% 
% Problem 4.2 
%
r_e = 1.496e+8;
r_m = 1.523691*r_e;
mu_e = 3.98601e+5;
mu_s = 1.32715e+11;
mu_m = 43058;
r_p = 6378 +200;
R_m = 3379;
% transfer time
T = pi*sqrt( (0.5*(r_e+r_m))^3/mu_s);
% converting in terms of days
T = T/24/3600;
disp(['Transfer time =  ',  num2str(T), '    days'])
%
V_p = sqrt(2*mu_s/r_e - 2*mu_s/(r_e+r_m));
disp(['V_p  =  ',  num2str(V_p), '    km/s'])
%
V_e = sqrt(mu_s/r_e );
disp(['V_e  =  ',  num2str(V_e), '    km/s'])
%
V_infty_e = V_p - V_e;
disp(['V_infty_e  =  ',  num2str(V_infty_e), '    km/s'])
%
vel_p =sqrt(2*mu_e/r_p + V_infty_e^2);
disp(['v_p, hyperbola escape velocity  =  ',  num2str(vel_p), '    km/s'])
%
vel_c =sqrt(mu_e/r_p);
disp(['v_c, parking velocity around the earth  =  ',  num2str(vel_c), '    km/s'])
%
delta_v_e  =vel_p-vel_c;
disp(['delta v  at the perigee  =  ',  num2str(delta_v_e), '    km/s'])
% 
a = -mu_e/V_infty_e^2;
disp(['semimajor axis, a  =  ',  num2str(a), '    km'])
% 
e = 1 +r_p*V_infty_e^2/mu_e;
disp(['eccentricity, e  =  ',  num2str(e), '   '])
%
p = a*(1-e^2);
disp(['orbit parameter, p  =  ',  num2str(p), '   '])
%
h = sqrt(p*mu_e);
disp(['specific angular momentum, h  =  ',  num2str(h), ' km^2/s'])
%
d = h/V_infty_e;
disp(['escape asymptotic distance, d  =  ',  num2str(d), ' km'])
%
theta_infty = acos(-1.0/e);
theta_infty = theta_infty*360/(2*pi);
disp(['asymptotic angle measured from perigee point, d  =  ',  num2str(theta_infty), '  angle '])
%
V_a = sqrt(2*mu_s/r_m - 2*mu_s/(r_e+r_m));
disp(['V_a  =  ',  num2str(V_a), '    km/s'])
%
V_m = sqrt(mu_s/r_m );
disp(['V_m  =  ',  num2str(V_m), '    km/s'])
%
V_infty_m = V_m - V_a;
disp(['V_infty_m  =  ',  num2str(V_infty_m), '    km/s'])
%
vel_p =sqrt(2*mu_m/R_m + V_infty_m^2);
disp(['v_p, hyperbola escape velocity  =  ',  num2str(vel_p), '    km/s'])
%
delta_v_m  =vel_p;
disp(['delta v  at the apogee  =  ',  num2str(delta_v_m), '    km/s'])
%
disp(['total delta v =  ',  num2str(delta_v_e+delta_v_m), '    km/s'])

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Solution Output of Problem 4.2
%% Problem4_2
%% Transfer time =  258.8706    days
%% V_p  =  32.7295    km/s
%% V_e  =  29.7848    km/s
%% V_infty_e  =  2.9447    km/s
%% v_p, hyperbola escape velocity  =  11.3958    km/s
%% v_c, parking velocity around the earth  =  7.7843    km/s
%% delta v  at the perigee  =  3.6114    km/s
%% semimajor axis, a  =  -45966.5788    km
%% eccentricity, e  =  1.1431   
%% orbit parameter, p  =  14097.3379   
%% specific angular momentum, h  =  74961.41 km^2/s
%% escape asymptotic distance, d  =  25455.9697 km
%% asymptotic angle measured from perigee point, d  =  151.0226  angle 
%% V_a  =  21.4804    km/s
%% V_m  =  24.1294    km/s
%% V_infty_m  =  2.6489    km/s
%% v_p, hyperbola escape velocity  =  5.7011    km/s
%% delta v  at the apogee  =  5.7011    km/s
%% total delta v =  9.3125    km/s
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%