# Planetary motion measurements of period. We used the commands:
#  rk4.sh -n -f 5 -- -10 0 1 0 0 <v_0x> 40000 0 <time>
#  planet_meas.awk rk4.dat > hi
#  grep T hi
#  grep A hi
#  grep B hi
#
# v_0x   T/2      2 a
# ===================
  3.2   1.030   2.049
  3.4   1.281   2.370
  3.6   1.682   2.841
  3.8   2.396   3.597
  4.0   3.927   5.000
  4.1   5.514   6.270
  4.2   8.665   8.475
  4.3  16.931  13.245
  4.38 42.652  24.522
  4.40 61.359  31.250
  4.42 99.526  43.141
# Check Kepler law by: T^2 = (4 pi^2)/(G M) r^3 where here G M= 10
# grep -v '#' planet_T|awk '{print ($3/2)^3,(2*$2)^2}'  | fit-straight-line -n
# slope = 3.94777(1)  (4 pi^2/10) = 3.9478 41760
# grep -v '#' planet_T|awk '{print log($3/2),log(2*$2)}'| fit-straight-line -n
# slope =  1.50006(3)  intercept: 0.68642(5)
# In gnuplot:
# plot [:12000] "planet_T" u (($3/2)**3):((2*$2)**2) notit , ((4*pi**2)/10)*x notit

