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 Recognitions: Science Advisor For hyperbolic orbits, we proceed as follows: B = cosh uJ = (1/e) (1 + rJ /a) uJ’ = ln [ B + (B^2 - 1)^0.5 ] = arc-cosh(B) (Depending on whether your calculator has an arc-cosh button on it.) If sin QJ < 0 then uJ = -uJ’ else uJ = uJ’ MJ = e sinh uJ - uJ For elliptical orbits, we proceed as follows: sin uJ = (rJ /a) sin QJ / (1-e^2)^0.5 cos uJ = e + (rJ /a) cos QJ uJ = arctan2(sin uJ , cos uJ) MJ = uJ - e sin uJ The proposed hyperbolic transfer orbit. e = 6.33678 a = 0.1883722 AU r1 = 2.179749 AU Q1 = 5.098051 radians u1' = 1.307609 radians sin Q1 is negative. u1 = -1.307609 radians M1 = -9.550008 radians The proposed elliptical transfer orbit. e = 0.6519092 a = 1.319533 r2 = 1.005301 Q2 = 4.327089 radians sin u2 = -0.9310417 cos u2 = +0.3655728 u2 = 5.086543 radians M2 = 5.693351 radians Jerry Abbott