# *************** #
#                 #
# GnuPlot script  #
#                 #
# *************** #

#
# Constants and functions
#
a = 1.03
l0 = 4
distance(t)=(1./2.)*a*t**2
v(x) = a*x
ls(t) = l0 - distance(t)
factor(x) = sqrt((1.+a*x)/(1.-a*x))
lm(x) = ls(x) * factor(x)

#
# Range and tics
#
set key left reverse
set parametric
set trange [0:30./365.25]
set xrange [*:*]
set yrange [*:*]
set xtic
set grid
set title "Distance moved, actual vs observed, during first 30 days"
set xlabel "Days"
set ylabel "Light-Years Traveled"

#
# Plot
#
plot t*365.25, distance(t) lw 2, \
     t*365.25, (l0 - lm(t)) lw 2