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Space Transport and Engineering Methods/Forces

1.0 - Introduction

 Space travel involves applying forces to get to a desired location. The forces produce acceleration to leave the current location, and deceleration as needed on arrival. Either natural or artificial energy sources can be used to produce these forces. The many existing, possible, and theoretical space transport methods in Part 2 can be categorized according to how the forces are applied, and what the energy sources are. Figure P2-2 at the start of Part 2 is a table organized this way.

 This chapter introduces the many ways to apply forces for space travel, and Chapter 4 introduces the energy sources for them. A given transport method is then a combination of force and energy types. Some methods share the same combination, and some combinations have no identified methods. Thinking about new combinations may inspire new ideas, which is one reason we try to identify all the ones that already exist. Another reason is when starting a project, it is worth briefly considering all the available options rather than assuming a particular choice.

 Transport methods can also be categorized by state of development, cost, exhaust velocity, efficiency, and other parameters. Chapter 21 will compare such factors among methods, to aid in choosing among them. The earlier chapters of Part 2 will introduce them individually. As space technology evolves, previously impractical methods may become useful, and others become outdated. Part 2 tries to identify all known methods, without regard to current practicality or state of development.

 Wikipedia's Spacecraft Propulsion article provides another listing of methods, and Future Spacecraft Propulsion Systems 3rd edition, Czysz, 2018 has broad coverage of the subject. Space propulsion is a rapidly evolving field. Sources for the latest information include new books and journal articles, NASA and other technical databases, and contacting specialists and researchers in the field.

 The forces listed here are arranged in two large groups. The first are the reaction forces from expelling internal material from the system (Section 2.0). The second are forces from interacting with an entity outside the system (Section 3.0). Conservation of Momentum (i.e the sum of changes in mass times velocity for the parts of a system is zero) requires the force on what you want to move is matched by an equal and opposite force on something else. That something else can be the mass expelled or an outside entity, but in either case the combined forces must be zero. Finally, Section 4.0 discusses differences and similarities among the forces and their associated methods.

 For both the expelled mass and external interaction forces types, the approximate range of exhaust or effective velocities is noted, and the two groups are generally in order of increasing performance. Combustion gas is the most-used type today. It is among the lowest in performance, but supplies the extremely large forces needed to accelerate from the Earth's surface to orbit.

 Total mission velocities can be higher than the characteristic performance of a given type. The required total velocity change can be reached by using large amounts of propellant, using multiple stages of the same type, or using multiple different types.

2.0 - Reaction from Expelled Mass

 Systems which react against an expelled mass for travel are generally called Rockets, and the devices which expel the materials are called Engines or Rocket Engines. Specific types each have a descriptive or or common name noted where they are discussed. The amount of force generated this way is derived from Newton's Laws of Motion. Where dm/dt is amount of mass expelled per second, and ve is how fast it leaves or Exhaust Velocity, the force F in Newtons is

 * $$ F = \frac{dm}{dt} v_e $$

 For accelerating vehicles, the force is called Thrust and given the symbol T. Based on this equation, the possible ways to increase thrust are (1) increase the mass flow rate, (2) increase the exhaust velocity, or (3) some combination of both. The available material to expel, also known as Reaction Mass or Propellant, is finite when coming from an internal source. So increasing velocity is usually preferred to get more total performance. Because this type of propulsion system is self-contained, it can operate in many environments, particularly the vacuum of space.

 * Exhaust Velocity

 In a parallel unidirectional flow, all the mass is moving in a single direction. An expanding gas exerts sideways forces and is emitted as a cone with some angular width (Figure 3-1). Molecules not moving parallel the axis of the cone only contribute the parallel component of their motion to the reaction force. This component can be calculated from the cosine of the average angle of motion times the average molecular velocity. Molecules in an expanding gas have a range of velocities determined by their temperature and how the flow was shaped. The average axial component over the whole flow is what determines the usable exhaust velocity. Forces can also be calculated from computer simulations and they can be measured on test stands, or from data collected on test flights.

 A derived unit is Specific Impulse. Where T is thrust, $$\dot{m_p}$$ is propellant flow rate in kg/s, and g is Standard Earth Gravity of 9.80665 m/s2 it is defined as

 * $$I_{sp} = {T \over \dot{m_p}g}$$

 Note that actual Earth surface gravity varies by a few percent from the standard depending on location. The unit for specific impulse is seconds, and is interpreted as how many seconds one unit of fuel can produce one unit of thrust at 1 gravity. For example, the high energy propellant combination of $$H_2 + O_2$$ produces a specific impulse of about 450 seconds. The SI unit of m/s is preferred for exhaust velocity since it is not Earth-centric and applies everywhere. The expelled mass types are:

A. Bulk Solids (0-10 km/s)

 Solid pellets or slugs are expelled by mechanical devices like a rotary centrifuge, or an electromagnetic accelerator like the Mass Driver Reaction Engine. An advantage is being able to use nearly any solid material as the reaction mass. One disadvantage is the relatively low exhaust velocity compared to electric engines. The extra work in extracting a suitable propellant for the electric types is usually much less than the gain from using 5-10 times less reaction mass. Another disadvantage of bulk solids is producing a debris impact hazard by emitting large numbers of uncontrolled objects.

 A bulk transport system using a centrifuge or mass driver launching from a large body, where the mass is then collected in orbit, does not create the same impact hazard, even though it uses the same kind of devices. Mechanical devices like centrifuges are limited by structural strength to fairly low velocity, while electromagnetic accelerators have higher theoretical velocities.

B. Microparticles (0 - 4 km/s)

 In addition to solid pellets or slugs, finely powdered solid micro-particles or droplets, such as from inkjet type devices, can be accelerated by electrostatic forces after giving them an electrical charge. Advantages of this type are using unprocessed rock dust or single fluids, and enabling very small engines. Compared to bulk solids, microparticles or droplets are less of an impact hazard, though they may pose a contamination problem.

 Disadvantages include only working well in a vacuum or a very low density non-conducting medium. Any appreciable outside pressure would stop the microparticles by drag or collision. Relative to electric engines, the charge to mass ratio is lower, so the same voltages result in lower exhaust velocity and less performance.

C. Gas Flow (0.1 - 10 km/s)

 In theory a liquid can be expelled to produce thrust, but in almost all cases gases produce better performance. However, storage in liquid form allows lighter tanks than storing gas under pressure. Hot gases have higher average molecule velocity and more ability to accelerate the flow by nozzle expansion. So a common system is storage as a liquid, some method to heat to a gas, and then expanding against a nozzle to maximize reaction force.

 The gas flow type includes ambient temperature or refrigerated gases, like the nitrogen Cold Gas Thrusters used in spacesuit maneuvering backpacks. The cold gas type is useful when you don't want to damage hardware with a hot or chemically reactive exhaust plume. Cold gases are very low performance (~0.5 km/s), so are only suited for small velocity changes.

