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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
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 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; end fprintf('Mean orbital inclination %4.5f [deg] \n',i);
Mean orbital inclination 99.43667 [deg]
Small Satellites 