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Sun-Synchronous Circular Orbit, Inclination vs Altitude (LEO,J2 perturbed)

This code is a MATLAB script that can be used to design and analyze Sun-synchronous orbits. A Sun-synchronous orbit is a geocentric orbit which combines altitude and inclination in such a way that an object in this orbit has an a nodal regression rate which is equals to Earth’s orbital rotation speed around the Sun. The object in this orbit constantly illuminated by the Sun.

Output: Inclination vs Altitude Plot

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;

Sun_sync_vs_Alt

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