]))/Sqrt[((x5[t]-x9[t])^2+(y5[t]-y9[t])^2+(z5[t]-z9[t])^2)^3]+(-q9*q6/(4π ε0 )/m9 (z6[t]-z9[t]))/Sqrt[((x6[t]-x9[t])^2+(y6[t]-y9[t])^2+(z6[t]-z9[t])^2)^3]+(-q9*q7/(4π ε0 )/m9 (z7[t]-z9[t]))/Sqrt[((x7[t]-x9[t])^2+(y7[t]-y9[t])^2+(z7[t]-z9[t])^2)^3]+(-q9*q8/(4π ε0 )/m9 (z8[t]-z9[t]))/Sqrt[((x8[t]-x9[t])^2+(y8[t]-y9[t])^2+(z8[t]-z9[t])^2)^3]+(-q9*q0/(4π ε0 )/m9 (z0[t]-z9[t]))/Sqrt[((x0[t]-x9[t])^2+(y0[t]-y9[t])^2+(z0[t]-z9[t])^2)^3]], vx0'[t] ==(G m1 (x1[t]-x0[t]))/Sqrt[((x1[t]-x0[t])^2+(y1[t]-y0[t])^2+(z1[t]-z0[t])^2)^3]+(G m2 (x2[t]-x0[t]))/Sqrt[((x2[t]-x0[t])^2+(y2[t]-y0[t])^2+(z2[t]-z0[t])^2)^3]+(G m3 (x3[t]-x0[t]))/Sqrt[((x3[t]-x0[t])^2+(y3[t]-y0[t])^2+(z3[t]-z0[t])^2)^3]+(G m4 (x4[t]-x0[t]))/Sqrt[((x4[t]-x0[t])^2+(y4[t]-y0[t])^2+(z4[t]-z0[t])^2)^3]+(G m5 (x5[t]-x0[t]))/Sqrt[((x5[t]-x0[t])^2+(y5[t]-y0[t])^2+(z5[t]-z0[t])^2)^3]+(G m6 (x6[t]-x0[t]))/Sqrt[((x6[t]-x0[t])^2+(y6[t]-y0[t])^2+(z6[t]-z0[t])^2)^3]+(G m7 (x7[t]-x0[t]))/Sqrt[((x7[t]-x0[t])^2+(y7[t]-y0[t])^2+(z7[t]-z0[t])^2)^3]+(G m8 (x8[t]-x0[t]))/Sqrt[((x8[t]-x0[t])^2+(y8[t]-y0[t])^2+(z8[t]-z0[t])^2)^3]+(G m9 (x9[t]-x0[t]))/Sqrt[((x9[t]-x0[t])^2+(y9[t]-y0[t])^2+(z9[t]-z0[t])^2)^3]+If[q0 == 0, 0, (-q0*q1/(4π ε0 )/m0 (x1[t]-x0[t]))/Sqrt[((x1[t]-x0[t])^2+(y1[t]-y0[t])^2+(z1[t]-z0[t])^2)^3]+(-q0*q2/(4π ε0 )/m0 (x2[t]-x0[t]))/Sqrt[((x2[t]-x0[t])^2+(y2[t]-y0[t])^2+(z2[t]-z0[t])^2)^3]+(-q0*q3/(4π ε0 )/m0 (x3[t]-x0[t]))/Sqrt[((x3[t]-x0[t])^2+(y3[t]-y0[t])^2+(z3[t]-z0[t])^2)^3]+(-q0*q4/(4π ε0 )/m0 (x4[t]-x0[t]))/Sqrt[((x4[t]-x0[t])^2+(y4[t]-y0[t])^2+(z4[t]-z0[t])^2)^3]+(-q0*q5/(4π ε0 )/m0 (x5[t]-x0[t]))/Sqrt[((x5[t]-x0[t])^2+(y5[t]-y0[t])^2+(z5[t]-z0[t])^2)^3]+(-q0*q6/(4π ε0 )/m0 (x6[t]-x0[t]))/Sqrt[((x6[t]-x0[t])^2+(y6[t]-y0[t])^2+(z6[t]-z0[t])^2)^3]+(-q0*q7/(4π ε0 )/m0 (x7[t]-x0[t]))/Sqrt[((x7[t]-x0[t])^2+(y7[t]-y0[t])^2+(z7[t]-z0[t])^2)^3]+(-q0*q8/(4π