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Sun-Synchronous (Heliosynchronous) Orbit, Mean Orbital Inclination (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. Input: a = Mean semimajor axis, e = Eccentricity

Output: i = Mean orbital inclination

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
a = 7378;           % Mean semimajor axis [km]
e = 0.05;           % 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;
fprintf('Mean orbital inclination %4.5f [deg] \n',i);
Mean orbital inclination 99.43667 [deg]
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