I need help with my MATLAB code. There is an error in the following code. The error says my orbitaldynamics function must return a column vector. Can you help me fix it? mu_earth = 398600.4418; % Earth's gravitational parameter (km^3/s^2) R_earth = 6378.137; % Earth's radius (km) C_d = 0.3; % Drag coefficient (assumed) A = 0.023; % Cross-sectional area of ISS (km^2) m = 420000; % Mass of ISS (kg) % Initial conditions: position and velocity (ISS state vector) % ISS initial state vector (km and km/s) - sample data state_ISS =[-2.1195e+03, 3.9866e+03, 5.0692e+03, -5.3489, -5.1772, 1.8324]; % Time span for 10 revolutions T_orbit = 2 * pi * sqrt((norm(state_ISS(1:3))^3) / mu_earth); time_span = [0, 10 * T_orbit]; % Step 3: Numerical integration using ODE solver options = odeset('RelTol', 1e-12, 'AbsTol', 1e-12); [t, state] = ode45(@orbitalDynamics, time_span, state_ISS, options); % Step 4: Plot the results figure; plot3(state(:, 1), state(:, 2), state(:, 3)); xlabel('X (km)'); ylabel('Y (km)'); zlabel('Z (km)'); title('ISS Orbit with Perturbations'); %% Functions function dstate_dt = orbitalDynamics(t, state) % Extract position and velocity from state vector r = state(1:3); % position vector (km) v = state(4:6); % velocity vector (km/s) % Compute Earth's gravitational acceleration r_norm = norm(r); mu_earth = 398600.4418; % Earth's gravitational parameter (km^3/s^2) a_earth = -mu_earth / r_norm^3 * r; r_sun = 1.0e+08 * [-1.3216, -0.6303, -0.2732]; r_moon = 1.0e+05 * [1.3924, 2.9851, 1.6094]; % Compute third-body perturbations (Sun, Moon) a_third_bodies = computeThirdBodyAcceleration(t, r, r_sun, r_moon); % Compute drag acceleration w = [0, 0, 7.272e-5]; v_rel = v - cross(w, r); rho = 8.19e-12; A = 0.023; m = 420000; C_d = 0.3; a_drag = -(C_d/2)*rho*(A/m)*dot(v_rel,v_rel)*(v_rel/norm(v_rel)); % Compute SRP acceleration S_unit = r_sun/norm(r_sun); a_srp = computeSRP(A, m, r, r_sun, C_d, S_unit); % Total acceleration a_total = a_earth + a_third_bodies + a_drag + a_srp; % Define the derivative of the state vector dstate_dt = [v, a_total]; end % Additional functions for third-body and SRP calculations function acc_third_bodies = computeThirdBodyAcceleration(t, r, r_sun, r_moon) % Compute third-body effects using SPICE/MICE functions % For simplicity, assume Sun and Moon as third-bodies mu_sun = 132712440018; % km^3/s^2 mu_moon = 4902.8; % km^3/s^2 % Accelerations due to Sun and Moon acc_sun = -mu_sun * ((r_sun - r) / norm(r_sun - r)^3 + r_sun / norm(r_sun)^3); acc_moon = -mu_moon * ((r_moon - r) / norm(r_moon - r)^3 + r_moon / norm(r_moon)^3); acc_third_bodies = acc_sun + acc_moon; end function a_srp = computeSRP(A, m, r, r_sun, C_d, S_unit) % Compute Solar Radiation Pressure (SRP) acceleration E = 1361; c = 299792.458; A_earth = 510072000; C_tilda = (1/4) + (1/9)*C_d; a_srp = -(A/m)*(E/c)*(A_earth^2/norm(r-r_sun)^2)*C_tilda*S_unit; end

I need help with my MATLAB code. There is an error in the following code. The error says my orbitaldynamics function must return a column vector. Can you help me fix it? mu_earth = 398600.4418; % Earth's gravitational parameter (km^3/s^2) R_earth = 6378.137; % Earth's radius (km) C_d = 0.3; % Drag coefficient (assumed) A = 0.023; % Cross-sectional area of ISS (km^2) m = 420000; % Mass of ISS (kg) % Initial conditions: position and velocity (ISS state vector) % ISS initial state vector (km and km/s) - sample data state_ISS =[-2.1195e+03, 3.9866e+03, 5.0692e+03, -5.3489, -5.1772, 1.8324]; % Time span for 10 revolutions T_orbit = 2 * pi * sqrt((norm(state_ISS(1:3))^3) / mu_earth); time_span = [0, 10 * T_orbit]; % Step 3: Numerical integration using ODE solver options = odeset('RelTol', 1e-12, 'AbsTol', 1e-12); [t, state] = ode45(@orbitalDynamics, time_span, state_ISS, options); % Step 4: Plot the results figure; plot3(state(:, 1), state(:, 2), state(:, 3)); xlabel('X (km)'); ylabel('Y (km)'); zlabel('Z (km)'); title('ISS Orbit with Perturbations'); %% Functions function dstate_dt = orbitalDynamics(t, state) % Extract position and velocity from state vector r = state(1:3); % position vector (km) v = state(4:6); % velocity vector (km/s) % Compute Earth's gravitational acceleration r_norm = norm(r); mu_earth = 398600.4418; % Earth's gravitational parameter (km^3/s^2) a_earth = -mu_earth / r_norm^3 * r; r_sun = 1.0e+08 * [-1.3216, -0.6303, -0.2732]; r_moon = 1.0e+05 * [1.3924, 2.9851, 1.6094]; % Compute third-body perturbations (Sun, Moon) a_third_bodies = computeThirdBodyAcceleration(t, r, r_sun, r_moon); % Compute drag acceleration w = [0, 0, 7.272e-5]; v_rel = v - cross(w, r); rho = 8.19e-12; A = 0.023; m = 420000; C_d = 0.3; a_drag = -(C_d/2)rho(A/m)dot(v_rel,v_rel)(v_rel/norm(v_rel)); % Compute SRP acceleration S_unit = r_sun/norm(r_sun); a_srp = computeSRP(A, m, r, r_sun, C_d, S_unit); % Total acceleration a_total = a_earth + a_third_bodies + a_drag + a_srp; % Define the derivative of the state vector dstate_dt = [v, a_total]; end % Additional functions for third-body and SRP calculations function acc_third_bodies = computeThirdBodyAcceleration(t, r, r_sun, r_moon) % Compute third-body effects using SPICE/MICE functions % For simplicity, assume Sun and Moon as third-bodies mu_sun = 132712440018; % km^3/s^2 mu_moon = 4902.8; % km^3/s^2 % Accelerations due to Sun and Moon acc_sun = -mu_sun * ((r_sun - r) / norm(r_sun - r)^3 + r_sun / norm(r_sun)^3); acc_moon = -mu_moon * ((r_moon - r) / norm(r_moon - r)^3 + r_moon / norm(r_moon)^3); acc_third_bodies = acc_sun + acc_moon; end function a_srp = computeSRP(A, m, r, r_sun, C_d, S_unit) % Compute Solar Radiation Pressure (SRP) acceleration E = 1361; c = 299792.458; A_earth = 510072000; C_tilda = (1/4) + (1/9)C_d; a_srp = -(A/m)(E/c)(A_earth^2/norm(r-r_sun)^2)C_tilda*S_unit; end