ε0 )/m0 (x8[t]-x0[t]))/Sqrt[((x8[t]-x0[t])^2+(y8[t]-y0[t])^2+(z8[t]-z0[t])^2)^3]+(-q0*q9/(4π ε0 )/m0 (x9[t]-x0[t]))/Sqrt[((x9[t]-x0[t])^2+(y9[t]-y0[t])^2+(z9[t]-z0[t])^2)^3]],  vy0'[t] ==(G m1 (y1[t]-y0[t]))/Sqrt[((x1[t]-x0[t])^2+(y1[t]-y0[t])^2+(z1[t]-z0[t])^2)^3]+(G m2 (y2[t]-y0[t]))/Sqrt[((x2[t]-x0[t])^2+(y2[t]-y0[t])^2+(z2[t]-z0[t])^2)^3]+(G m3 (y3[t]-y0[t]))/Sqrt[((x3[t]-x0[t])^2+(y3[t]-y0[t])^2+(z3[t]-z0[t])^2)^3]+(G m4 (y4[t]-y0[t]))/Sqrt[((x4[t]-x0[t])^2+(y4[t]-y0[t])^2+(z4[t]-z0[t])^2)^3]+(G m5 (y5[t]-y0[t]))/Sqrt[((x5[t]-x0[t])^2+(y5[t]-y0[t])^2+(z5[t]-z0[t])^2)^3]+(G m6 (y6[t]-y0[t]))/Sqrt[((x6[t]-x0[t])^2+(y6[t]-y0[t])^2+(z6[t]-z0[t])^2)^3]+(G m7 (y7[t]-y0[t]))/Sqrt[((x7[t]-x0[t])^2+(y7[t]-y0[t])^2+(z7[t]-z0[t])^2)^3]+(G m8 (y8[t]-y0[t]))/Sqrt[((x8[t]-x0[t])^2+(y8[t]-y0[t])^2+(z8[t]-z0[t])^2)^3]+(G m9 (y9[t]-y0[t]))/Sqrt[((x9[t]-x0[t])^2+(y9[t]-y0[t])^2+(z9[t]-z0[t])^2)^3]+If[q0 == 0, 0, (-q0*q1/(4π ε0 )/m0 (y1[t]-y0[t]))/Sqrt[((x1[t]-x0[t])^2+(y1[t]-y0[t])^2+(z1[t]-z0[t])^2)^3]+(-q0*q2/(4π ε0 )/m0 (y2[t]-y0[t]))/Sqrt[((x2[t]-x0[t])^2+(y2[t]-y0[t])^2+(z2[t]-z0[t])^2)^3]+(-q0*q3/(4π ε0 )/m0 (y3[t]-y0[t]))/Sqrt[((x3[t]-x0[t])^2+(y3[t]-y0[t])^2+(z3[t]-z0[t])^2)^3]+(-q0*q4/(4π ε0 )/m0 (y4[t]-y0[t]))/Sqrt[((x4[t]-x0[t])^2+(y4[t]-y0[t])^2+(z4[t]-z0[t])^2)^3]+(-q0*q5/(4π ε0 )/m0 (y5[t]-y0[t]))/Sqrt[((x5[t]-x0[t])^2+(y5[t]-y0[t])^2+(z5[t]-z0[t])^2)^3]+(-q0*q6/(4π ε0 )/m0 (y6[t]-y0[t]))/Sqrt[((x6[t]-x0[t])^2+(y6[t]-y0[t])^2+(z6[t]-z0[t])^2)^3]+(-q0*q7/(4π ε0 )/m0 (y7[t]-y0[t]))/Sqrt[((x7[t]-x0[t])^2+(y7[t]-y0[t])^2+(z7[t]-z0[t])^2)^3]+(-q0*q8/(4π ε0 )/m0 (y8[t]-y0[t]))/Sqrt[((x8[t]-x0[t])^2+(y8[t]-y0[t])^2+(z8[t]-z0[t])^2)^3]+(-q0*q9/(4π ε0 )/m0 (y9[t]-y0[t]))/Sqrt[((x9[t]-x0[t])^2+(y9[t]-y0[t])^2+(z9[t]-z0[t])^2)^3]],  vz0'[t] ==(G m1 (z1[t]-z0[t]))/Sqrt[((x1[t]-x0[t])^2+(y1[t]-y0[t])^2+(z1[t]-z0[t])^2)^3]+(G