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Thrust into Space Maxwell W. Hunter, II

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Newton’s 3rd Law of Motion Momentum is conserved, equation 1- 1

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Force Force, equation 1-2 Weight, equation 1-3

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Energy Kinetic energy, equation 1-4 Ratio of kinetic energy of gun to bullet, equation 1-5

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Guns as Rockets Paris Gun, WW I Change in velocity, equation 1-6

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Rocket Engines Thrust, equation 1-7

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Rocket Nomenclature Figure 1-1

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Fuel Consumption Specific impulse of engine, equation 1-8 Effective exhaust velocity, equation 1-9

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Power Power expended, equation 1-10 Effective power, equation 1-11

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Internal Energy Release Exit velocity, equation 1-12 Combustion temperature, equation 1-13 Velocity of molecule, equation 1-14

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Rocket Energy Efficiency Figure 1-2

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Nozzle Altitude Effect Figure 1-3

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Nozzle Altitude Performance Figure 1-4

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Pump Power Pump power, equation 1-15 Pump power for both propellants, equation 1-16

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The Rocket Equation Change in velocity, equation 1-17 Impulsive velocity, equation 1-18

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The Rocket Equation Figure 1-5

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Useful Load Useful load, equation 1-19

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The Rocket Equation Figure 1-6

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Energy Efficiency Kinetic energy of useful load, equation 1-20 Total energy expended by exhaust, equation 1-21

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External Energy Efficiency Figure 1-7

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Effect of Initial Velocity Increase of kinetic energy of useful load, equation 1-22 Total kinetic energy expended, equation 1- 23

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External Energy Efficiency Figure 1-8

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Ballistics Flat earth, no drag From Newton’s Laws of Motion, equations in 2-1 Range vs. velocity, equation 2-2

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Energy Potential energy, equation 2-3 Ratio of kinetic energy increase to initial kinetic energy, equation 2-4

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Forces During Motor Burning Velocity loss due to gravity, equation 2-5 Figure 2-1

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Airplane Lift/Drag Ratio Airplane energy, equation 2-6 Cruising efficiency, equation 2-7 Velocity equivalent of energy used, equation 2-8

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Airplane Lift/Drag Ratio Figure 2-2

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Automobile Lift/Drag Ratio Figure 2-3

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Ship Lift/Drag Ratio Figure 2-4

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Solid-Propellant Rockets Figure 2-5

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Solid Rockets Acceleration of guns or rockets, equation 2- 9 Honest John Missile

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Required Acceleration Figure 2-6

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Four Decades of Development Figure 2-7

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Theoretical Propellant Performance Vacuum ε = 40 Sea Level OxidizerFuel Mixture Ratio Specific Gravity I sp (sec) NH 4 ClO 4 20% Al H2O2H2O2 N2H4N2H N2O4N2O4 N2H4N2H O 2 ( cyro)Kerosene O 2 ( cyro)N2H4N2H

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Elliptical Orbit Nomenclature Figure 3-1

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Circular Orbits Gravity as a function of distance, equation 3-1 Velocity of satellite, equation 3-2 Period, equation 3-3 Period, equation 3-4

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Potential Energy Potential energy, equation 3-5 Maximum potential energy, equation 3-6

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Escape Velocity Escape velocity, equation 3-7

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The Vis-Vita Law Kinetic and potential energy, equation 3-8 Conservation of angular momentum, equation 3-9 Perigee velocity vs. escape velocity at perigee, equation 3-10 Velocity, equation 3-11

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The Vis-Vita Law Velocity and circular velocity, equation 3-12 Orbital period, equation 3-13

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Optimum Ballistic Missile Trajectories Figure 3-2

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Global Rocket Velocities Figure 3-3

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Hohmann Transfer Figure 3-4

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Velocities Required to Establish Orbit Figure 3-5 Potential energy and kinetic energy, equation 3-14

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Planet Escape Velocities and Radii Planet Escape Velocity (feet/sec) Radius (Earth = 1.0) Earth36, Venus33, Pluto32, Mars16, Mercury13,

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Satellite Escape Velocities and Radii Satellite (Planet) Escape Velocity (feet/sec) Radius (Earth = 1.0) Triton (Neptune)10, Ganymede (Jupiter)9, Titan (Saturn)8, Io (Jupiter)8, Moon (Earth)7, Callisto (Jupiter)7, Europa (Jupiter)6,

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Gravity Losses Effective gravity, equation 3-15

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Large, Solid Propellant Motors Figure 3-6

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The Planets Orbital Data Planet Semi-Major Axis AU Perihelion AU Aphelion AU Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune

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The Planets Orbital Data Mean Celestial Longitude Planet Off Ascending Node of Perihelion Epoch, 1/1/1996 Mercury 47.93°76.93°210.29° Venus °84.87° Earth °98.89° Mars 49.3°335.44°324.31° Jupiter °13.5°87.32° Saturn °91.5°347.57° Uranus 73.9°168.65°166.43° Neptune 131.4°53°230.02°

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The Planets Orbital Data Inclination Planet Orbital to Ecliptic Equatorial to Orbit Mercury 7.00 Venus 3.39 Earth Mars Jupiter Saturn Uranus Neptune

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The Planets Orbital Data Planet Orbital Velocity About Sun (ft/sec) Period of Revolution (years) Mercury 157, Venus 114, Earth 97, Mars 79, Jupiter 42, Saturn 31, Uranus 22, Neptune 17,

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Solar System Data Jupiter’s Moons Diamete r (miles) Surfac e Gravit y Perio d (days ) Escape Velocity (fps) Io2, ,250 Europa1, ,900 Ganymed e 3, ,430 Callisto2, ,450