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

I need help with my MATLAB code. There is an error in the following code. The error says my orbitaldynamics function must return a column vector. Can you help me fix it?

mu_earth = 398600.4418; % Earth's gravitational parameter (km^3/s^2)

R_earth = 6378.137; % Earth's radius (km)

C_d = 0.3; % Drag coefficient (assumed)

A = 0.023; % Cross-sectional area of ISS (km^2)

m = 420000; % Mass of ISS (kg)

% Initial conditions: position and velocity (ISS state vector)

% ISS initial state vector (km and km/s) - sample data

state_ISS =[-2.1195e+03, 3.9866e+03, 5.0692e+03, -5.3489, -5.1772, 1.8324];

% Time span for 10 revolutions

T_orbit = 2 * pi * sqrt((norm(state_ISS(1:3))^3) / mu_earth);

time_span = [0, 10 * T_orbit];

% Step 3: Numerical integration using ODE solver

options = odeset('RelTol', 1e-12, 'AbsTol', 1e-12);

[t, state] = ode45(@orbitalDynamics, time_span, state_ISS, options);

% Step 4: Plot the results

figure;

plot3(state(:, 1), state(:, 2), state(:, 3));

xlabel('X (km)');

ylabel('Y (km)');

zlabel('Z (km)');

title('ISS Orbit with Perturbations');

%% Functions

function dstate_dt = orbitalDynamics(t, state)

% Extract position and velocity from state vector

r = state(1:3); % position vector (km)

v = state(4:6); % velocity vector (km/s)

% Compute Earth's gravitational acceleration

r_norm = norm(r);

mu_earth = 398600.4418; % Earth's gravitational parameter (km^3/s^2)

a_earth = -mu_earth / r_norm^3 * r;

r_sun = 1.0e+08 * [-1.3216, -0.6303, -0.2732];

r_moon = 1.0e+05 * [1.3924, 2.9851, 1.6094];

% Compute third-body perturbations (Sun, Moon)

a_third_bodies = computeThirdBodyAcceleration(t, r, r_sun, r_moon);

% Compute drag acceleration

w = [0, 0, 7.272e-5];

v_rel = v - cross(w, r);

rho = 8.19e-12;

A = 0.023;

m = 420000;

C_d = 0.3;

a_drag = -(C_d/2)*rho*(A/m)*dot(v_rel,v_rel)*(v_rel/norm(v_rel));

% Compute SRP acceleration

S_unit = r_sun/norm(r_sun);

a_srp = computeSRP(A, m, r, r_sun, C_d, S_unit);

% Total acceleration

a_total = a_earth + a_third_bodies + a_drag + a_srp;

% Define the derivative of the state vector

dstate_dt = [v, a_total];

end

% Additional functions for third-body and SRP calculations

function acc_third_bodies = computeThirdBodyAcceleration(t, r, r_sun, r_moon)

% Compute third-body effects using SPICE/MICE functions

% For simplicity, assume Sun and Moon as third-bodies

mu_sun = 132712440018; % km^3/s^2

mu_moon = 4902.8; % km^3/s^2

% Accelerations due to Sun and Moon

acc_sun = -mu_sun * ((r_sun - r) / norm(r_sun - r)^3 + r_sun / norm(r_sun)^3);

acc_moon = -mu_moon * ((r_moon - r) / norm(r_moon - r)^3 + r_moon / norm(r_moon)^3);

acc_third_bodies = acc_sun + acc_moon;

end

function a_srp = computeSRP(A, m, r, r_sun, C_d, S_unit)

% Compute Solar Radiation Pressure (SRP) acceleration

E = 1361;

c = 299792.458;

A_earth = 510072000;

C_tilda = (1/4) + (1/9)*C_d;

a_srp = -(A/m)*(E/c)*(A_earth^2/norm(r-r_sun)^2)*C_tilda*S_unit;

end

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