(a) 11112dVrVrdrr≈D(b) ()11122 60 1%120%!drrdVrrV===DThe 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! 6.16From section 6.5, 0.967ε=and mi. 655 10r=×DFrom equations 6.5.21a&b, 111+=−D616155102110.96793 10rmiAUarrmi×=+= =×−−×DD1U17.92aA=From equation 6.6.5, 32caτ=3322117.92yr AUAU−=⋅×3275.9yr=From equation 6.5.21a and 6.5.19 … 200mlrkrα=−=−21mrvk=DD−and kGMm=121GMvrDDFrom Example 6.5.3 we can translate the factor GM into the more convenient 2eeGMa v=… with
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