function laguerre_conway(state::Vector{<:Real}, time::Float64, primary::Body=Sun)

  μ = primary.μ
  n = 5                               # Choose LaGuerre-Conway "n"
  i = 0

  r0 = state[1:3]                     # Are we in elliptical or hyperbolic orbit?
  r0_mag = √(state[1]^2 + state[2]^2 + state[3]^2)
  v0 = state[4:6]
  v0_mag = √(state[4]^2 + state[5]^2 + state[6]^2)
  σ0 = (r0 ⋅ v0)/√(μ)
  a = 1 / ( 2/r0_mag - v0_mag^2/μ )
  coeff = 1 - r0_mag/a

  if a > 0    # Elliptical
    ΔM = ΔE_new = √(μ) / sqrt(a^3) * time
    ΔE = 1000
    while abs(ΔE - ΔE_new) > 1e-10
      ΔE = ΔE_new
      F = ΔE - ΔM + σ0 / √(a) * (1-cos(ΔE)) - coeff * sin(ΔE)
      dF = 1 + σ0 / √(a) * sin(ΔE) - coeff * cos(ΔE)
      d2F = σ0 / √(a) * cos(ΔE) + coeff * sin(ΔE)
      sign = dF >= 0 ? 1 : -1
      ΔE_new = ΔE - n*F / ( dF + sign * √(abs((n-1)^2*dF^2 - n*(n-1)*F*d2F )))
      i += 1
      if i > 100 throw(LaGuerreConway_Error()) end
    end
    F = 1 - a/r0_mag * (1-cos(ΔE))
    G = a * σ0/ √(μ) * (1-cos(ΔE)) + r0_mag * √(a) / √(μ) * sin(ΔE)
    r = a + (r0_mag - a) * cos(ΔE) + σ0 * √(a) * sin(ΔE)
    Ft = -√(a)*√(μ) / (r*r0_mag) * sin(ΔE)
    Gt = 1 - a/r * (1-cos(ΔE))
  else      # Hyperbolic or Parabolic
    ΔN = √(μ) / sqrt(-a^3) * time
    ΔH = 0
    ΔH_new = time < 0 ? -1 : 1
    while abs(ΔH - ΔH_new) > 1e-10
      ΔH = ΔH_new
      F = -ΔN - ΔH + σ0 / √(-a) * (cos(ΔH)-1) + coeff * sin(ΔH)
      dF = -1 + σ0 / √(-a) * sin(ΔH) + coeff * cos(ΔH)
      d2F = σ0 / √(-a) * cos(ΔH) + coeff * sin(ΔH)
      sign = dF >= 0 ? 1 : -1
      ΔH_new = ΔH - n*F / ( dF + sign * √(abs((n-1)^2*dF^2 - n*(n-1)*F*d2F )))
      i += 1
      if i > 100 throw(LaGuerreConway_Error()) end
    end
    F = 1 - a/r0_mag * (1-cos(ΔH))
    G = a * σ0/ √(μ) * (1-cos(ΔH)) + r0_mag * √(-a) / √(μ) * sin(ΔH)
    r = a + (r0_mag - a) * cos(ΔH) + σ0 * √(-a) * sin(ΔH)
    Ft = -√(-a)*√(μ) / (r*r0_mag) * sin(ΔH)
    Gt = 1 - a/r * (1-cos(ΔH))
  end


  return [ F*state[1:3] + G*state[4:6]; Ft*state[1:3] + Gt*state[4:6]]

end