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The Outer Solar System Figure 4-1

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Hyperbolic Excess Velocity Vis-Viva Law, hyperbolic excess velocity, equation 4-1 Equation 4-2 Equation 4-3

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Hyperbolic Excess Velocity Figure 4-2

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Solar System Hyperbolic Excess Velocity Figure 4-3

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Hohmann Transfer Velocities Figure 4-4

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Hohmann Transfer Travel Time Figure 4-5

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Synodic Period of Planets Synodic period, equation 4-4 Figure 4-6

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Solar Probe Type Missions with Two Impulse Transfers Figure 4-7

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Elastic Impact Analogy for the Use of Planetary Energy Figure 4-8

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Use of Planetary Energy Weight of vehicle, equation 4-5 Equation 4-6

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Planetary Swing- Around Angle Figure 4-9

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Distance from Center of Sun (Astronomical Units) Solar Probe Velocity Requirements Figure 4-10

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Out-of-Ecliptic Velocity Requirements Figure 4-11

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Solar System Travel Times Figure 4-12

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Planetary Arrival Velocities Figure 4-13

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Planetary Capture Velocities Figure 4-14

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Payload Velocity Requirements Figure 4-15

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Selected Comets Comet Perihelio n (AU) Aphelion (AU) Period (years ) Perihelio n Time Encke Forbes D’Arrest Faye Halley

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Earth-Mars Launch Windows Figure 4-16

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Earth-Mars Launch Windows Figure 4-17

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Round Trip Synodic Period Effects Figure 4-18

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Theoretical Liquid Propellant Performance Equilibrium Flow Vacuum Sea Level OxidizerFuel Mixture Ratio Specific Gravity I sp OxygenHydrogen FluorineHydrogen FluorineAmmonia O2-DifluorideKerosene HydrazineDiborate Hydrazine Pentaboran e

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High-Performance Chemical Rockets Figure 4-19

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New Types of Engines Wall stress, equation 4-7 Engine chamber weight, equation 4-8

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New Engine Types Figure 4-20

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Nuclear Thermal Rockets Einstein’s famous equation 4-9 Kiwi-A rocket engine

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Graphite Solid-Core Engine Figure 4-21

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Isotopic Heat Sources Parent Isotope Half- Life (years ) Type of Decay Specific Power (watts/gm) Shieldin g Pure Fuel Compound Cesium β/γ Heavy Plutonium α Minor Curium α Moderate Polonium α141134Minor Cobalt β/γ Heavy

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Nuclear Vehicle Shielding Comparison Figure 4-22

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Required Fuel Weights for Single-Stage Space Launch Vehicles Figure 4-23

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Heavy Velocity Rockets and Gravity Fields Travel time, equation 5-1 Minimum travel time in terms of inner and outer distance, equation 5-2 Maximum travel time, equation 5-3

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Minimum Travel Times from Earth Including Braking Requirements Figure 5-1

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Average Travel Times from Earth Including Braking Requirements Figure 5-2

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Solar System Synodic Periods Figure 5-3

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Travel Times Between Planets Figure 5-4

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Escape with Low Acceleration Velocity required to escape, equation 5-4 For launch from circular orbit, equation 5-5

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Total Velocity to Escape Figure 5-5

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Heliocentric Velocity Requirements Time to generate velocity at constant acceleration, equation 5-6 Figure 5-6

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Specific Impulse From Nuclear Reactions Figure 5-7

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Typical Gaseous Core Engines Figure 5-8 Power output, equation 5-7

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Cost of Nuclear Fission Fuel and Propellant Figure 5-9

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Cooling Limitations Amount by which gaseous heating raises specific impulse, equation 5-8

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Thrust/Weight Ratio of Gaseous Fission Engines Figure 5-10

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Types of Electrical Rocket Thrusters Figure 5-11

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Electric Rocket Performance Characteristic velocity, equation 5-9 For perfect efficiency, weight of power supply relates to weight of propellant, equation 5- 10

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Electrical Rocket Performance Figure 5-12

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Single-Stage Spaceship Fuel and Propellant Costs Figure 5-13

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Transportation vs. Ammunition Re-Use Assumptions Figure 5-14

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Spaceship Payload Capability Figure 5-15

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Single-Stage Spaceship Fuel, Propellant, and Structure Costs Figure 5-16

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Single-Stage Spaceship Fuel, Propellant, and Structure Costs Figure 5-17

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Dose to Ground Observer from Gaseous Core Rockets Figure 5-18

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Gaseous Fission Powered Spaceship Figure 5-19

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Acceleration Distance Figure 5-20

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The Near Stars Figure 6-1

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The Galaxy Figure 6-2

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Hypothetical Galactic Community Figure 6-3

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Time Dilation Ship time, equation 6- 1

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Interstellar Travel Time Dilation Effects Figure 6-4

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Fusion Rockets Initial weight vs. final weight, equation 6-2 Rocket braking on arrival, equation 6-3

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Fusion Starship Weight Ratio Figure 6-5

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Fusion Starship Power Figure 6-6

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Cost of Nuclear Rocket Fuel and Propellant Figure 6-7

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Photon Rockets Effective exhaust velocity, equation 6-4 Relativistic rocket equation 6-5 Exhaust power of photon beam, equation 6-6

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Starship Weight Ratio Figure 6-8

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Mass Annihilation Rockets Mass annihilation rocket equation 6-7 Mass annihilation rocket braking equation 6-8

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Starship Power Figure 6-9

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Mass Annihilation Rockets Overall time dilation effect, equation 6-9 Relation between time dilation achieved and rocket weight, equation 6-10 Equation 6-11

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