model the earth's orbit around the sun using keplers laws in matlab. show 'real-time' calculated values for speed and time in simulation. make a simulation of it in matlab

main.m
% Simulation parameters
t_start = 0;                % Start time (in seconds)
t_end = 365 * 24 * 60 * 60; % End time (1 year)
dt = 60 * 60;               % Time step (1 hour)

% Earth's orbital parameters
semi_major_axis = 1.496e11; % Semi-major axis (m)
eccentricity = 0.017;       % Eccentricity
mean_motion = 2*pi / (365 * 24 * 60 * 60); % Mean motion (rad/s)
mean_anomaly_0 = 0;         % Initial mean anomaly (rad)

% Calculate orbital parameters
eccentric_anomaly_0 = 2*atan(sqrt((1 - eccentricity) / (1 + eccentricity)) * tan(mean_anomaly_0/2));
true_anomaly_0 = 2*atan(sqrt((1 + eccentricity) / (1 - eccentricity)) * tan(eccentric_anomaly_0/2));

% Initialize variables
position = zeros(2, length(t_start:dt:t_end));
velocity = zeros(2, length(t_start:dt:t_end));

% Simulate Earth's orbit
for t = t_start:dt:t_end
    % Calculate orbital parameters at current time
    mean_anomaly = mean_anomaly_0 + mean_motion * t;
    eccentric_anomaly = fzero(@(E) E - eccentricity * sin(E) - mean_anomaly, eccentric_anomaly_0);
    true_anomaly = 2*atan(sqrt((1 + eccentricity) / (1 - eccentricity)) * tan(eccentric_anomaly/2));

    % Calculate position and velocity at current time
    radius = semi_major_axis * (1 - eccentricity^2) / (1 + eccentricity * cos(true_anomaly));
    position(:, t/dt + 1) = [radius*cos(true_anomaly); radius*sin(true_anomaly)];
    velocity(:, t/dt + 1) = [-radius*mean_motion*sin(true_anomaly); radius*mean_motion*cos(true_anomaly)];

    % Update plot in real-time
    plot(position(1, :), position(2, :))
    xlabel('X position (m)')
    ylabel('Y position (m)')
    title('Earth Orbit Simulation')
    axis equal
    drawnow

    % Display speed and time in real-time
    speed = norm(velocity(:, t/dt + 1));
    disp(['Speed: ', num2str(speed), ' m/s | Time: ', num2str(t), ' s'])
end
1820 chars
44 lines