m2 (z2[t]-z0[t]))/Sqrt[((x2[t]-x0[t])^2+(y2[t]-y0[t])^2+(z2[t]-z0[t])^2)^3]+(G m3 (z3[t]-z0[t]))/Sqrt[((x3[t]-x0[t])^2+(y3[t]-y0[t])^2+(z3[t]-z0[t])^2)^3]+(G m4 (z4[t]-z0[t]))/Sqrt[((x4[t]-x0[t])^2+(y4[t]-y0[t])^2+(z4[t]-z0[t])^2)^3]+(G m5 (z5[t]-z0[t]))/Sqrt[((x5[t]-x0[t])^2+(y5[t]-y0[t])^2+(z5[t]-z0[t])^2)^3]+(G m6 (z6[t]-z0[t]))/Sqrt[((x6[t]-x0[t])^2+(y6[t]-y0[t])^2+(z6[t]-z0[t])^2)^3]+(G m7 (z7[t]-z0[t]))/Sqrt[((x7[t]-x0[t])^2+(y7[t]-y0[t])^2+(z7[t]-z0[t])^2)^3]+(G m8 (z8[t]-z0[t]))/Sqrt[((x8[t]-x0[t])^2+(y8[t]-y0[t])^2+(z8[t]-z0[t])^2)^3]+(G m9 (z9[t]-z0[t]))/Sqrt[((x9[t]-x0[t])^2+(y9[t]-y0[t])^2+(z9[t]-z0[t])^2)^3]+If[q0 == 0, 0, (-q0*q1/(4π ε0 )/m0 (z1[t]-z0[t]))/Sqrt[((x1[t]-x0[t])^2+(y1[t]-y0[t])^2+(z1[t]-z0[t])^2)^3]+(-q0*q2/(4π ε0 )/m0 (z2[t]-z0[t]))/Sqrt[((x2[t]-x0[t])^2+(y2[t]-y0[t])^2+(z2[t]-z0[t])^2)^3]+(-q0*q3/(4π ε0 )/m0 (z3[t]-z0[t]))/Sqrt[((x3[t]-x0[t])^2+(y3[t]-y0[t])^2+(z3[t]-z0[t])^2)^3]+(-q0*q4/(4π ε0 )/m0 (z4[t]-z0[t]))/Sqrt[((x4[t]-x0[t])^2+(y4[t]-y0[t])^2+(z4[t]-z0[t])^2)^3]+(-q0*q5/(4π ε0 )/m0 (z5[t]-z0[t]))/Sqrt[((x5[t]-x0[t])^2+(y5[t]-y0[t])^2+(z5[t]-z0[t])^2)^3]+(-q0*q6/(4π ε0 )/m0 (z6[t]-z0[t]))/Sqrt[((x6[t]-x0[t])^2+(y6[t]-y0[t])^2+(z6[t]-z0[t])^2)^3]+(-q0*q7/(4π ε0 )/m0 (z7[t]-z0[t]))/Sqrt[((x7[t]-x0[t])^2+(y7[t]-y0[t])^2+(z7[t]-z0[t])^2)^3]+(-q0*q8/(4π ε0 )/m0 (z8[t]-z0[t]))/Sqrt[((x8[t]-x0[t])^2+(y8[t]-y0[t])^2+(z8[t]-z0[t])^2)^3]+(-q0*q9/(4π ε0 )/m0 (z9[t]-z0[t]))/Sqrt[((x9[t]-x0[t])^2+(y9[t]-y0[t])^2+(z9[t]-z0[t])^2)^3]],  x1[0] == x1x, y1[0] == y1y, z1[0] == z1z, x2[0] == x2x, y2[0] == y2y, z2[0] == z2z, x3[0] == x3x, y3[0] == y3y, z3[0] == z3z, x4[0] == x4x, y4[0] == y4y, z4[0] == z4z, x5[0] == x5x, y5[0] == y5y, z5[0] == z5z, x6[0] == x6x, y6[0] == y6y, z6[0] == z6z, x7[0] == x7x, y7[0] == y7y, z7[0] == z7z, x8[0] == x8x, y8[0] == y8y, z8[0] == z8z, x9[0] == x9x, y9[0] == y9y, z9[0] == z9z, x0[0] == x0x, y0[0] == y0y, z0[0] == z0z,  