Thrust into Space Maxwell W. Hunter, II

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

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

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

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

Rocket Engines Thrust, equation 1-7

Rocket Nomenclature Figure 1-1

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

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

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

Rocket Energy Efficiency Figure 1-2

Nozzle Altitude Effect Figure 1-3

Nozzle Altitude Performance Figure 1-4

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

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

The Rocket Equation Figure 1-5

Useful Load Useful load, equation 1-19

The Rocket Equation Figure 1-6

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

External Energy Efficiency Figure 1-7

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

External Energy Efficiency Figure 1-8

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

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

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

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

Airplane Lift/Drag Ratio Figure 2-2

Automobile Lift/Drag Ratio Figure 2-3

Ship Lift/Drag Ratio Figure 2-4

Solid-Propellant Rockets Figure 2-5

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

Required Acceleration Figure 2-6

Four Decades of Development Figure 2-7

Theoretical Propellant Performance Vacuum ε = 40 Sea Level Oxidizer Fuel Mixture Ratio Specific Gravity Isp (sec) NH4ClO4 20% Al 1.74 314 266 H2O2 N2H4 2.09 1.26 325 287 N2O4 1.40 1.22 324 292 O2 (cyro) Kerosene 2.67 1.02 300 0.95 1.07 343 313

Elliptical Orbit Nomenclature Figure 3-1

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

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

Escape Velocity Escape velocity, equation 3-7

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

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

Optimum Ballistic Missile Trajectories Figure 3-2

Global Rocket Velocities Figure 3-3

Hohmann Transfer Figure 3-4

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

Planet Escape Velocities and Radii Escape Velocity (feet/sec) Radius (Earth = 1.0) Earth 36,700 1.0 Venus 33,600 0.97 Pluto 32,700 1.1 Mars 16,400 0.53 Mercury 13,700 0.38

Satellite Escape Velocities and Radii Satellite (Planet) Escape Velocity (feet/sec) Radius (Earth = 1.0) Triton (Neptune) 10,400 0.31 Ganymede (Jupiter) 9,430 0.39 Titan (Saturn) 8,900 Io (Jupiter) 8,250 0.26 Moon (Earth) 7,800 0.272 Callisto (Jupiter) 7,450 0.37 Europa (Jupiter) 6,900 0.23

Gravity Losses Effective gravity, equation 3-15

Large, Solid Propellant Motors Figure 3-6

The Planets Orbital Data Semi-Major Axis AU Perihelion AU Aphelion AU Mercury 0.387 0.308 0.467 Venus 0.723 0.718 0.728 Earth 1.000 0.983 1.017 Mars 1.524 1.381 1.666 Jupiter 5.203 4.951 5.455 Saturn 9.539 9.008 10.070 Uranus 19.182 18.277 20.087 Neptune 30.058 29.800 30.315

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 76.38 131.1° 84.87° Earth 102.12° 98.89° Mars 49.3° 335.44° 324.31° Jupiter 100.11° 13.5° 87.32° Saturn 113.42° 91.5° 347.57° Uranus 73.9° 168.65° 166.43° Neptune 131.4° 53° 230.02°

The Planets Orbital Data Inclination Planet Orbital to Ecliptic Equatorial to Orbit Mercury 7.00 Venus 3.39 Earth 23.45 Mars 1.85 25.20 Jupiter 1.31 3.12 Saturn 2.49 26.75 Uranus 0.77 97.98 Neptune 1.77 29

The Planets Orbital Data Orbital Velocity About Sun (ft/sec) Period of Revolution (years) Mercury 157,000 0.240 Venus 114,800 0.615 Earth 97,600 1.0 Mars 79,100 1.881 Jupiter 42,800 11.86 Saturn 31,600 29.46 Uranus 22,200 84.02 Neptune 17,800 164.78

Solar System Data Jupiter’s Moons Diameter (miles) Surface Gravity Period (days) Escape Velocity (fps) Io 2,060 0.195 1.77 8,250 Europa 1,790 0.156 3.55 6,900 Ganymede 3,070 0.170 7.15 9,430 Callisto 2,910 0.112 16.69 7,450

The Outer Solar System Figure 4-1

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

Hyperbolic Excess Velocity Figure 4-2

Solar System Hyperbolic Excess Velocity Figure 4-3

Hohmann Transfer Velocities Figure 4-4

Hohmann Transfer Travel Time Figure 4-5

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

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

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

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

Planetary Swing-Around Angle Figure 4-9

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

Out-of-Ecliptic Velocity Requirements Figure 4-11

Solar System Travel Times Figure 4-12

Planetary Arrival Velocities Figure 4-13

Planetary Capture Velocities Figure 4-14

Payload Velocity Requirements Figure 4-15

Selected Comets Comet Perihelion (AU) Aphelion (AU) Period (years) Perihelion Time Encke 0.339 4.09 3.30 1967-9-12 Forbes 1.545 5.36 6.42 1967-12-21 D’Arrest 1.378 5.73 6.70 1967-6-17 Faye 1.652 5.95 7.41 1969-12-29 Halley 0.587 35.0 76.03 1910-4-20

Earth-Mars Launch Windows Figure 4-16

Earth-Mars Launch Windows Figure 4-17

Round Trip Synodic Period Effects Figure 4-18

Theoretical Liquid Propellant Performance Equilibrium Flow Vacuum Sea Level Oxidizer Fuel Mixture Ratio Specific Gravity Isp Oxygen Hydrogen 4.5 0.31 456 391 Fluorine 9.0 0.50 475 411 Ammonia 3.31 1.12 416 360 O2-Difluoride Kerosene 3.8 1.28 396 341 Hydrazine Diborate 1.16 0.63 401 339 Pentaborane 1.26 0.79 390 328

High-Performance Chemical Rockets Figure 4-19

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

New Engine Types Figure 4-20

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

Graphite Solid-Core Engine Figure 4-21

Specific Power (watts/gm) Isotopic Heat Sources Parent Isotope Half-Life (years) Type of Decay Specific Power (watts/gm) Shielding Pure Fuel Compound Cesium-137 30 β/γ 0.42 0.067 Heavy Plutonium-238 89 α 0.56 0.39 Minor Curium-244 18 2.8 2.49 Moderate Polonium-210 0.38 141 134 Cobalt-60 5.3 17.4 1.7

Nuclear Vehicle Shielding Comparison Figure 4-22

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

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

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

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

Solar System Synodic Periods Figure 5-3

Travel Times Between Planets Figure 5-4

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

Total Velocity to Escape Figure 5-5

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

Specific Impulse From Nuclear Reactions Figure 5-7

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

Cost of Nuclear Fission Fuel and Propellant Figure 5-9

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

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

Types of Electrical Rocket Thrusters Figure 5-11

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

Electrical Rocket Performance Figure 5-12

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

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

Spaceship Payload Capability Figure 5-15

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

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

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

Gaseous Fission Powered Spaceship Figure 5-19

Acceleration Distance Figure 5-20

The Near Stars Figure 6-1

The Galaxy Figure 6-2

Hypothetical Galactic Community Figure 6-3

Time Dilation Ship time, equation 6- 1

Interstellar Travel Time Dilation Effects Figure 6-4

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

Fusion Starship Weight Ratio Figure 6-5

Fusion Starship Power Figure 6-6

Cost of Nuclear Rocket Fuel and Propellant Figure 6-7

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

Starship Weight Ratio Figure 6-8

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

Starship Power Figure 6-9

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