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(* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *) (* ||||||||| Mathematica Syntax || yukterez.net || Perihelion Shift of Mercury |||||||||| *) (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *) 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 century" (* 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 century" (* Gesamter Shift *) "Δφ" -> (ΔΑ+ΔΒ) "arcsec per century"
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