 Heating a gas allows much better performance due to the higher average molecule velocity. There are numerous possible methods of heating a gas, including electric discharge through the gas (arcjet), concentrated sunlight (solar-thermal), electric filament heaters (resistojet), or heat from a nuclear reactor (nuclear-thermal). Which gas to use and how to heat it depends on multiple factors like mission velocity and storage methods.

 Hydrogen has the lowest molecular weight and provides the highest performance, but requires very low temperatures for liquid storage. The liquid is also very low density, requiring large tanks. At sufficiently high temperature molecules will collide violently enough to split into individual atoms, and at even higher temperatures the nucleus and electrons split, further increasing velocity.

D. Combustion Gas (2 - 5 km/s)

 In this type, hot gas is generated by chemical reactions of the propellant. For rockets the hot gas is generally expelled through a supersonic De Laval Nozzle. This converts thermal to kinetic energy with high efficiency in a single direction. Performance is limited by the reaction energy in the propellant, which is a maximum of about 15 MJ/kg for non-exotic fuel combinations. This yields a theoretical exhaust velocity of 5.5 km/s. Rocket engines are not perfectly efficient, so about 4.5 km/s is the limit in practice.

 Types - Combustion gas rocket types include

 * Monopropellant with a single ingredient which is decomposed and heated by passing over a catalyst bed.
 * Bi-Propellant has two ingredients, a fuel and an oxidizer, which are generally mixed and burned in a Combustion Chamber.
 * In a Liquid Rocket the two ingredients are stored in liquid form in separate propellant tanks, although one or both may be converted to gas before reaching the combustion chamber.
 * In a Hybrid Rocket (Figure 3-2) one of the ingredients is in solid form (usually the fuel), and the other in liquid form.
 * In a Solid Rocket the ingredients are a finely mixed powder which has been cast into a solid form. A typical solid rocket formulation has an oxidizer like Ammonium Perchlorate (NH4ClO4), and a complex fuel containing powdered aluminum, rubber, and epoxy.  The epoxy both binds all the ingredients together and is part of the fuel being burned.

 There are a large number of combinations of form and fuel mixtures for rockets, but only a few are used with any frequency. Because of their high thrust-to-mass ratio and ability to work in many environments, combustion gas systems have been by far the most popular space transport type so far, and almost exclusively the one for launch to Earth orbit. Their disadvantage is the exhaust velocity of the best propellants are half or less of the needed velocity to reach Earth orbit. The needed velocity includes various flight losses and gains from the Earth's rotation.

 Solving the Rocket Equation (Chapter 2, 4.2) for ve = 0.5 vo, the mass ratio is then at least 7.4, which leaves only 13.5% of liftoff mass for the vehicle hardware and payload. The best propellant includes liquid Hydrogen as the fuel, which is very low density. Keeping the hardware mass low enough for reasonable payload is then difficult. If a denser and lower performance fuel is chosen, less structural mass is needed for propellant tanks, but the mass ratio is higher. This still leaves small payload mass.

 The early solution was to use the rocket once, which allows lighter hardware, and discarding part of the hardware once some of the propellant has been used (staging). This is very expensive. More recently the trend has been to reuse some or all of the rocket parts. Since the hardware is much more expensive than the propellants, this significantly reduces cost. Hardware that has to survive multiple uses under the stresses of rocket operation becomes somewhat heavier. This reduces the net payload mass relative to the total launch mass, but cost/kg of delivered payload is still lower.

 Neither he mass and radius of the Earth, which determines the energy to reach orbit, nor the chemical energy in a given propellant combination, are going to change. So neither will the limitations of combustion gases for launch from Earth. Large future improvements in travel from Earth will require moving away from purely using chemical rockets. Fortunately there are many possibilities among the transport technologies in Part 2 of this volume.

 Jet Engines also use combustion to generate forces, and can be used to support space missions. In jets, some of the combustion gas can be used to drive a turbine and bypass fan blades, which greatly increases the mass flow by using outside air. The remainder is expelled by a nozzle, but the nozzle is typically a simpler geometry than for rockets. On Earth jets can use external oxygen from the air flow, reducing or eliminating the need for stored oxygen for combustion. On other bodies with suitable atmospheres, the fuel component can come from outside air and only oxygen supplied internally. Jets can dramatically reduces propellant consumption, but at the same time aerodynamic drag and heating limit flight velocity.

E. Plasma (5 - 200 km/s)

 In a Plasma Engine a propellant is heated until the atoms disassociate into charged components (ions and electrons), then directed by internal currents and potentials or outside magnetic fields. Heating can be by by vigorous electric discharge, intense microwaves, laser, or internal heating in a fusion plasma.

 Plasmas are hot enough to melt most materials, including the engine parts. So they are often confined by magnetic fields to prevent contact. They also emit light that escapes to their surroundings. The surface of the Sun, for example, is a 5780 K plasma. The plasma density (and hence the thrust) can be kept low enough to preven engine overheating. There is no theoretical limit to how hot a plasma can be. The kinetic energy of the exhaust, and thus the power required for the engine, increase as the square of the velocity. So there is a practical limit to thrust and performance based on the power source.

 Many plasma confinement techniques derive from fusion research, which deals with extremely hot plasmas. Recent development of superconducting coils can improve engine efficiency, but design of plasma engines to use them is still ongoing. Because of their high performance, plasma engines are in active development, but many types have not reached operational use as of 2023.

F. Electrostatic (2 - 200 km/s)

 Electrostatic engines separate the ions and electrons in a plasma, then accelerate the much heavier ions with an electric potential. The electrons are added to the emitted beam afterwards to prevent charge build-up. In a Gridded Ion Thruster the propellant is first ionized using electron bombardment or RF oscillations (Figure 3-3). The positive ions are accelerated across a voltage between two plates or screens. An electron gun separately emits the negative charges.

 Compared to a plasma, an ion beam is generally lower density, so requires lower power levels to operate and generates lower thrust. The main difference is creating high ion velocity via electric forces rather than heating or magnetic fields. Efficiency in converting power to thrust is similar (60-75%), as is maximum exhaust velocity. Like plasma engines, the energy required rises as the square of exhaust velocity. Practical limits on the power source then limits performance. Because ion engines can operate with less overhead in small sizes than plasma engines, and are derived from vacuum tube technology, they were developed earlier.

 Both plasma and electrostatic engine types are in uses as of 2023 on many communications satellites, and a few planetary spacecraft where high total mission velocity is needed. Their use is expected to increase as improved solar and nuclear electric power sources are developed since they use roughly an order of magnitude less propellant than chemical rockets. Their disadvantage is low thrust relative to system mass, so they cannot be used on their own for launch or landing on large bodies. This can be overcome by combining them with other transport methods.

G. Atomic Particles (1000 km/s to near c)

 Atomic particles include nuclei of atoms from which all electrons have been removed, single electrons, neutrons, or protons, or more exotic particles such as muons. Where an ion engine typically uses a single voltage gradient, a particle accelerator has multiple chambers that add successive amounts of energy to the particles. This enables exhaust velocities up to near the speed of light, c, or 299,792 km/s.

