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Analytical Mech Homework Solutions 71

# Analytical Mech Homework Solutions 71 - dV V 1 r(b dr1 =...

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(a) 1 1 1 1 2 dV r V r dr r    D (b) () 11 1 2 2 60 1% 120%! dr r dV rr V === D The approximation of a differential has broken down – a correct result can be obtained by calculating finite differences, but the implication is clear – a 1% error in boost causes rocket to miss the moon by a huge factor --- 2! 6.16 From section 6.5, 0.967 ε = and mi. 6 55 10 r D From equations 6.5.21a&b, 1 1 1 + = D 6 1 6 15 5 1 0 2 1 1 0.967 93 10 r mi AU ar r mi × =+ = = × −− × D D 1 U 17.92 aA = From equation 6.6.5, 3 2 ca τ = 33 22 1 17.92 yr AU AU =⋅ × 3 2 75.9 yr = From equation 6.5.21a and 6.5.19 … 2 00 ml rk r α =− = 2 1 mrv k = DD and kG M m = 1 2 1 GM v r    D D From Example 6.5.3 we can translate the factor GM into the more convenient 2 ee GM a v = … with
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