# # Plot the velocity & stuff during the trip from Earth to AC # # # set terminal x11 0 # set output set key left set xrange [0:5.66] set yrange [*:*] set grid set title "From Earth to Alpha Centaurus, in the Earth FoR" set xlabel "Earth Time" t(x) = x tc(t) = tf - t # Earth time at turnover and arrival tt = 2.83 tf = 5.66 # Distance at turnover and arrival xt = 2 xf = 4 # Ship time at turnover and arrival taut = 1.76 tauf = 3.52 # Velocity before and after turnover, and combined v0(t) = t/sqrt(1 + t**2) v1(t) = tc(t)/sqrt(1 + tc(t)**2) v(t) = t<(tf/2) ? v0(t) : v1(t) # Ship time before and after turnover, and combined tau0(t) = log(t + sqrt(t**2 + 1)) tau1(t) = tauf - tau0(tf - t) tau(t) = (t <= tt) ? tau0(t) : tau1(t) # Ship location before and after turnover, and combined dx0(t) = sqrt(t**2 + 1) - 1 dx1(t) = xf - dx0(tc(t)) distance(t) = (t <= tt) ? dx0(t) : dx1(t) # Gamma Gamma(t) = 1/sqrt(1 - v(t)**2) plot \ v(x) with lines linewidth 2, \ tau(x) with lines linewidth 2, \ distance(x) with lines linewidth 2, \ Gamma(x) with lines linewidth 2