 Another approach is direct emission of atomic particles from fission decay, fusion reactions, or antimatter decay. These have particle velocities that are a significant fraction of c. Charged particles (generally those besides neutrons) can be directed by magnetic or electric fields, while neutral particles must be allowed to leave in one direction and absorbed in the others to produce net thrust.

 Particle accelerators on Earth have reached very close to c, but their weight and power needs are far beyond what is practical for space, and no space mission has yet required this high a performance. So this type remains theoretical at present. Direct emission of particles tends to be limited by heating and radiation damage effects to low thrust levels.

 This type includes the Bussard Ramjet concept, which is a kind of fusion rocket. Rather than carry all the fuel on-board, it would use a huge electromagnetic field as a funnel to collect and compress hydrogen from the interstellar medium. The hydrogen is compressed until fusion occurs, then the high energy particles are directed out the back to produce thrust. The incoming gas produces drag, so net thrust is the difference between the two forces. The practical problems of atomic particle types and lack of need for their performance has kept them theoretical for now.

H. Photon Emission (1.0 c exactly)

 Photons are the quantum particles of light and carriers of the electromagnetic force. By definition they travel at the speed of light c in a vacuum, which is a defined constant of exactly 299,792,458 m/s. Photons carry momentum, which is calculated by E/c, where E is their combine energy. The force created by light is then P/c where P is the emitted power.

 Direct emission of photons, while low in thrust, has the highest possible exhaust velocity. For practical use, an extremely high energy source needs to be used, such as fusion or antimatter decay. Fairly simple thermal (black body) emission and reflector arrangements can align the light beam to produce useful thrust. A laser aligns the light very accurately, but the gain is small compared to a light beam with a width of a few degrees. The momentum contribution for an off-axis photon is cosine(a), where a is the off axis angle. For small angles that is very close to 1.0. Like atomic particles, no space transport mission has needed this high a performance, so it is a theoretical method at present.

 Unbalanced photon emission as an incidental effect has been noted for the Pioneer spacecraft and with respect to small asteroids, where it is called the Yarkovsky Effect. However these accelerations are very small and not intentional. For useful propulsion a very large amount of photon energy needs to be emitted in a chosen direction.

3.0 - External Interaction

 The second major group of propulsive forces are applied by or against some external object or field, rather than expelling some material from the vehicle. Since no reaction mass is consumed, the Tsiolkovsky rocket equation does not apply. We list them roughly in order of performance, but in this group the measure is effective velocity change rather than exhaust velocity.

I. Mechanical Traction (5 km/s)

 This method uses mechanical forces applied to a vehicle or payload from an external source. Applications of this method include:

 * Using a cable or net to capture and decelerate the vehicle relative to a destination.
 * An elevator to climb a tower or cable at a constant velocity.
 * A tow cable between two vehicles or between a fixed installation and a vehicle, for acceleration or lift.
 * A rotating structure or cable to provide radial or angular acceleration.

 Mechanical devices transmit forces by atomic bonds in the materials used. They are limited by the strength of the bonds, and so the bulk material strength, to around 3-5 km/s for existing materials. The theoretical strength limits for carbon nanotubes (100 GPa tension, per Zhou, Ultimate Strength of Carbon Nanotubes, Phys. Rev. B, v 65 p144105, 2002) and diamond (90 GPa compression, per Telling Theoretical Strength and Cleavage of Diamond Phys. Rev. Lett. v84 n22 p5160, 2000), given a density of 3500 kg/m^3 and a design margin of 2.8, produce a theoretical velocity of around 12 km/s. However, real materials accumulate defects, even if at an atomic scale. So the usable strength in practice is much lower than the theoretical value. A large advantage for mechanical systems is their inherent ability for repetitive use. This divides the initial cost by the number of uses over the economic life of the system.

J. Friction (2 km/s)

 This method uses frictional forces against a solid surface to lower relative velocity. If your intent is to slow down on, for example, the Moon, you can have a flat paved runway or a raised rail, and simply use mechanical braking against the runway or rail to stop. To accelerate to orbit, you can grasp a trailing cable or rail on an orbiting platform and apply friction to gain velocity. This method has the virtue of being simple. Space velocities, however, often represent more kinetic energy than it takes to heat and melt materials. So the friction forces must be distributed in time, rate, or total amount to prevent overheating. It is therefore more useful for planets or satellites with low orbital velocities, and for small velocity changes as part of a larger total.

K. Gas Pressure (6 km/s)

 This method uses external gas pressure differences to apply forces to a vehicle. It includes all types of guns, where the gas is confined in a tube to accelerate linearly. Gas expansion is limited by the temperature and molecular weight of the gas. Hot Hydrogen then yields the best performance, which is limited to around 9 km/s in the best case, and about 6 km/s for practical designs. There are a variety of methods to generate hot gases. The oldest, conventional firearms, depend on fast combustion of a solid propellant grain. Newer versions function via combustors, fuel-air detonation, particle bed heaters, or other methods to create heat and pressure in a short time. When the hot gas so created is not sufficient, a two-stage method transfers the energy by means of a piston to a lighter gas (usually Hydrogen). A properly tuned piston mass can result in higher temperatures and pressures in the light gas than in the first stage.

 Various kinds of guns have been used for high velocity research since about the 1960's. Most have been used indoors, but at least two have seen outdoor use. They have not been used for space launch yet, but that is a matter of size and location, rather than technology level. An extreme use of gas pressure is to use a fission or fusion device to heat a large amount of gas to plasma temperatures in a chamber, which then is applied to accelerate a vehicle. This concept remains theoretical because of bans on testing and the tendency to destroy the chamber.

L. Aerodynamic Forces (4 km/s)

 These forces include lift, buoyancy, and drag. Wings and fan blades develop lift by pressure difference across the upper and lower surfaces when a fluid such as air flows across them. At higher velocities, a WaveRider type inclined surface rides the lower shock wave it generates to create lift. Buoyancy develops lift by having a lower density than the surrounding fluid, such as in a balloon. Drag generates forces by accelerating the surrounding fluid in the direction you are moving, thus producing a force opposite your motion. A parachute, for example, is shaped to capture and accelerate the maximum amount of air, producing the maximum amount of drag to slow you down. Lifting forces invariably create drag, and tend to create more at higher velocities. Heating also becomes a limiting factor at high velocity, tending to set a limit of about 4 km/s for aerodynamic forces, except for re-entry systems where the heating is efficiently dissipated. Since aerodynamic forces in themselves always create friction and other dissipation, by themselves they can only slow a vehicle relative to the fluid. They require a source of thrust, like a jet engine, to accelerate.

M. Photon Reflection (185 km/s)

 Instead of an internal source, as in H. Photon Emission above, this method uses an external source of photons, such as a star or laser. Normal (perpendicular) reflection produces a force of

 * $$ F = \frac{E(1+R)}{c}$$

 where E is the incident energy on the reflector, R is the reflectivity (fraction of incident light reflected), and c is the speed of light. This is nearly twice the force from emission, because the photon changes velocity by twice the speed of light from forward to backward. It is slightly less than twice because no reflector is 100% efficient. When the reflection is not perpendicular, the force is reduced by off-axis cosine losses. The quantity of light (photons) is not limited by an internal power source, so can reach relatively higher forces than emission, but still generally low compared to other methods. A solar or light sail uses thin but very large reflectors in order to intercept the maximum amount of light. To get the highest accelerations, the maximum ratio of reflected energy to mass is desired. Tungsten may be a dense element, but can operate at much higher temperature close to the Sun where the light intensity is higher. Where maximum temperature is not required, a light alloy like Magnesium-Aluminum, with high reflectivity, is preferred.

