Design of a Planetary Explorer Third Year Project Jack Andrews (ChCh) Aamir Aziz (New) Nicholas Baker (SJC) Alexander Chadwick (SJC) James Coates (BNC) Oliver Cohen (LMH) Liam Donovan (Hert) Hugo Grimmett (BNC) James Hawkes (Keb) Michael May (Worc) Joshua McFarlane (SJC) 2009-2010 Contents 1 Introduction 13 1.1 Mission to Titan . 13 1.2 Titan's Characteristics . 13 1.3 Mission Components . 14 2 Delivery of the Orbiter 15 2.1 Introduction . 15 2.2 Orbital Mechanics . 15 2.2.1 Kepler's Laws . 15 2.2.2 Energy Considerations . 17 2.2.3 Characterising Orbits . 18 2.3 Transfer Orbits . 20 2.4 The N-Body Problem . 20 2.4.1 A Computational Model . 20 2.4.2 Sourcing Planetary Data . 21 2.5 Simulating the Problem in Matlab . 22 2.6 Fly-by Manoeuvres . 22 2.6.1 The Origin of Gravity-Assist Velocity Increase . 22 1 CONTENTS 2.6.2 Calculating the Velocity Increase . 23 2.7 The Oberth Effect . 23 2.8 Time-to-Intercept & Mean Anomaly . 23 2.9 Targetting Manoeuvres . 24 2.10 Planning out the route to Titan . 26 2.11 Launch . 26 2.11.1 Calculating the Relative Launch Velocity . 28 2.11.2 Optimal Launch Window . 29 2.12 The Control System . 31 2.12.1 Implementing the Control System in Matlab . 31 2.13 The Simulation . 32 2.14 Conclusions . 35 3 Attitude Control System 36 3.1 Introduction . 36 3.1.1 Purpose . 36 3.1.2 Control Goal . 37 3.1.3 System Overview . 37 3.1.4 Aim . 38 3.2 Mathematical model of the orbiter dynamics . 38 3.2.1 Reference Frames . 38 3.2.2 Rigid body Dynamics . 39 3.2.3 Attitude Kinematics . 40 3.2.4 Actuator Dynamics . 40 3.2.5 Gravity Gradient Torque . 41 2 CONTENTS 3.2.6 Linearisation of the model . 42 3.3 Continuous-time Controller . 43 3.3.1 Plant Model . 43 3.3.2 Design Specifications . 44 3.3.3 PID Control . 45 3.3.4 Optimal Control . 47 3.4 Discrete-time Controller . 50 3.4.1 Discrete Plant Model . 50 3.4.2 Design by Emulation . 51 3.4.3 Estimator Design . 51 3.4.4 Regulator Design . 53 3.5 Conclusions . 54 4 Landing the Probe 56 4.1 Introduction . 56 4.2 Gathering Data . 56 4.2.1 Wind Speed . 57 4.2.2 Pressure and Density . 59 4.3 Simulation Engine . 60 4.3.1 Gravity . 60 4.3.2 Drag . 60 4.3.3 First Simulation . 61 4.3.4 Drift . 62 4.4 A Safe Landing . 62 4.4.1 Parachutes/Thrusters . 62 3 CONTENTS 4.4.2 Simulating Parachutes . 63 4.4.3 Test Data . 63 4.5 Analysis . 66 4.5.1 Test Plan . 66 4.5.2 The Need For Analysis . 67 4.5.3 Analysis Example - Drift . 68 4.5.4 Parameter Weighting . 70 4.5.5 Result Weighting . 72 4.5.6 Finding the Optimal Area . 72 4.6 Final Design . 75 4.6.1 Results . 76 4.7 Errors . 78 4.7.1 Systematic Errors . 78 4.7.2 Theoretical Wind Model . 80 4.8 Predicted Landing Zone . 81 5 Problems Faced by the Explorer During its Voyage Through Space 83 5.1 Introduction . 83 5.2 Problems . 83 5.2.1 Problems Encountered on Earth . 84 5.2.2 Problems Encountered whilst en Route to Titan . 84 5.2.3 Problems Encountered whilst in Orbit around Titan . 85 5.3 Effects . 87 5.3.1 Heating Effects . 87 5.3.2 Radiation Effects . 88 4 CONTENTS 5.3.3 Power Requirement Effects . 90 5.4 Solutions . 91 5.4.1 Solving the Heating Problem . 91 5.4.2 Solving the Radiation Problem . 94 5.4.3 Solving the Electrostatic Discharge Problem . 97 5.4.4 Solving the Power Demand Problem . 99 5.4.5 Solving the.