#!/usr/bin/gnuplot # tisserand.plt # Vypocet Tisserandova parametru pro teleso Kuiperova pasu # a excentricity po rozptylu Neptunem, ... # Miroslav Broz (miroslav.broz@email.cz), Sep 1st 2008 AU = 1 # astronomicka jednotka a = 39.5*AU # pocatecni orbita v Kuiperove pasu I = 0. a_N = 30.10*AU # velke poloosy planet a_U = 19.18*AU a_S = 9.55*AU a_J = 5.20*AU e = 1-a_N/a # excentricita takova, aby se teleso priblizovalo k Neptunu # definice Tisserandova parametru T_p(a,e,I,a_N) = a_N/a + 2 * cos(I) * sqrt(a/a_N*(1-e**2)) # reseni pro excentricitu: e_T_p(T_p) = T_p-3 + 2*sqrt(3-T_p) print "########################################################################" T_N = T_p(a,e,I,a_N) print "e_pocatecni = ", e print "T_N = ", T_N ######################################################################## print "\n# rozptyl Neptunem:" e = e_T_p(T_N) a = a_N/(1+e) q = a*(1-e) Q = a*(1+e) T_N = T_p(a,e,I,a_N) print "T_N = ", T_N, " (je stejne)" print "e_po_rozptylu_Neptunem = ", e print "a = ", a, " AU" print "q = ", q, " AU", " (toto dosahuje maximalne k Uranu, a_U = ", a_U, " AU)" print "Q = ", Q, " AU" print "# uprava a, e tak, aby draha byla presne mezi Neptunem & Uranem:" e = (a_N-a_U)/(a_N+a_U) a = a_N/(1+e) print "a = ", a, " AU" print "e = ", e ######################################################################## print "\n# rozptyl Uranem:" T_U = T_p(a,e,I,a_U) print "T_U = ", T_U e = e_T_p(T_U) a = a_U/(1+e) q = a*(1-e) Q = a*(1+e) T_U = T_p(a,e,I,a_U) print "T_U = ", T_U, " (je stejne)" print "e_po_rozptylu_Uranem = ", e print "a = ", a, " AU" print "q = ", q, " AU", " (toto dosahuje maximalne k Saturnu, a_S = ", a_S, " AU)" print "Q = ", Q, " AU" print "# uprava a, e tak, aby draha byla presne mezi Uranem & Saturnem:" e = (a_U-a_S)/(a_U+a_S) a = a_U/(1+e) print "a = ", a, " AU" print "e = ", e ######################################################################## print "\n# rozptyl Saturnem:" T_S = T_p(a,e,I,a_S) print "T_S = ", T_S e = e_T_p(T_S) a = a_S/(1+e) q = a*(1-e) Q = a*(1+e) T_S = T_p(a,e,I,a_S) print "T_S = ", T_S, " (je stejne)" print "e_po_rozptylu_Saturnem = ", e print "a = ", a, " AU" print "q = ", q, " AU", " (toto dosahuje maximalne k Jupiteru, a_J = ", a_J, " AU)" print "Q = ", Q, " AU" print "# uprava a, e tak, aby draha byla presne mezi Saturnem & Jupiterem:" e = (a_S-a_J)/(a_S+a_J) a = a_S/(1+e) print "a = ", a, " AU" print "e = ", e ######################################################################## print "\n# rozptyl Jupiterem:" T_J = T_p(a,e,I,a_J) print "T_J = ", T_J e = e_T_p(T_J) a = a_J/(1+e) q = a*(1-e) Q = a*(1+e) T_J = T_p(a,e,I,a_J) print "T_J = ", T_J, " (je stejne)" print "e_po_rozptylu_Jupiterem = ", e print "a = ", a, " AU" print "q = ", q, " AU" print "Q = ", Q, " AU"