 Given a sufficiently powerful light source, quite high velocities are possible. Using natural light sources such as the Sun we get approximately 8.2 microNewtons/m2 at the Earth's distance. The gravitational force from the Sun on a lightweight sail may be 0.35 times this. The Lightness Ratio, LR, or ratio of light pressure to gravity then determines the maximum escape velocity by

 * $$V_{max} = (LR-1)V_e$$

where V(e) is the local escape velocity. So paradoxically, to reach maximum final velocity you want to start as close to the Sun as possible, where local escape velocity is higher. For a lightweight sail, this might be 0.2 AU, limited by the melting point, and an escape velocity of 100 km/s. Thus the maximum final velocity is 185 km/s. Any velocity less than this maximum is possible. The practical limits using artificial light sources such as a laser are unknown, since no lasers with high enough sustained power to be useful for this purpose exist. In theory a powerful enough laser can accelerate a sail to substantial fractions of the speed of light, before accounting for drag from the interstellar medium.

 By tilting a sail from perpendicular to the light source, off-axis forces can be generated. The net force will be approximately perpendicular to the sail and allow inward spiral orbits by directing the force against the orbital velocity, or tilting of the orbit plane by directing the reflection perpendicular to velocity. Sub-orbital or zero velocity motion can be produced by balancing light pressure against local gravity. These are not orbits because they depend on constant forces. Rather they fall into the class of powered trajectories.

N. Particle Deflection (100 km/s)

 The thin plasma and gas emitted by the Sun's heated outer layers is called the Solar wind. The wind has typical velocities of 400-750 km/s relative to the Sun, and extends outwards to about 125 AU, where it encounters the interstellar medium. The force per area due to light pressure is much greater than that due to solar wind flux. A Magnetic Sail is a proposed method of spacecraft propulsion. It would use a magnetic field to deflect charged particles in the plasma wind. Since the field itself is non-material, in theory it can be large enough to get useful thrust, even though the area density of the solar wind is very low. By tilting the field, a sideways force can be generated. This method is limited to the velocity of the wind, and generally to producing forces away from the Sun. An artificial beam of particles could also, in theory, be used to apply a force to a vehicle, which either absorbs or deflects the beam. This remains theoretical because powerful enough beams are not available, and keeping them focused over typical distances in space is difficult.

O. Magnetic Field (20 km/s)

 This method generates a force by using a current carrying wire, coil, or magnet to react against other magnetic fields (natural or man-made). In this category fall magnetic levitation or Maglev; Coilguns, which use a series of timed coils; Railguns, which use two high current rails and a plasma short across them; and Electrodynamic Propulsion, which reacts against a natural magnetic field. It can be used both for net thrust and drag, or for torque forces to rotate a vehicle. Magnetic flywheels are often used to orient or rotate spacecraft. The Sun and some planets have a natural magnetic field to react against. Many artificial satellites also use the magnetic field to rotate the satellite to a desired orientation using a Magnetorquer. For example, see Galysh et al, . In theory there is no limit to the velocity you can reach using magnetic fields. In practice, the natural fields such as the strong one around Jupiter, or the practical scale or field strength of an artificial accelerator, limit velocity changes to around 20 km/s.

P. Gravity Field (20 km/s)

 Gravity forces accelerate objects towards any nearby mass. Normally this results in an orbit or simply falling towards an object. A Gravity Assist is purposely choosing a hyperbolic path to change the direction, but not the total amount, of your velocity relative to a given object. The maximum change is twice the escape velocity of the object, when the direction is changed 180 degrees. To reach a desired mission destination, usually much less than this can be done. Since a planet, for example, is moving with respect to the Sun, changing direction relative to the planet can change the total velocity relative to the Sun. By conservation of momentum, the planet also must change velocity, but since it is much more massive, the velocity change is small enough to ignore in most cases. Within the Solar System, the achievable velocity changes are about 20 km/s, and may need multiple gravity assists to reach this level. The major advantage of gravity assist is it does not need internal propulsion except to line up the flyby, and therefore saves propellant mass. A disadvantage is one or more gravity assists take extra time to complete, and restrict the choice of trajectories because you can't choose where the moon or planet you are using will be at a given time.

 Gravity fields extend to infinity, so every place in the Universe has a field, and almost everywhere has a non-zero net field. So all space transport has to account for gravity forces in mission planning. Usually it is an obstacle to overcome, in reaching orbit or changing orbits, but in some cases, such as gravity assist, it can be used to advantage. Gravity changes as the inverse square of distance from an object. If your vehicle or object is elongated, the Gravity Gradient, or difference in gravity between the lower and upper ends, can also be used as a torque to stabilize your orientation. These gravity gradients exist whether or not you use them, so they must also be taken into account as a force to be overcome in system design.

4.0 - Discussion

Split Energy Source:

 Many of the above listed propulsion methods have separate propellant mass and energy to accelerate that mass. With these methods there is a design trade between mass and energy. The equation above gives force as mass flow rate times exhaust velocity. To get a desired mission velocity change, or $$\Delta V$$, you can minimize the mass used, and use a lot of energy to generate a high exhaust velocity. Alternately you can minimize energy and accelerate a larger propellant mass. It is a trade-off where using more of one requires less of the other. The kinetic energy required for a given exhaust velocity is KE = mv2/2, so it increases faster than the mass flow is reduced. Typically engine efficiency is relatively constant in the normal operating range. So source power level, which is KE/efficiency, also tends to increase as the square of exhaust velocity. Higher power levels require more power source mass, and represent overhead beyond the cargo you are delivering. Whether that mass increases linearly with power level or not will affect the optimum exhaust velocity. In addition, the choice of completing the mission in the least time, least propellant used, or somewhere between those extremes will affect the optimum exhaust velocity to use.

 Once a design has been set for a vehicle, there is additional optimization possible within a particular mission. The design and mission fix the quantities of propellant mass and mission $$\Delta V$$. If the engine type allows variable exhaust velocity, it takes less total energy to "dump" the early exhaust mass at a lower exhaust velocity $$V_e$$, and then eject the later mass with a higher $$V_e$$, than to eject at a constant $$V_e$$. If the goal is minimum time and you have a fixed energy source, this will be the optimum operating profile.

