# # Plot Earth time and dt/dtau in the revolving ship's MCRF # # # set terminal x11 0 # set output set key left set xrange [0:6.283] set yrange [-11:13] set grid set xtics border 0.5 set ytics -12,2 set title "Earth Time in the MCRF of the Revolving Ship" set xlabel "Theta" t(x) = x # General parameters v = 0.5 r = 0.1 xe = 4 # Gamma Gamma = 1/sqrt(1 - v**2) # Ship time as a function of theta ts(q) = (r / v) * q # Time on Earth te(q) = ts(q) + v * xe * cos(q) # Clock rate of Earth clock dte_dtau(q) = Gamma * (1 - v**2 * (xe/r) * sin(q)) # Ship's velocity in the direction of Earth ve(q) = v * cos(q) plot \ [q = ] \ te(q) with lines linewidth 2, \ dte_dtau(q) with lines linewidth 2, \ ve(q), \ ts(q)