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Non-impulsive Orbital Maneuvers, Constant Thrust

In non-impulsive orbital maneuvers the thrust acts over a significant period of time. In this case we can’t ignore the change in position vector. Given the initial state of the spacecraft we calculate the state after the burn

clear all;
global g0 mu T Isp M0;
mu = 398600;             %[km^3/s^2] Earth’s gravitational parameter
M0 = 4000;               %[kg] Gross mass before ignition
R = [ 7200,   0,  0];    %[km] Position vector:
V = [ 0,     7.6,  0];   %[km/s] Velocity vector
g0 = 9.81;               %[km/s^2]
T   = 20;                %[kN] Thrust, const
t_b =  200;              %[s] Burn time
m =  1000;               %[kg] Mass after burn
dm = (M0 - m)/t_b;
Isp = T/(dm*g0);
tspan = [0,t_b];
% Constructing initial state vector
y0 = [R(1),R(2),R(3),V(1),V(2),V(3),M0];
% Using ODE45 to solve  ordinary differential equations of motion
% for the given initial values
[time,f_y] = ode45(@f_yt,tspan,y0);
fs = f_y(end,:);
Rf = [fs(1),fs(2),fs(3)];
Vf = [fs(4),fs(5),fs(6)];
Mf = fs(7);
fprintf('Position vector after burn R = [%4.2f %4.2f %4.2f] km\n',Rf);
fprintf('Velocity vector after burn V = [%4.4f %4.2f %4.2f] km/s\n',Vf);
fprintf('Mass after burn M = %4.2f kg\n',Mf);
Position vector after burn R = [7035.78 1651.64 0.00] km
Velocity vector after burn V = [-1.7367 9.26 0.00] km/s
Mass after burn M = 1000.00 kg
function  dfdt = f_yt(t,y)
global mu g0 T Isp;
r = (y(1)^2+y(2)^2+y(3)^2)^0.5;
v = (y(4)^2+y(5)^2+y(6)^2)^0.5;
m = y(7);
dfdt = [y(4),y(5),y(6),-mu*y(1)/r^3 + T/m*y(4)/v,...
         -mu*y(2)/r^3 + T/m*y(5)/v, -mu*y(3)/r^3 + T/m*y(6)/v,...

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