 For missions which use solar power as a source, the optimal operation is more complex. First, solar flux varies as the inverse square of distance from the Sun. Second, solar powered orbit changes around a large body introduces shadowing and a stronger gravity field, which takes longer to traverse. For low thrust engines, short thrust intervals require less $$\Delta V$$ by up to a factor of $$\sqrt{2}$$, but close orbits are in shadow up to half the time and limit when you can generate thrust. When the local gravity acceleration is low relative to the vehicle acceleration, which happens farther from the body, then short thrust intervals do not impose a large time penalty. Deeper in a gravity well, they do. Lastly, for bodies with radiation belts, like Earth and Jupiter, time spent climbing through those belts can damage solar arrays, other hardware, and human passengers. In complex cases like these, the best thrust plan is found using a numerical simulation which divides the mission into small time steps and adjusts the variables looking for the best result for whatever parameters the mission planner wants to optimize (time, fuel used, radiation exposure, or others).

Combined Energy Source:

 Other propulsion methods listed above, such as combustion gas rockets, have propellants which provide both the mass flow and energy supply to generate an exhaust velocity, $$V_e$$. In these cases the Tsiolkovsky rocket equation shows that higher velocity is always better. Combustion engines have been developed with extraordinary power/mass ratios, up to 2.7 MW/kg. This enables them to lift not only themselves, but the entire vehicle's mass against the Earth's gravity. This makes possible launch to orbit without external assistance. Their performance is limited, however, by the available energy in the fuel, which in the case of Earth is about half that needed to reach orbit. Atmospheric engines obtain much of the mass flow and energy from outside the vehicle, so they bypass the limits of a purely internal propellant. This usually comes at the expense of increased mass from items like inlets, turbines, and wings. This lowers the power/mass ratio, and of course only functions while you are still in the atmosphere. The choice to use atmospheric engines will therefore depend on many factors beyond propellant energy. Atmospheric engines can have as much as 10-20x lower fuel use for a given thrust, so that is a strong incentive despite the complications.

 Comparing split vs combined energy sources, a separate energy source relieves the limits on energy per propellant mass used. This allows higher exhaust velocities and lower propellant use, often by an order of magnitude or more. The drawback is current technology for these methods usually generates much less than one Earth gravity, because energy sources like solar panels are below 200 W/kg, far below combustion engines. This limits their use for the important job of getting from the ground to Earth orbit. Once in orbit, their performance advantage will often make them the preferred option. This is because the best chemical propellants contain about 15 MJ/kg of energy. A 175 W/kg space solar panel (state of the art as of 2016) will produce that much energy in about a day. Since the panel typically lasts 15 years, it will produce about 5000 times more total energy over its life.

 Compared to the expelled mass group, external interactions do not consume a finite supply of reaction mass. So these methods would be preferred, all other factors being equal. Reaction mass, though, can be expelled under a wider range of circumstances in most cases, and usually with a higher thrust/mass ratio. So it is not possible to state a general conclusion as to which approach is better. The choice would depend on a variety of detailed circumstances, including destination, trajectory, desired trip time, cargo mass, frequency of trips, and how far in the future the transport occurs. The latter affects what technologies are available and how ready for use they are. One approach to selection is to look at the external interaction group first, to see if any can be applied to the job at hand, then look at the group that uses up reaction mass second, since that requires overhead above whatever cargo you are trying to deliver.


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Space Transport and Engineering Methods/Energy

Energy in General
All of civilization requires energy to function, including about 8 MJ/day (~2000 Calories) of food energy per person. Space systems are no exception, They require energy both for propulsion and for other systems like life support, computers, and materials processing. The general field of energy is vast, involving many fields of engineering. Energy for space projects involves an equally wide range. So we can only provide an introduction, and supply references for further study. In this section we survey the range of possible energy sources for all types of space systems. Since the book is oriented to future space projects, we list a number of sources that are not developed yet, but are possible according to known physics. These sources can then be used for the propulsion methods tabulated in Part 2, and for other engineering purposes described in Part 3 and later. By making a two dimensional table of energy sources vs propulsive forces, we can categorize all possible propulsion methods, and we do this at the start of Part 2 of the book. We have not yet developed a similar table to neatly categorize the other systems in a space project.

Proximate vs Ultimate Energy

The principle of Conservation of Energy states that energy can neither be created nor destroyed, merely transformed from one kind to another. So all energy for a project must come from a preexisting source. For a given project you can distinguish a proximate energy source, which is in the form consumed by the project, and an ultimate energy source, which traces the proximate source back through previous transformations to it's original form. Ultimately, all energy traces back to the creation of the Universe, but for engineering purposes we rarely go back that far, and are generally concerned with proximate sources.

For current space systems the energy is typically stored internally as chemical energy in the case of launch vehicles, or uses sunlight in the case of satellites. In the future, energy needs are likely to change, and the sources of energy will also change. Permanent locations, such as a large orbiting habitat or surface base, generally need continuous sources of energy to operate. Devices like batteries become unwieldy at that scale to supply power for the night part of Earth orbit or the two week Lunar night. Future projects may also need much greater power levels for tasks like processing of local materials. So the following headings attempt to include all potential energy sources, including many not yet used, but which may become useful in the future space projects. We list them all so that designers know the full range of possibilities, from which they can then select viable options for a given task. We exclude sources such as human and animal power from consideration here, both due to their low power levels, and because living things are not subject to the same kind of engineering design as we apply to non-living system. We also exclude sources like wind and geothermal, which mostly apply to Earth. Last, we includes some energy storage methods, which are not strictly sources. Energy storage, however, is often a necessary and important part of system design.

Energy References

A starting point for understanding energy sources in general, not just as they apply to space projects, is a National Academies book America's Energy Future, 2009. About 150 other books are available for free download in the Energy and Conservation topic from the same site. Encyclopedic references on the topic of energy, include the Encyclopedia of Energy, Encyclopedia of Energy Engineering and Technology, and the Macmillan Encyclopedia of Energy. These are often expensive reference books, so library or other sources are recommended to get access. There are numerous engineering books on more specific aspects of energy systems. Wikipedia also has an Outline of Energy article, with many links. Some of the concepts listed below are currently theoretical, so they are not well covered in reference books about current energy use or engineering. Information about them will mostly be found in research reports and scientific/technical papers.

Mechanical Sources
Mechanical Energy includes energy stored by virtue of previous work, as in compressed gases, and that which exists by virtue of position (potential) and motion (kinetic). Objects in orbital motion have a combination of potential and kinetic energy.

A. Compressed Gas
Although Pressure vessels are strictly an energy storage method, for space missions the tanks are normally pre-filled. So they operate as a proximate energy source in flight. The available energy, W, stored in a pressurized tank, can be found from

 * $$W = p_B v_B \ln \frac{p_A}{p_B}$$

where B represents the high pressure and A represents the low pressure, and p and v are pressure and volume respectively. So a 1 cubic meter tank with a high pressure of 20 MPa and a low pressure of 10 Mpa would provide 13.8 MJ of available energy. Compressed gas is a low density energy storage method. It is often used in space vehicles for tasks like cold gas thrusters and pressurizing liquid fuel tanks. Its chief advantages are simplicity, requiring just a storage tank and a valve, and rapid release of the stored energy. When larger total amounts of energy are needed, a higher density but more complex system is often preferred.

