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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

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;
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;




  1. William F. says:

    Always in the sun? Is that certain? From my understanding, the nodal regression is about ~1 deg/day. Therefore, the beta angle you launch into would be about constant. If you launched into a beta angle that was close to ~70 to 90 (dusk or dawn), then I can see not having an eclipse. But if you launch at Noon…then you would have a 0 beta angle…and your max eclipse time of close to 30 minutes (~1/3 of an orbit). Or thereabout.


    (P.S. I don’t know, but I would think that you would only be able to achieve max beta anlge close to 90 at certain time of the year. My though is that would be around the Spring/Fall Equinox.)

    • Debdeeprc says:

      Hi William, I am working on a project which involve studies about sun synchronous orbits, and I believe what you said is correct. Sun synchronous orbits have a constant Beta angle. So, if the Beta angle is close to +90° or -90°, it would mean constant illumination. A Beta angle of 0° will have maximum eclipse time.

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