Mini-Project 4

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% ------------------------------ Eas 4510 ------------------------------- %

% ---------------------------- Spring 2020 -------------------------------%

% -------------------------- Mini Project #4 -----------------------------%

% --------------------------- James Crouse -------------------------------%

clc; clear; close all;

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% Question #1 : 30 Points

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%developing the two impulse Hohmann transfer

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% earth parameters

mu = 398600; % earth's gravitational parameter

Re = 6371; % earth's radius (km)

M = 500; %number of desired points

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% parameters initial orbit

e0 = 0; % eccentricity is zer b/c circular

alt0 = 500; %altitude of the orbit (km)

r0 = alt0 + Re; %semimajor axis

inc0 = 28.5*pi/180; % orbital inclination (rad)

Omega0 = 60*pi/180; % longitude of the ascending node (rad)

w0 = 0; % argument of the periapsis

nu0 = 0; % true anomaly

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% parameters final orbit

ef = 0; % eccentricity is zer b/c circular

altf = 20200; %altitude of the orbit (km)

rf = altf + Re; %semimajor axis

incf = 57*pi/180; % orbital inclination (rad)

Omegaf = 120*pi/180; % longitude of the ascending node (rad)

wf = 0; % argument of the periapsis

nuf = 0; % true anomaly

[R,t,vv1delta,vv2delta] = twoImpulseHohmann_Crouse_James(r0,rf,inc0,incf,Omega0,Omegaf,mu);

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% Question #2 and #3 : 70 Points

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N = [1:6]; %number of impulse pairs;

for jj = 1:length(N)

%3D plot

figure (jj);

earthSphere(50)

hold on

[R,t,vdeltp,vdelta,vdelt,tr] = twoNImpulseOrbitTransfer_Crouse_James(r0,rf,inc0,incf,Omega0,Omegaf,N(jj),mu);

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%saving variables for plotting

vdp(jj,1:N(jj)) = vdeltp;

vda(jj,1:N(jj)) = vdelta;

t_total(N(jj)) = tr;

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%plotting the transfer in 3D

str = sprintf('2xN Impulse Orbit Transfer, N = %g',jj);

t1 = title(str);

set(t1,'Fontweight','bold','FontSize',20,'Interpreter','LaTeX');

xl = xlabel('$x$ (km)');

yl = ylabel('$y$ (km)');

zl = zlabel('$z$ (km)');

set(xl,'FontSize',16,'Interpreter','LaTeX');

set(yl,'FontSize',16,'Interpreter','LaTeX');

set(zl,'FontSize',16,'Interpreter','LaTeX');

set(gca,'FontSize',16,'TickLabelInterpreter','LaTeX');

grid on;

axis equal;

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%plotting the mercator display

OmegaE = 2*pi/(24*60*60);

rvValuesECEF = eci2ecef(t,R,OmegaE);

[lonE,lat] = ecef2LonLat(rvValuesECEF);

figure(N(end)+jj);

clf

earth = imread('earth.jpg');

image('CData',earth,'XData',[-180 180],'YData',[90 -90])

hold on

plot(lonE*180/pi,lat*180/pi,'w.','Markersize',8);

str2 = sprintf('2xN Impulse Orbit Transfer, N = %g',jj);

title(str2);

hold off

end

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%plotting impulse at apoapsis as a function of n

figure ((3*jj)+1);

for ii = 1:jj

plot(vda(ii,1:ii),'.-','LineWidth',2,...

'Markersize',12)

hold on

end

hold off

xlabel('n')

ylabel('delta v')

title('Total Impulse at Apoapsis vs n');

legend('N = 1','N = 2','N = 3','N = 4','N = 5','N = 6');

set(gca,'FontSize',16,'TickLabelInterpreter','LaTeX');

grid on;

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%plotting impulse at periapsis as a function of n

figure ((3*jj)+2);

for ii = 1:jj

plot(vdp(ii,1:ii),'.-','LineWidth',2,...

'Markersize',12)

hold on

end

hold off

xlabel('n')

ylabel('delta v')

title('Total Impulse at Periapsis vs n');

legend('N = 1','N = 2','N = 3','N = 4','N = 5','N = 6');

set(gca,'FontSize',16,'TickLabelInterpreter','LaTeX');

grid on;

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%plotting total impulse as a function of N

figure ((3*jj)+3);

for ii = 1:jj

vdt(ii) = sum(vdp(ii,:)) + sum(vdp(ii,:));

end

plot(vdt,'.-','LineWidth',2,...

'Markersize',12)

xlabel('n')

ylabel('delta v')

title('Total Impulse vs N');

set(gca,'FontSize',16,'TickLabelInterpreter','LaTeX');

grid on;

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%plotting time required as a function of N

figure ((3*jj)+4);

plot(N(:),t_total(:),'.-','LineWidth',2,...

'Markersize',12)

xlabel('N')

ylabel('time [s]')

title('Time Required to Complete the Transfer vs N');

set(gca,'FontSize',16,'TickLabelInterpreter','LaTeX');

grid on;

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%print statements

fprintf('The total impulse required to complete the transfer decreases\n');

fprintf('as a function of N. This is because the total energy change of\n');

fprintf('transfer stays constant, and change in energy = sum(1/2*deltav^2\n');

fprintf('+ 2*vinitial*deltav*cos(theta)).During an multiple impulse orbit\n');

fprintf('transfer this second term accounts for more of the total energy\n');

fprintf('change, so the deltav required becomes smaller.\n');

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