B. Potential Energy
Potential Energy is the ability of a system to do work by virtue of it's position or configuration. In space projects this is usually position relative to the gravity well of a massive object such as a planet. A simple hypothetical example is a stationary space elevator cable. While raising a cargo, electricity is converted to potential energy of height. When lowering a cargo, the potential energy can be extracted back to electricity. The formula for potential energy U was given in Section 1.1 – Physics as

 * $$U = -G \frac{m_1 M_2}{r} $$

The difference in energy at two radii gives the amount of potential energy stored or released over the distance. For small changes in radius (height) relative to the distance r, the potential difference can be approximated by the average gravitational force (weight) times height. On planetary surfaces, large amounts of available mass can be used to store potential energy. On Earth this is done with dams for hydroelectric power. On other bodies, a mountain and a pile of rocks can serve the same purpose. Transporting the rocks up and down the mountain can serve to store or release energy.

C. Kinetic Energy
Kinetic Energy is that which an object possesses by virtue of it's motion. Its formula was given in Section 1.1 – Physics as

 * $$KE = \tfrac{1}{2} mv^2 = Fd$$

where KE is the kinetic energy, m is the object's mass, and v is the velocity. It is also equal to an accelerating force F times the distance d it is applied over. An object in orbit has both kinetic energy in it's orbital velocity and potential energy in it's altitude. In an elliptical orbit, it continuously exchanges altitude for velocity. So it also exchanges potential and kinetic energy, but the combined total stays the same.

Rotating objects such as a space station or reaction flywheel have a form of kinetic energy in it's motion around an axis. Rotational energy is E(k) calculated by

 * $$E_k=\frac{1}{2} I \omega^2$$

Where $$ \omega $$ is the Angular Velocity in units of radians/second, and $$ I $$ is the Moment of Inertia of the mass about the center of rotation. The moment of inertia is the measure of resistance to Torque, or rotational force, applied on a spinning object. The higher the moment of inertia, the slower it will spin when a given force is applied. Moment of inertia depends on the distribution of mass in the rotating object. The farther out a given portion of the mass is, the larger the contribution. Formulas for many shapes are found in the List of Moments of Inertia. For complex shapes, the total moment can be found by dividing it into simpler parts and summing the individual moments.

Some examples of moment of inertia formulas are:

 * $$I = \frac{1}{2} mr^2$$ for a solid cylinder,

 * $$I = m r^2$$ for a thin-walled empty cylinder, and

 * $$I = \frac{1}{2} m({r_{external}}^2 + {r_{internal}}^2)$$ for a thick-walled empty cylinder

Kinetic energy can be exchanged for other forms of energy by gravitational forces, as in gravity assist maneuvers; or electromagnetic forces, as in many electromechanical devices. Potential energy can also be exchanged for kinetic energy via the Oberth effect by expending propellant deep in a gravity well.

Chemical Sources
Chemical sources are an arrangement of atoms in a higher energy state which are converted to a lower energy state by a Chemical Reaction, releasing the difference. Combustion is the most common way to release this energy, accounting for over 80% of total human energy use. Batteries are characterized by a reversible reaction, so that the same device can store and release energy multiple times.

D. Fuel-Atmosphere Combustion
The Earth's atmosphere, neglecting the variable amounts of water vapor, contains 20.95% Oxygen (O2) molecules, which react with many other compounds to release energy. This Oxygen is the byproduct of Photosynthesis in living things. In the case of aircraft, a hydrocarbon fuel such as Kerosene is reacted with the atmospheric Oxygen in an engine. Since only the fuel is carried internally to the vehicle, the energy released, about 43 MJ/kg, is about three times as much as when both ingredients are carried internally, such as in a typical rocket. Large amounts of Oxygen in an atmosphere is unstable, because it is so chemically reactive. It only exists on Earth in this form because plants constantly produce it. So this energy source is not available on other bodies. The reverse option is available on a body such as Titan, which has a hydrocarbon atmosphere. In that case, Oxygen can be the carried ingredient, and burned with the surrounding atmosphere. For atmospheres which are mostly CO2 (Venus and Mars), which is an end product of combustion, or bodies with no atmosphere at all, this energy source is not available.

E. Fuel-Oxidizer Combustion
The energy source in conventional rockets is Combustion, where both the fuel and oxidizer are supplied from internal sources. The ingredients with the highest reaction energy, Hydrogen and Oxygen, provide 15 MJ/kg of propellant. Although lower in Specific Energy than D. Fuel-Atmosphere Combustion, it is not restricted to operating in the Earth's atmosphere. Liquid rocket engines also have extraordinary power-to-mass ratios. This enables launch trajectories from large bodies like planets. Combustion can also be used as a secondary power source in Auxiliary Power Units. Because the rate of energy release is very high, combustion is useful when high power levels are needed. The efficiency of combustion engines is typically 1/3 to 2/3, so other options may be preferred when that is an important factor.

F. Chemical Battery
An Electric Battery is a device which converts stored chemical energy to electricity, and in a storage battery also reverses the reaction. Common examples of chemical batteries include the Lead-Acid type used in automobiles, and the Lithium-Ion type used in many portable devices. Depending on battery type, they generally store less then 1 MJ/kg, considerably less than combustion. The ability to cycle energy in and out multiple times can outweigh the lower energy density. An example is the International Space Station, where large batteries supply power in the shadowed part of its orbit.

A Fuel Cell is a type of battery where the reactants are stored in external tanks, rather than in a sealed battery case. It can have high specific energy because the tanks are lightweight compared to electrolyte solutions. Fuel cells have therefore been used in space projects, such as the Space Shuttle Orbiter. A Hydrogen-Oxygen fuel cell combined with an Electrolysis unit to convert the resulting water back to Hydrogen and Oxygen can supply energy storage with a specific in the range of 3-10 MJ/kg. Sealed batteries are simple and reliable, and can be made in very small sizes. Fuel cells have higher specific energies, but are more complicated devices, since they need valves and a way to pump and store the various chemicals.

Thermal Sources
Thermal Energy is the internal energy of a system due to its temperature. It comes from the kinetic and vibration energies, and the attractive potentials of the molecules or other particles making up the system. Thermal energy can be stored for later use, or added from an outside energy source for immediate use. We sense high temperatures as heat, and even higher temperatures as visible light. Energy naturally flows from higher to lower temperature areas by conduction, radiation, and convection. When a temperature difference exists, some of the thermal energy can be converted to other forms and used. An example is a steam turbine that generates electricity from the difference between hot steam and the cooled outlet.

G. Thermal Storage Bed
For locations like the Lunar surface, which has a long night, solar power is not effective half the time. So storing heat in a Thermal Energy Storage system may be a viable option. Heat is put into rocks during the daytime and extracted from them at night to run a generator. The rock bed is enclosed in a container, and gas transfers heat to a turbine for generation, and from a solar collector for storage. Since the rock can be obtained locally, the energy stored per mass of installed equipment is fairly high. Environment temperatures during the Lunar night are quite low, and this can be enhanced by thermal shields between a radiator and the ground and daytime Sun. So the temperature difference between the storage and rejection temperature, and therefore efficiency, can be fairly high.

