#!/usr/bin/gnuplot
# kolize.plt
# Vypocet koliznich frekvenci pro Hildy, Trojany a hlavni pas.
# Calculation of collisional rates for Hildas, Trojans and main belt.
# Miroslav Broz (miroslav.broz@email.cz), Oct 15th 2008
# This version is with corrected numbers of MB bodies!
print "\nHildas vs main belt collisions:"
V_imp = 4.78e3 # m/s; average impact velocity
Q_star = 1.e5 # J/kg; from scaling law (in gravity regime)
D_target = 100. # km; target diameter
d_disrupt = (2*Q_star/V_imp**2)**(1./3.) * D_target # projectile size needed (Bottke etal 2006)
n_project = 2000. # MB bodies larger than 20 km, according to (Bottke etal 2006)
n_target = 8. # number of 100 km Hildas; two of them are just below 100 km limit
P_i = 0.62e-18 # km^-2 yr^-1; intrinsic collisional probability for HM collisions (Dahlgren 1998)
T_SS = 4.0e9 # yr; age of the Solar System (after LHB)
f_disrupt = P_i * D_target**2/4. * (n_project*n_target)
tau_disrupt = 1./f_disrupt
n_events = T_SS/tau_disrupt # number of events during the existence of SS
print "\nV_imp = ", V_imp/1.e3, " km/s"
print "Q_star = ", Q_star, " J/kg"
print "D_target = ", D_target, " km"
print "n_target = ", n_target
print "\nd_disrupt = ", d_disrupt, " km"
print "n_project = ", n_project
print "\nP_i = ", P_i, " km^-2 yr^-1"
print "f_disrupt = ", f_disrupt, " yr^-1"
print "tau_disrupt = ", tau_disrupt, " yr = ", tau_disrupt/1.e9, " Gyr"
print "n_events = ", n_events
print "\n########################################################################"
print "\nHildas vs main belt, but for LARGER bodies:"
D_target = 200. # km
Q_star = 4.e5 # J/kg; (it scales as D^2)
d_disrupt = (2*Q_star/V_imp**2)**(1./3.) * D_target
n_project = 160. # MB bodies larger than ~65 km
n_target = 1. # current number of 200 km Hildas
f_disrupt = P_i * D_target**2/4. * (n_project*n_target)
tau_disrupt = 1./f_disrupt
n_events = T_SS/tau_disrupt
print "\nV_imp = ", V_imp/1.e3, " km/s"
print "Q_star = ", Q_star, " J/kg"
print "D_target = ", D_target, " km"
print "n_target = ", n_target
print "\nd_disrupt = ", d_disrupt, " km"
print "n_project = ", n_project
print "\nP_i = ", P_i, " km^-2 yr^-1"
print "f_disrupt = ", f_disrupt, " yr^-1"
print "tau_disrupt = ", tau_disrupt, " yr = ", tau_disrupt/1.e9, " Gyr"
print "n_events = ", n_events
print "\n########################################################################"
print "\nmain belt vs main belt (a check):"
V_imp = 5.28e3 # m/s
Q_star = 1.5e5 # J/kg; slightly larger than for H, because MB asteroids might be more resistant
D_target = 100. # km
d_disrupt = (2*Q_star/V_imp**2)**(1./3.) * D_target
n_project = 2000. # MB bodies larger than ~20 km
n_target = 200. # number of 100 km main belt asteroids
P_i = 3.10e-18 # km^-2 yr^-1; intrinsic collisional probability for MM collisions (Dahlgren 1998)
f_disrupt = P_i * D_target**2/4. * (n_project*n_target)
tau_disrupt = 1./f_disrupt
n_events = T_SS/tau_disrupt
print "\nV_imp = ", V_imp/1.e3, " km/s"
print "Q_star = ", Q_star, " J/kg"
print "D_target = ", D_target, " km"
print "n_target = ", n_target
print "\nd_disrupt = ", d_disrupt, " km"
print "n_project = ", n_project
print "\nP_i = ", P_i, " km^-2 yr^-1"
print "f_disrupt = ", f_disrupt, " yr^-1"
print "tau_disrupt = ", tau_disrupt, " yr = ", tau_disrupt/1.e9, " Gyr"
print "n_events = ", n_events
print "\n########################################################################"
print "\nTrojans vs Trojans:"
V_imp = 5.20e3 # m/s
Q_star = 1.e5 # J/kg
d_disrupt = (2*Q_star/V_imp**2)**(1./3.) * D_target
n_project = 464. # number of Trojans larger than 20 km
n_target = 12. # number of 100 km Trojans
P_i = 5.94e-18 # km^-2 yr^-1; intrinsic collisional probability for TT collisions (Dahlgren 1998)
f_disrupt = P_i * D_target**2/4. * (n_project*n_target)
tau_disrupt = 1./f_disrupt
n_events = T_SS/tau_disrupt
print "\nV_imp = ", V_imp/1.e3, " km/s"
print "Q_star = ", Q_star, " J/kg"
print "D_target = ", D_target, " km"
print "n_target = ", n_target
print "\nd_disrupt = ", d_disrupt, " km"
print "n_project = ", n_project
print "\nP_i = ", P_i, " km^-2 yr^-1"
print "f_disrupt = ", f_disrupt, " yr^-1"
print "tau_disrupt = ", tau_disrupt, " yr = ", tau_disrupt/1.e9, " Gyr"
print "n_events = ", n_events
########################################################################
print ""