Certainly! Below is a conceptual MATLAB code that simulates a **three-stage reusable rocket launch vehicle** to **geostationary orbit (GEO)**. This script models the mass, velocity, and altitude profile through each stage using the Tsiolkovsky rocket equation, simple kinematics, and basic assumptions. **Assumptions:** - Vertical ascent (no gravity or drag losses for simplicity; you can add them for realism). - Each stage has its own specific impulse and structural mass fraction. - The payload is delivered to GEO (altitude ≈ 35,786 km). - Reusable stages return after separation (not simulated in detail here). --- ```matlab % Three-Stage Reusable Rocket to GEO Simulation clc; clear; % Constants g0 = 9.80665; % m/s^2, standard gravity Re = 6371e3; % Earth radius in meters GEO_alt = 35786e3; % GEO altitude in meters % Payload parameters payload_mass = 5000; % kg % Stage parameters: [propellant_mass, structural_mass_fraction, Isp (s)] stages = [ ... 200000, 0.07, 300; % Stage 1: 200 t prop, 7% structure, 300 s 50000, 0.08, 350; % Stage 2: 50 t prop, 8% structure, 350 s 15000, 0.10, 420]; % Stage 3: 15 t prop, 10% structure, 420 s n_stages = size(stages,1); % Initialize m_payload = payload_mass; deltaV = zeros(n_stages,1); masses = zeros(n_stages+1,1); velocities = zeros(n_stages+1,1); % Start from payload mass masses(end) = m_payload; % Loop backwards to calculate initial mass of each stage for i = n_stages:-1:1 m_prop = stages(i,1); f_struct = stages(i,2); Isp = stages(i,3); m_struct = m_prop * f_struct; m_stage = m_prop + m_struct + masses(i+1); % Delta-V for this stage deltaV(i) = Isp * g0 * log(m_stage / (m_struct + masses(i+1))); masses(i) = m_stage; end % Total delta-V (ideal, no gravity/drag losses) total_deltaV = sum(deltaV); % GEO requirements (approximate, for LEO to GEO transfer) V_LEO = sqrt(g0 * Re); % Orbital speed at LEO (~7.8 km/s) V_GEO = sqrt(g0 * (Re+GEO_alt)); % Orbital speed at GEO (~3.1 km/s) deltaV_required = 11200; % m/s (rough estimate including losses) % Output results fprintf('--- Three-Stage Reusable Rocket to GEO Simulation ---\n\n'); for i = 1:n_stages fprintf('Stage %d:\n', i); fprintf(' Propellant mass: %.0f kg\n', stages(i,1)); fprintf(' Structural mass: %.0f kg\n', stages(i,1)*stages(i,2)); fprintf(' Initial mass: %.0f kg\n', masses(i)); fprintf(' Burnout mass: %.0f kg\n', masses(i+1) + stages(i,1)*stages(i,2)); fprintf(' Isp: %.0f s\n', stages(i,3)); fprintf(' Delta-V delivered: %.1f m/s\n\n', deltaV(i)); end fprintf('Total initial mass (on pad): %.0f kg\n', masses(1)); fprintf('Total delta-V (ideal): %.1f m/s\n', total_deltaV); fprintf('Delta-V required to GEO: %.1f m/s\n', deltaV_required); % Plot Delta-V per stage figure; bar(1:n_stages, deltaV); xlabel('Stage'); ylabel('Delta-V (m/s)'); title('Delta-V delivered per stage to GEO'); grid on; % Plot mass after each stage figure; stairs(0:n_stages, masses, 'LineWidth', 2); xlabel('Stage separation'); ylabel('Mass (kg)'); title('Rocket mass after each stage'); grid on; ``` --- ## Notes: - **This is a simplified model!** For a more realistic simulation, you should account for **gravity losses**, **drag losses**, **flight path angle**, **staging time**, and **real trajectory integration**. - You can **adjust the stage parameters** and **payload mass** to explore different designs. - The **delta-V required** is a rough estimate for Earth to GEO including losses. - **Reusable stages**: This code doesn't model the return/landing of stages. If you want to account for recovery, reserve extra propellant accordingly. If you want a more advanced simulation (with trajectory integration, gravity, drag, etc.), let me know!