Some bodies, like Earth and Jupiter's moon Io, have relatively high interior temperatures. They serve as a natural thermal storage bed by the low thermal conductivity of surface rock. The source of heat can be radioactive decay or tides. This energy can be put to use by drilling down to high temperature regions, and exploiting the difference between those and surface temperatures.

H. Concentrated Light
A number of industrial tasks require heating, which is easily done in space by concentrating sunlight. Examples are heating of raw materials to extract volatiles, or maintaining temperature and growing ability in a Mars greenhouse. The concentration ratio determines the maximum Black Body temperature that can be reached, up to the temperature of the light source. In the case of the Sun, the upper limit is the Sun's surface temperature, 5,775 K, less reflection losses and radiation losses from the object you are heating. Since Tantalum-Hafnium-Carbide, the highest melting point substance known, melts at 4200 K, concentrated sunlight should be sufficient for most industrial processes.

For space transport, a reaction mass can also be heated by concentrated solar or artificial light. Lighter molecules can be used than the exhaust products of chemical reactions, so higher performance can be reached. Lack of powerful enough lasers limits their use for propulsion at present, but sunlight is widely available in space.

Electrical Sources
Electricity is the set of phenomena associated with the presence and flow of electric charge. Common examples are Electric Current, in the form of electrons moving in a conducting wire, and Lightning, a powerful electrostatic discharge through a plasma channel in a storm. Electricity is a very versatile energy source because it can be converted to other forms efficiently, controlled in both tiny and large amounts, and moved about from place to place relatively easily. There are a number of ways to produce and distribute electrical energy.

I. Power Line
Most space projects use electrical energy in some form. The parts of a project on Earth are often by far the largest. These include factories to produce the vehicles and spacecraft, launch sites, and control centers. Typically they get their electricity from a network of Electric Power Transmission and Distribution lines. This is distributed to the point of use by local Electrical Wiring. What distinguishes these three is the scale of power, P, in Joules/second, or Watts, and the voltage and distance the power is moved. Most wires have electrical Resistance, R, which is a measure of the difficulty in carrying a current, I, using a voltage V. They are related by the formulas

 * $$ V = IR \qquad and \qquad P = VI $$

The resistance causes some of the energy to be converted to heat. The amount of power converted, P, is found by

 * $$P = I^2R$$

When efficient delivery of energy, and not heating, is the intended purpose, you want to minimize the resistance heating. Since resistance is a material property, by this formula you want to use a low current, I. By the previous formula, the useful power P = VI, so a low current implies a high voltage. Therefore long distance lines are operated at higher voltages, and voltage changes are provided by Transformers as needed.

The same principles will apply to the space portion of a project when the distance between the point of generation and the point of use is large. Additionally, mass is usually a factor for space systems. So besides minimizing losses from resistance and transformer efficiency, you want to minimize the mass of the wires. The International Space Station is an example where generation and use are separated by an average of about 50 meters. This is because the Station is intended as a zero gravity laboratory, but the solar arrays need to rotate to follow the Sun. Since they are quite large, they are placed to the sides with rotating joints.This option mostly applies to fixed locations rather than vehicles. This is not a large enough distance to require high voltage lines for efficiency. Examples of future projects with longer power lines include mining water ice in shadowed craters at the Lunar poles. Solar arrays at the crater rim may have continuous sunlight while the mining area has none. So a transmission line can bridge the gap. Another example is a nuclear power source for nighttime power for a Mars Base. In that case the source is separated from the rest of the base for safety. Finally, large orbital habitats and industrial plants may use centralized generators that are lighter and more efficient, and need long power lines due to the size of the facility.

All types of wires need isolation from other system elements and each other, to prevent power leakage, shorts, arcing, and for safety. In a vacuum or non-conducting atmosphere, which the Earth's mostly is, isolation can be provided by mechanical gaps and spacing of wires. When the wires must be spaced close together, an Electrical Insulator can provide isolation, and combinations of spacing and insulation can also be used.

J. Electric Generator
An Electric Generator converts mechanical energy to electric energy. The two general types are a Dynamo which produces direct current, where electrons flow in one direction; and an Alternator which produces alternating current, where electrons flow in both directions in an alternating cycle. Most of the Earth's electric power is produced by large alternators. The mechanical energy enters the device via a rotating shaft, and an arrangement of magnetic fields induces a current in coils of wire. The mechanical energy can come from any of a number of sources. On Earth it is usually from high pressure steam or falling water acting on a turbine whose shaft is connected to the generator. In the case of steam, it is created by burning fossil fuels or a nuclear reactor, and more recently, from concentrated sunlight. A growing number of Wind Turbines are being used to produce electricity. The wind rotates aerodynamic blades mounted on a central shaft, and the shaft is connected to a generator.

K. Magnetic Storage
Some space projects, such as electromagnetic launch from Earth, require very high electric power levels for short periods of time. These power levels can exceed what is available from the power grid. Magnetic storage accumulates energy over a longer period of time, then releases it quickly when needed. It uses a 'Superconducting or high inductance/low resistance coil to store energy in a magnetic field. Superconductors eliminate resistance heating losses, but require cryogenic refrigeration to maintain the superconducting state. A large coil, cooled to lower resistance but not cryogenic, may be sufficient for some purposes. The energy, E (in Joules) stored in a magnetic field can be found from

 * $$E=\frac {1}{2} L I^2$$

L is inductance in Henries, and I is current in Amperes. Storing energy in this way causes structural loads from the field back to the coil, so the total storage amount is limited by the strength of the structure. Some uses in space, like pulsed plasma propulsion systems, can benefit from smaller magnetic storage units to produce high power pulses from a lower power steady source.

L. Semiconductors

Photovoltaic cells convert light, usually from the Sun, into direct current electricity using semiconductor materials. This technology is rapidly developing and has multiple materials and techniques (Figure 1.4-1). Conversion efficiency from sunlight of the best research cells, using multiple layers to capture different wavelengths, has reached 46.0% as of 2015. Production panels for use in space, made of multiple cells each, are near 30% efficiency, and the more common but less expensive single layer panels on Earth are typically 20% or less. Note that the efficiency on Earth vs in space are based on different solar intensity and spectra, because the Earth's atmosphere absorbs some wavelengths.

Thermophotovoltaic devices convert infrared and visible light from any hot object into electricity. They use similar semiconductors as photovoltaic cells, but optimized for the lower temperature source. A Thermoelectric Generator uses semiconductors to convert a temperature difference into electricity. The most common use in space is generating power from radioisotope decay, in locations where solar panels are cumbersome, is not available all the time, or is too dim, such as beyond Jupiter. An isotope like Plutonium-238 produces decay heat on a steady basis, which thermoelectric cells convert to electricity. For space applications, pure efficiency is not the only significant measure. Variation with temperature, radiation exposure, and the specific power (W/kg) are also important. Given the trend of past improvements, it is expected semiconductor devices will continue to improve, at least in the short term. The latest data should be checked for current performance.