vx1[0] == v1x, vy1[0] == v1y, vz1[0] == v1z, vx2[0] == v2x, vy2[0] == v2y, vz2[0] == v2z, vx3[0] == v3x, vy3[0] == v3y, vz3[0] == v3z, vx4[0] == v4x, vy4[0] == v4y, vz4[0] == v4z, vx5[0] == v5x, vy5[0] == v5y, vz5[0] == v5z, vx6[0] == v6x, vy6[0] == v6y, vz6[0] == v6z, vx7[0] == v7x, vy7[0] == v7y, vz7[0] == v7z, vx8[0] == v8x, vy8[0] == v8y, vz8[0] == v8z, vx9[0] == v9x, vy9[0] == v9y, vz9[0] == v9z, vx0[0] == v0x, vy0[0] == v0y, vz0[0] == v0z},  {x1, x2, x3, x4, x5, x6, x7, x8, x9, x0, y1, y2, y3, y4, y5, y6, y7, y8, y9, y0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z0, vx1, vx2, vx3, vx4, vx5, vx6, vx7, vx8, vx9, vx0, vy1, vy2, vy3, vy4, vy5, vy6, vy7, vy8, vy9, vy0, vz1, vz2, vz3, vz4, vz5, vz6, vz7, vz8, vz9, vz0},  {t, 0, T0}, WorkingPrecision-> wp, MaxSteps-> Infinity, Method-> mta, InterpolationOrder-> All, StepMonitor :> (laststep=plunge; plunge=t;stepsize=plunge-laststep;), Method->{"EventLocator", "Event" :> (If[stepsize<1*^-4, 0, 1])}]; (* Position, Geschwindigkeit *) 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]}, {x0[t], y0[t], z0[t]}}/.nds[[1]];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]}, {vx0[t], vy0[t], vz0[t]}}/.nds[[1]];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]]]+m0 Evaluate[f2p[t][[10]]])/(m1+m2+m3+m4+m5+m6+m7+m8+m9+m0); (* Merkurjahr *) ym = 87969/1000 dy;(* Funktionen *)w[n_, t_] := ArcTan[f2p[t][[n, 1]]-f2p[t][[1, 1]], f2p[t][[n, 2]]-f2p[t][[1, 2]]]r[n_, t_] := Norm[f2p[t][[n]]-f2p[t][[1]]]μ[n_, t_] := Quiet[τ/.FindMinimum[r[n, τ], {τ, t}][[2]]]t1 = Quiet[μ[2, T1]]; "t1" -> t1/yr "yr"t2 = Quiet[μ[2, T2]]; "t2" -> t2/yr "yr"Δt = t2-t1; "Δt" -> Δt/yr "yr"(* neutonischer Shift *)Δα = (w[2, t2]-w[2, t1]);ΔΑ = Δα*3600*180/π/Δt*100 yr;"Δα" -> ΔΑ "arcsec per 100 years"`

