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I applied Rationalize to every decimal constant feeding into the computation of Soln and rm, and replaced AccuracyGoal -> 10, PrecisionGoal -> 10 by WorkingPrecision -> 60. The change in rm was negligible, {3.69158*10^6, {t -> 2.10981*10^7, p -> 0.938622}} before, and {3.69179*10^6, {t -> 2.10981*10^7, p -> 0.938622}} after these ...


8

NMinimize[{Norm[{xm[t][p], ym[t][p]} - {xsc[t][p], ysc[t][p]}] /. soln, 0 < t < tmax && 0 < p < 5}, {t, p}, Method -> "SimulatedAnnealing"] (* {71729.9, {t -> 118.095, p -> 5.}} *)



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