Sun Synchronous with For Loop
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Daynah Rodriguez
le 30 Mai 2021
Commenté : Alan Stevens
le 30 Mai 2021
Hello,
I am trying to perform plot a of sun synchronous orbit using GMAT (a mission design software which has a script format). I found this code for matlab:
clc;
clear all;
mu = 398600.440; % Earth’s gravitational parameter [km^3/s^2]
Re = 6378; % Earth radius [km]
J2 = 0.0010826269; % Second zonal gravity harmonic of the Earth
we = 1.99106e-7; % Mean motion of the Earth in its orbit around the Sun [rad/s]
% Input
Alt = 250:5:1000; % Altitude,Low Earth orbit (LEO)
a = Alt + Re; % Mean semimajor axis [km]
e = 0.0; % Eccentricity
h = a*(1 - e^2); % [km]
n = (mu./a.^3).^0.5; % Mean motion [s-1]
tol = 1e-10; % Error tolerance
% Initial guess for the orbital inclination
i0 = 180/pi*acos(-2/3*(h/Re).^2*we./(n*J2));
err = 1e1;
while(err >= tol )
% J2 perturbed mean motion
np = n.*(1 + 1.5*J2*(Re./h).^2.*(1 - e^2)^0.5.*(1 - 3/2*sind(i0).^2));
i = 180/pi*acos(-2/3*(h/Re).^2*we./(np*J2));
err = abs(i - i0);
i0 = i;
end
plot(Alt,i,'.b');
grid on;hold on;
xlabel('Altitude,Low Earth orbit (LEO)');
ylabel('Mean orbital inclination');
title('Sun-Synchronous Circular Orbit,Inclination vs Altitude(LEO,J2 perturbed)');
hold off;
However, GMAT does not interpret Alt = 250:5:1000. And so I've been trying to modify it such as using the for loop on matlab first
for Alt = 250:5:1000
a = Alt + Re; % Mean semimajor axis [km]
e = 0.0; % Eccentricity
h = a*(1 - e^2); % [km]
n = (mu./a.^3).^0.5; % Mean motion [s-1]
end
But it's not working...
This is the graph Im trying to achieve with matlab if the modification is done right and before applying it on GMAT
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/635635/image.jpeg)
Thank you
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Réponse acceptée
Alan Stevens
le 30 Mai 2021
When I run the program you've listed above it produces the graph you show!
2 commentaires
Alan Stevens
le 30 Mai 2021
Ok. Like this then:
mu = 398600.440; % Earth’s gravitational parameter [km^3/s^2]
Re = 6378; % Earth radius [km]
J2 = 0.0010826269; % Second zonal gravity harmonic of the Earth
we = 1.99106e-7; % Mean motion of the Earth in its orbit around the Sun [rad/s]
% Input
Alt = 250:5:1000; % Altitude,Low Earth orbit (LEO)
i = zeros(1,numel(Alt)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for k = 1:numel(Alt) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
a = Alt(k) + Re; % Mean semimajor axis [km] %%%%%%%%%%%%%%%%%%
e = 0.0; % Eccentricity
h = a*(1 - e^2); % [km]
n = (mu./a.^3).^0.5; % Mean motion [s-1]
tol = 1e-10; % Error tolerance
% Initial guess for the orbital inclination
i0 = 180/pi*acos(-2/3*(h/Re).^2*we./(n*J2));
err = 1e1;
while(err >= tol )
% J2 perturbed mean motion
np = n.*(1 + 1.5*J2*(Re./h).^2.*(1 - e^2)^0.5.*(1 - 3/2*sind(i0).^2));
i(k) = 180/pi*acos(-2/3*(h/Re).^2*we./(np*J2)); %%%%%%%%%%%%%%%%%%
err = abs(i(k) - i0); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
i0 = i(k); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end
end
plot(Alt,i,'.b');
grid on;hold on;
xlabel('Altitude,Low Earth orbit (LEO)');
ylabel('Mean orbital inclination');
title('Sun-Synchronous Circular Orbit,Inclination vs Altitude(LEO,J2 perturbed)');
hold off;
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