Created
March 4, 2013 17:56
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Pluto simulation v0.1
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| module Integrator | |
| export PlutoSim | |
| const G = 1.48811382e-34 # G in units of AU and day | |
| function potential{T<:Real}(mass::Vector{T}, r::Matrix{T}) | |
| N = size(r,1) | |
| out = zeros(N,3) | |
| d = zeros(1,3) | |
| a = zeros(1,3) | |
| for i = 1:N | |
| for j = i+1:N | |
| d[1] = r[j,1]-r[i,1] | |
| d[2] = r[j,2]-r[i,2] | |
| d[3] = r[j,3]-r[i,3] | |
| F = G/norm(d)^3 | |
| a[1] = d[1] * F | |
| a[2] = d[2] * F | |
| a[3] = d[3] * F | |
| out[i,1] += mass[j] * a[1] | |
| out[i,2] += mass[j] * a[2] | |
| out[i,3] += mass[j] * a[3] | |
| out[j,1] -= mass[i] * a[1] | |
| out[j,2] -= mass[i] * a[2] | |
| out[j,3] -= mass[i] * a[3] | |
| end | |
| end | |
| out | |
| end | |
| # Velocity Verlet | |
| function Verlet{T<:Real}(mass::Vector{T}, r0::Matrix{T}, v0::Matrix{T}, h::Real) | |
| a0 = potential(mass, r0) | |
| r_new = r0 + v0*h + 0.5*a0*h^2 | |
| v_new = v0 + 0.5*(a0 + potential(mass, r_new)) * h | |
| return (r_new, v_new) | |
| end | |
| function PlutoSim(N::Integer, h::Real) | |
| r = zeros(6,3) | |
| v = zeros(6,3) | |
| mass = zeros(6) | |
| # Set masses | |
| mass[1] = 1.988435e30 # Sun | |
| mass[2] = 1.8988e27 # Jupiter | |
| mass[3] = 5.685e26 # Saturn | |
| mass[4] = 8.6625e25 # Uranus | |
| mass[5] = 1.0278e26 # Neptune | |
| mass[6] = 1.314e22 # Pluto | |
| # Sun | |
| r[1,:] = [-9.001119860001391E-04, -2.518569331216286E-03, -5.035993149103694E-05] | |
| v[1,:] = [ 6.249336869691155E-06, -7.202874592454979E-07, -1.368159714329672E-07] | |
| # Jupiter | |
| r[2,:] = [ 9.637969147947649E-01, 4.988694611226984E+00, -4.236695676623525E-02] | |
| v[2,:] = [-7.500214649417347E-03, 1.791097950812253E-03, 1.603945618163088E-04] | |
| # Saturn | |
| r[3,:] = [-7.901119375041307E+00, -5.800240922607197E+00, 4.152972681975652E-01] | |
| v[3,:] = [ 2.998916003562968E-03, -4.511136746229775E-03, -4.061079792754435E-05] | |
| # Uranus | |
| r[4,:] = [ 1.985459827926987E+01, 2.801201477916861E+00, -2.468196041542967E-01] | |
| v[4,:] = [-5.782111510118402E-04, 3.711193104939768E-03, 2.130487704096845E-05] | |
| # Neptune | |
| r[5,:] = [ 2.664809431198752E+01, -1.375183029235338E+01, -3.309310983483438E-01] | |
| v[5,:] = [ 1.419153776960717E-03, 2.808496228357725E-03, -9.056396274034148E-05] | |
| # Pluto | |
| r[6,:] = [5.303572815981638E+00, -3.190544944470667E+01, 1.879962140526394E+00] | |
| v[6,:] = [3.156551097775996E-03, -1.132909607403660E-04, -9.009397396467777E-04] | |
| NSteps = N | |
| result = zeros(12,fld(NSteps, 100)) | |
| println(size(result)) | |
| println("Begin.") | |
| tic() | |
| sample = 0 | |
| t = 0.0 | |
| for i = 1:NSteps | |
| if i % 100 == 0 | |
| sample += 1 | |
| result[ 1,sample] = r[1,1] | |
| result[ 2,sample] = r[1,2] | |
| result[ 3,sample] = r[2,1] | |
| result[ 4,sample] = r[2,2] | |
| result[ 5,sample] = r[3,1] | |
| result[ 6,sample] = r[3,2] | |
| result[ 7,sample] = r[4,1] | |
| result[ 8,sample] = r[4,2] | |
| result[ 9,sample] = r[5,1] | |
| result[10,sample] = r[5,2] | |
| result[11,sample] = r[6,1] | |
| result[12,sample] = r[6,2] | |
| end | |
| r,v = Verlet(mass, r, v, h) | |
| end | |
| toc() | |
| writecsv("output.txt", result) | |
| run(`python plotorbits.py`) | |
| end | |
| end # module |
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