Find the position and velocity if the planet given orbit and elements. ******************************************************************************* Given k = .01720209895 gravity constant q = .4255 AU perihelion e = .2 eccentricity t = 40 days past perihelion i = 72 degrees inclination w = 105 degrees argument of perigee o = 293 degrees longitude of ascending node ie = 23.441028 degrees tilt of earth Use data from orbit-1 p = q*(1+e) =.5106 M = 1.77389155705 mean anomaly EE= 1.95900897924 radians The first derinitive of each is d(th)/dt = k*SQRT[p]/r^2 = dth =.037550416193 radians/day dr/dr = k*e* Sin[th] /SQRT[p] = drt = 4.05910212681E-3 AU/day r * Sin[th] = a * ( Cos[EE] - e ) r * Cos[th] = a * (SQRT[ 1 - e^2 ]) * Sin[EE] r=.5721416260 AU and th=122.535231561 degrees. U = th + w = 227.535231561 degrees x1 = r * Cos[U] = -0.386273822557 AU y = r * Sin[U] = -0.422064656473 AU dx1 = drt * Cos[U] - r * Sin[U] * dth AU/day dy = drt * Sin[U] + r * Cos[U] * dth AU/day y1 = y * Cos[I] = -0.130425151575 AU z2 = y * Sin[I] = -0.401407341836 AU dz2 = dy * Sin[i] = -1.41790996032E-2 AU/day dy1 = dy * Cos[i] = -5.40752314709E-3 AU/day x3 = x1 * Cos[O] - y1 * Sin[O] = -0.27098619163 AU y2 = y1 * Cos[O] + x1 * Sin[O] = 0.304605761767 AU dx3 = dx1 * Cos[O] - dy1 * Sin[O] = 1.4415181119E-4 AU/day dy2 = dy1 * Cos[O] + dx1 * Sin[O] = -1.41790996032E-2 AU/day y3 = y2 * Cos[IE] - z2 * Sin[IE] = -0.27098619163 AU z3 = z2 * Cos[IE] + y2 * Sin[IE] = -0.247105509699 AU dy3 = dy2 * Cos[IE] - dz2 * Sin[IE] = -6.38837169935E-3 AU/day dz3 = dz2 * Cos[IE] + dy2 * Sin[IE] = -2.09096438056E-3 AU/day