Output:

2) Einstein (gravitoelektrischer Effekt)

Input:

Code: Alles auswählen

`(* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)(* ||| Mathematica Syntax || yukterez.net || Perihelionshift, Relativistic Weak Field ||| *)(* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)(* große Halbachse, Exzentrizität, Umlaufperiode *)a  = 0.387099273 Au;e  = 0.205635934;Δt = ym;(* gravitoelektrischer Shift *)Δβ = (24 π^3 a^2)/(Δt^2 c^2 (1-e^2));ΔΒ = Δβ*3600*180/π/Δt*100yr;"Δβ" -> ΔΒ "arcsec per 100 years"`

Output:

3) Summe (neutonischer und einsteinscher Anteil addiert)

Input:

Code: Alles auswählen

`"Δφ" -> (ΔΑ+ΔΒ) "arcsec per 100 years"`

Output:

4) Vergleich mit der Literatur:

Wiki, 2019:

Křížek, 2017:

Ryan, 2017:

Verrier, 1859:

5) Text (Lorem ipsum)

Der Zeitrahmen über den in Code 1 integriert wurde ist die historische Zeitspanne von 1697 bis 1848 (die Ephemeriden von 2019 wurden dafür in der Zeit zurückintegriert). Berücksichtigt sind alle Planeten inklusive Pluto/Charon und die Reflexbewegung der Sonne um das Baryzentrum des Sonnensystems, der Einfluss von Asteroiden und Planetoiden wurde vernachlässigt (diese tragen ca. 0.13"/Jahrhundert bei). Die Startpositionen und Geschwindigkeiten der Planeten wurden von JPL übernommen, und ihre Massen von Wolframalpha. Je nach Quelle können die Massen der Planeten an den hinteren Kommastellen auch etwas von den hier verwendeten Zahlen abweichen. Wenn man es ganz genau will kann man statt der Planetenmasse die Masse der Planeten samt ihrer Monde eingeben, wofür ich hier da das Ergebnis auch so ganz gut passt zu faul war. Arbeitsblatt: merkurs.periheldrehung.nb, all in 1 Code: controlc.com/cf7be975

6) Mathematik (Newton und Einstein)

Bewegungsgleichung für die Mehrkörpersimulation des Sonnensystems:

wobei der zweite Term aufgrund der elektrischen Neutralität wegfällt. Dabei ist

der Abstand zwischen Körper i und j. Die azimutale Winkelkoordinate des Merkur relativ zur Sonne ist

mit dem Subscript m für Merkur und s für die Sonne. Nun wird numerisch nach der Zeit des Perigäums

gesolved. t₀ bis t₀+Δt ist dabei die Zeitspanne in der nach der nächsten Annäherung gesucht wird, wobei Δt Merkurs Umlaufperiode ist. Vergleicht man nun zwei Φms die sich zu den Minima von dms gehörigen t bei unterschiedlichen t₀ ergeben erhält man die sich aus der Wechselwirkung mit den anderen Planeten ergebende Periheldrehung innerhalb des jeweiligen Zeitrahmens. Der gravitoelektrische Shift pro Umlaufperiode ist

wobei a die große Halbachse und e die Exzentrizität des Merkur ist. Die gravitoelektrische Formel funktioniert nur im schwachen Feld, für die Rechnung die auch im starken Feld gilt siehe hier.

by Simon Tyran, Vienna @ youtube || rumble || odysee || minds || wikipedia || stackexchange || License: CC-BY 4 ▣ If images don't load: [ctrl]+[F5]

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