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MAIN.m
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%% LEO BOOK CHAPTER PLOTS
%
% Stanford GPS Lab
%
% Plots for LEO Book Chapter
%
% Written by: Tyler Reid
%
%% WORKSPACE SETUP
clc
clear all
close all
colors = lines(10);
lw = 3; % line width
figFont = 22; % figure font
mu = 3.986004418e14;
R_e = 6378000;
h = [200:100:50000] * 1000;
R_SV = R_e + h;
% altitudes of operational systems
aGPS = 20350;
aGAL = 23200;
aGLO = 19100;
aBei = 21150;
aTransit = 1200;
aOneWeb = 1200;
aIridium = 780;
aGSO = 35786;
aQZSS = (1+0.075)*(35786+R_e/1000)-R_e/1000;
line_types = {'-','--', '-.','-','--', '-.'};
line_colors = gray(4);
%% SPREADING LOSS
lw = 4;
el = [5, 30, 90] * pi/180;
figure;
left_color = [0 0 0];
right_color = [0 0 0];
set(gcf,'defaultAxesColorOrder',[left_color; right_color]);
for i = 1:length(el)
slant_range = -R_e * sin(el(i)) + sqrt( R_e^2 * (sin(el(i))^2 - 1) + R_SV.^2 );
spreading_loss = 10 * log10( slant_range.^-2 / 4 / pi );
yyaxis left % plot against left y-axis
semilogx(h / 1000, spreading_loss, line_types{i},'color', line_colors(i,:), 'LineWidth', lw)
ylabel('Spreading Loss [dB]')
xlabel('Altitude [km]')
hold on
% yyaxis right % plot against right y-axis
% loglog(h / 1000, slant_range / 1000, 'LineWidth', lw);
% ylabel('Slant Range [km]')
end
grid on
lw = 2;
% figure out the transformation for the axis label.
min_slant_range = sqrt(1 / (10^(-115 / 10) * 4 * pi)) / 1000 ;
max_slant_range = sqrt(1 / (10^(-170 / 10) * 4 * pi)) / 1000 ;
step_slant_range = logspace(log10(min_slant_range), log10(max_slant_range),12) ;
step_slant_range = round(fliplr(step_slant_range)/100) * 100 ;
yyaxis right
yticks(-170:5:-115)
ylim([-170, -115])
yticklabels({ step_slant_range })
ylabel('Slant Range [km]')
yyaxis left
yticks(-170:5:-115)
% plot satellites
plot(aGPS*[1,1],[-1e3,1e5],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
plot(aOneWeb*[1,1],[-1e3,1e5],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
plot(aIridium*[1,1],[-1e3,1e5],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
plot(aGSO*[1,1],[-1e3,1e5],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
text(aIridium, -155, 'Iridium', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aOneWeb, -155, 'OneWeb', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aGPS, -140, 'GPS', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aGSO, -140, 'GSO', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
legend('el = 5^o', 'el = 30^o', 'el = 90^o',...
'location', 'south')
legend('boxoff')
xlim([300, 50000])
ylim([-170, -115])
xticks([500, 1000, 2000, 5000, 10000, 20000, 40000])
set(gca,'XTickLabelRotation',-45)
exportfig(gcf,'spreading_loss.tiff','height',8,'width',10,'fontsize',22,'LineWidth',10,'resolution',300);
exportfig(gcf,'spreading_loss.eps','height',8,'width',10,'fontsize',22,'LineWidth',10,'resolution',300);
%% FOOTPRINT
lw = 4;
el = [5, 10, 15] * pi/180;
figure;
for i = 1:length(el)
Area = 2 * pi * R_e^2 * (1 - sin(el(i) + asin(R_e./R_SV * cos(el(i))) ));
radius_footprint = sqrt(Area/pi);
radius_footprint = R_e * acos(1 - Area / R_e^2 / 2 / pi);
semilogx(h / 1000, radius_footprint / 1000, line_types{i},'color', line_colors(i,:), 'LineWidth', lw)
hold on
end
grid on
xlabel('Altitude [km]')
ylabel('Satellite Footprint Radius [km]')
legend('el = 5^o', 'el = 10^o', 'el = 15^o',...
'location', 'south')
legend('boxoff')
lw = 2;
% plot satellites
semilogx(aGPS*[1,1],[1e-13,1e5],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
semilogx(aOneWeb*[1,1],[1e-13,1e5],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
semilogx(aIridium*[1,1],[1e-13,1e5],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
semilogx(aGSO*[1,1],[1e-13,1e5],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
text(aIridium, 5000, 'Iridium', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aOneWeb, 5000, 'OneWeb', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aGPS, 5000, 'GPS', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aGSO, 5000, 'GSO', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
xlim([300, 50000])
ylim([0, 10000])
xticks([500, 1000, 2000, 5000, 10000, 20000, 40000])
set(gca,'XTickLabelRotation',-45)
exportfig(gcf,'footprint.tiff','height',8,'width',10,'fontsize',22,'LineWidth',10,'resolution',300);
exportfig(gcf,'footprint.eps','height',8,'width',10,'fontsize',22,'LineWidth',10,'resolution',300);
%% MEAN MOTION / PERIOD
n = sqrt(mu./R_SV.^3);
T = 2 * pi ./ n;
lw = 4;
figure;
left_color = [0 0 0];
right_color = [0 0 0];
set(gcf,'defaultAxesColorOrder',[left_color; right_color]);
yyaxis left
loglog(h / 1000, T / 3600, 'linewidth',4);
hold on
% semilogy(h / 1000, n * 180 / pi);
xlabel('Altitude [km]')
ylabel('Orbital Period [hours]')
% yyaxis right
% semilogy(h / 1000, T / 3600);
% ylabel('Orbital Period [hours]')
grid on
lw = 2;
% plot satellites
loglog(aGPS*[1,1],[1e-13,50],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
loglog(aOneWeb*[1,1],[1e-13,50],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
loglog(aIridium*[1,1],[1e-13,50],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
loglog(aGSO*[1,1],[1e-13,50],'-.','color',[1,1,1]*0.7,'LineWidth',lw)
hold on
text(aIridium, 6, 'Iridium', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aOneWeb, 6, 'OneWeb', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aGPS, 6, 'GPS', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
text(aGSO, 6, 'GSO', 'Rotation', 90,...
'HorizontalAlignment', 'center', 'VerticalAlignment', 'bottom')
yticks([1, 2, 3, 6, 12, 24])
xlim([300, 50000])
ylim([1, 30])
yyaxis right
loglog(10000,10000)
yticks(log([1, 2, 3, 6, 12, 24]))
rat(360./[1, 2, 3, 6, 12, 24]/3600)
yticklabels({ '1/10','1/20','1/30','1/60','1/120','1/240' })
ylabel('Mean Motion [deg/s]')
xlim([300, 50000])
ylim(log([1, 30]))
xticks([500, 1000, 2000, 5000, 10000, 20000, 40000])
set(gca,'XTickLabelRotation',-45)
exportfig(gcf,'period.tiff','height',8,'width',10,'fontsize',22,'LineWidth',10,'resolution',300);
exportfig(gcf,'period.eps','height',8,'width',10,'fontsize',22,'LineWidth',10,'resolution',300);