Bachelor Thesis: Analytical Study of SpaceX Mission Architecture to reach Mars Macía Fernández, O. BACHELOR’S DEGREE IN AEROSPACE VEHICLE ENGINEERING Bachelor Thesis ANALYTICAL STUDY OF SPACEX MISSION ARCHITECTURE TO REACH MARS Annex Student: Oscar Macía Fernández Director: Miquel Sureda Anfres Co-Director: David de la Torre Sangra Delivery date: June, 30th 2020 (30.06.2020) 1 Bachelor Thesis: Analytical Study of SpaceX Mission Architecture to reach Mars Macía Fernández, O. TABLE OF CONTENTS 1 Introduction ...................................................................................................................... 4 2 ArcHitecture analysis tool codes ....................................................................................... 4 2.1 Patched conic approxiMation ................................................................................... 4 2.2 Trajectory calculation .............................................................................................. 6 2.3 Starship launching ................................................................................................... 6 2.4 LauncHing inputs ..................................................................................................... 7 2.5 EartH atMospHere ..................................................................................................... 8 2.6 Mars atmospHere ...................................................................................................... 9 2.7 EartH Hyperbolic trajectory ................................................................................... 11 2.8 Mars Hyperbolic trajectory .................................................................................... 12 2.9 Hyperbolic anoMaly ............................................................................................... 13 2.10 Rendezvous ............................................................................................................ 13 2.11 Starship reentry ...................................................................................................... 14 2.12 Ballistic entry inputs .............................................................................................. 15 2.13 Manoeuvring entry inputs ...................................................................................... 16 2.14 Transfer orbit ......................................................................................................... 17 2.15 LaMbert solver ....................................................................................................... 18 2.16 Minimum Energy Transfer .................................................................................... 18 2.17 State transition Matrix ............................................................................................ 19 2.18 Orbital eleMents ..................................................................................................... 19 2.19 Planet position and velocity ................................................................................... 20 2.20 Plot orbit ................................................................................................................ 21 2.21 Keplerian eleMents to cartesian position and velocity .......................................... 21 2.22 Porkchop plot ......................................................................................................... 22 2.23 Date to Mjd2000 conversion .................................................................................. 23 3 Mars society competition case study tables .................................................................... 24 4 EconoMic plan tables ...................................................................................................... 31 2 Bachelor Thesis: Analytical Study of SpaceX Mission Architecture to reach Mars Macía Fernández, O. TABLE OF TABLES Table 1. Weight budget for Starship and Super Heavy rocket ............................................... 24 Table 2. Main materials estimation for Starship and Super Heavy rocket ............................ 24 Table 3. Summary of architecture vehicles ............................................................................ 25 Table 4. Weight budget for Shuttle 1 ...................................................................................... 25 Table 5. Weight budget for Rocket 1 ...................................................................................... 25 Table 6. Main materials estimation for Shuttle 1 and Rocket 1 ............................................. 26 Table 7. Weight budget for Shuttle 2 ...................................................................................... 26 Table 8. Weight budget for Rocket 2 ...................................................................................... 26 Table 9. Main materials estimation for Shuttle 2 and Rocket 2 ............................................. 27 Table 10. Main materials budget for Shuttle 1 and 2, including Rocket 1 and 2 ................... 27 Table 11. Weight budget for Launcher type I ......................................................................... 27 Table 12. Main materials estimation for Launcher type I ...................................................... 27 Table 13. Weight budget for Launcher type II ....................................................................... 28 Table 14. Main materials estimation for Launcher type II .................................................... 28 Table 15. Weight budget for Launcher type III ...................................................................... 28 Table 16. Weight budget for Booster of Launcher type III .................................................... 29 Table 17. Main materials estimation for Launcher type III ................................................... 29 Table 18. Weight budget for Launcher type IV ...................................................................... 29 Table 19. Weight budget for Booster of Launcher type IV ..................................................... 30 Table 20. Main materials estimation for Launcher type IV ................................................... 30 Table 21. Total weight budget for all vehicles ....................................................................... 30 Table 22. Mars population and Starships sent to Mars per year ........................................... 31 Table 23. Main materials price evolution data ...................................................................... 31 Table 24. Fuel required per period ........................................................................................ 31 Table 25. Total cost estimation for performing Mars' colonization process ......................... 31 3 Bachelor Thesis: Analytical Study of SpaceX Mission Architecture to reach Mars Macía Fernández, O. 1 INTRODUCTION The Main aiM of tHis document is to give extent inforMation of certain aspects that in the report document does not fit. This inforMation is related to the codes developed so as to obtain the results of the architecture interplanetary mission analysis tool developed for the thesis, and to the tables done so as to estiMate the Main Materials needed for the Mars society coMpetition case study and to the tables for developing the economic plan. 2 ARCHITECTURE ANALYSIS TOOL CODES In this first section, the different algorithMs for eacH pHase of the mission are presented. 2.1 PATCHED CONIC APPROXIMATION %Constant definition mu_S = 1.3271544*10^11; %Gravitational parameter of the Sun, km^3/s^2 mu_E = 3.986012*10^5; %Gravitational parameter of the Earth, km^3/s^2 mu_M = 4.282837*10^4; %Gravitational parameter of Mars d_1 = 1.4959965*10^8; %Distance between Earth and Sun, km d_2 = 1.524*d_1; %Distance between Mars and Sun, km r_E = 6370; %Earth radius, km r_M = 3389.5; %Mars radius, km v_E = 29.78; %Orbital speed of the Earth around the Sun, km/s v_M = 24.077; %Orbital speed of Mars around the Sun, km/s w_M = v_M/r_M; %Angular velocity of Mars around the Sun, rad/s t_1 = 0; %Time when the spacecraft departs %Heliocentric Transfer Orbit %1.Definition of the transfer orbit r_1 = d_1 + 100 + r_E; %Distance of departure of the spacecraft r_2 = d_2 + 300 + r_M; %Distance of arrival of the spacecraft a_t = (r_1 + r_2)/2; %Semimajor axis of the Hohmann transfer e_t = (r_2-r_1)/(r_2+r_1); %Eccentricity of the transfer orbit p = a_t*(1-e_t^2); %Parameter or semilatus rectum nu_1 = acos((p-r_1)/(e_t*r_1)); %Initial true anomaly nu_2 = acos((p-r_2)/(e_t*r_2)); %Final true anomaly i = 0; %Inclination Long_asc_node = 0; %Longitude of the ascending node Arg_per = 0; %Argument of periapsis %2.Obtainment of the required velocities E_t = - mu_S/(r_1+r_2); %Energy of the Hohmann transfer v_1 = sqrt(2*((mu_S/r_1)+E_t));%Heliocentric speed Delta_t = pi*sqrt(a_t^3/mu_S); %Time of flight t_2 = Delta_t + t_1; %Arrival time v_1cs = sqrt(mu_S/r_1); %Velocity in initial parking orbit Delta_v1 = v_1 - v_1cs; %Increment of velocity gamma_1 = (nu_2 - nu_1 - w_M*(t_2-t_1)); %Phase angle at departure h_t = r_1*v_1; %Angular momentum of the transfer orbit %Hyperbolic trajectories %1.Departure from Earth v_inf = Delta_v1; %Hyperbolic excess speed r_0 = r_E + 100; %Initial height v_0 = sqrt(v_inf^2+((2*mu_E)/(r_0))); %Injection speed h = r_0*v_0; %Angular momentum E_h = v_0^2/2 - mu_E/r_0; %Mechanical energy of the hyperbolic escape 4 Bachelor Thesis: Analytical Study of SpaceX Mission Architecture to reach Mars Macía Fernández,