(The following are old references, and should be updated)

 * Anonymous "Conference Record of the Nineteenth IEEE Photovoltaic Specialists Conference- 1987", New Orleans, Louisiana, 4-8 May 1987.
 * Anonymous "NASA Conference Publication 2475: Space Photovoltaic Research and Technology 1986: High Efficiency, Space Environment, and Array Technology", Cleveland, Ohio, 7-9 October 1986.
 * Chubb, Donald L. "Combination Solar Photovoltaic Heat Engine Energy Converter", Journal of Propulsion and Power, v 3 no 4 pp 365-74, July-August 1987.

M. Solar-Driven Turbine/Generator
In space, most electrical power so far comes from photovoltaics, since solar panels are lightweight and simple for small to medium amounts of power. For large scale power, Brayton Cycle turbines have been proposed, because of their potential high efficiency and low mass. The turbine shaft then drives an electric generator. The high and low temperatures for the cycle would be produced by solar concentrators and radiator panels. Stirling type engines have also been proposed for space use. Sunlight is abundant in space, and lightweight reflectors to concentrate it and feed a heat engine may be lower mass than photovoltaics.

(The following is an old reference, and should be updated)

 * Spielberg, J. I. "A Solar Powered Outer Space Helium Heat Engine", Appl. Phys. Commun. vol 4 no 4 pp 279-84, 1984–1985.

N. Rectenna Array
A rectifying antenna, or Rectenna is an antenna that is used to convert electromagnetic energy into direct current electricity. A single antenna element can be a Dipole, with a Diode connected across the dipole arms. The incoming electromagnetic waves induce alternating currents in the dipole. Since diodes conduct in only one direction, a direct current is passed on. Many antenna elements are combined into an array to capture the whole of the incoming energy. Rectennas have been proposed as the receiving element of a long distance microwave power transmission system, such as from Earth orbit to the ground. Much more solar energy is available in space, which results in more net energy delivered on the ground, despite conversion losses. The beam can also travel from the ground to orbit to deliver power to a satellite.

The length of a dipole antenna scales with the Wavelength of the incoming energy. In principle, microscopic antenna arrays can be made by the same methods used for integrated circuits. This would allow for the direct conversion of infrared or visible light. Small scale antennas are in an early stage of research. Their advantage for long-range transmission is in a smaller transmitter for a given distance. Microwave technology, by comparison, is well developed, and high efficiency rectenna conversion has already been demonstrated.

Beam Sources
Entropy is a measure of disorder in a system. A directional beam of energy has low entropy because the waves are highly ordered (parallel). Useful work can be extracted from a low entropy system. This results in increased entropy (disorder), typically as random motion of atoms in thermal equilibrium and random thermal emission. Beams can be natural or artificial, and consist of electromagnetic waves or particles. Energy beams can be used for various kinds of Beamed power propulsion, or for powering more stationary activities.

O. Sunlight
At increasing distances from the Sun, around 14 million km or more, sunlight becomes highly directional. The source, which is 1.392 million km in diameter, then fills a small angular part of the sky. At the Earth's distance it appears 0.5 degrees in width. The small angle allows directional reflection as a controlled propulsion method. It also allows for concentration by lenses or mirrors, to generate high temperatures for industrial or propulsion purposes. This source includes direct use of sunlight, while the items under electrical sources are for sunlight converted to electricity.

The center of the Sun is at about 15.7 million degrees K, and has a core density of about 160,000 kg/m3. Under these conditions Hydrogen undergoes Nuclear Fusion to Helium, releasing 3.846 x 1026 Watts of energy. This energy works its way from the core to the surface, where the temperature has fallen to 5,780K. At this point the intensity is 63.1 MW/m2. At greater distances the same energy flow is spread over larger spherical surfaces, reaching 1362 W/m^2 at the Earth.

At a distance of more than 550 AU, the Sun acts as a Gravitational Lens, bringing the light of other stars to a focus. Light which passes farther from the Sun's edge is bent less, and comes to a focus farther away. This creates a radial focal line of concentrated light from every other star or light source in the sky. The same process happens around every other star that has visible neighboring stars. These Star Lines may be intense enough to be useful, since they concentrate light from the whole circumference of a star to a point.

P. Laser
A Laser emits light through a process of optical amplification by stimulated emission. The output of a laser is coherent and collimated, allowing it to be tightly focused, or travel long distances without spreading out. The output can also be in a very narrow range of wavelengths. Because of the narrow wavelength, it can be coupled efficiently to an absorber, or a high reflectivity reflector for that specific wavelength. It can also be coupled to a photovoltaic device with high efficiency. As an energy source for propulsion it can supply higher intensity light than natural sources like stars. High power lasers have been proposed for launch from Earth, but sufficiently high power ones to make that use practical do not yet exist. Lower power lasers can augment natural sunlight falling on spacecraft solar arrays. Very high power lasers focused by the Sun's gravity have been suggested to power interstellar vehicles, but that use would far in the future.

Q. Microwave
This energy source involves direct use of the microwave beam, while item N. Rectenna Array converts it to electricity. A microwave beam can be absorbed and converted directly to heat, or it can be used to create photon pressure. Any suitable wavelength can be used to create a directional energy beam. However some wavelengths are absorbed by the Earth's or other atmospheres. Shorter wavelengths can be focused more easily, since that depends on the ratio of antenna size to wavelength. The efficiency of producing shorter wavelengths is typically lower, and generators with high enough power to be useful may not be available. Microwave band equipment is developed enough to not suffer from these limitations.

R. Neutral Particles
A Particle Beam is a collimated stream of high energy particles to deliver energy from one place to another. The concept was originally developed as a weapon, but less lethal amounts of energy can be used as a power source. Charged particles, such as protons in a Particle Accelerator repel each other, so a beam would spread out once it leaves the confinement of the accelerator. To prevent this, the charged particles are allowed to combine with electrons to form neutral atoms, or neutral particles like Neutrons are used. Particle beams are in an early state of development, and mostly for military use, rather than energy delivery.

Nuclear Sources
Nuclear energy sources involve a change in one or more types of Atomic Nucleii, with the release of net energy. The protons and neutrons in a nucleus are bound together by the strong nuclear force. A change in their arrangement involves typically a million times as much energy than rearranging electrons, which is what chemical reactions do. So nuclear energy sources are potentially very powerful. Although the Sun operates by nuclear fusion, we consider it a source of light energy. The fusion happens in the Sun's core, where it is not accessible, and what reaches us is blackbody radiation from the surface.

S. Radioactive decay
Radioactive Decay is the spontaneous change of unstable atomic nucleii by the emission of particles or electromagnetic energy. Unstable natural elements were created before the formation of the Solar System, most likely in supernova explosions. The less unstable ones, such as Uranium and Thorium, still survive after billions of years, and continue to decay at a steady rate. Artificial radioactive materials, such as Plutonium-238, are created in nuclear reactors or particle accelerators. They are more unstable, and thus decay faster (an 88 year half-life in the case of Pu-238). This element produces 500 Watts/kg of heat, when fresh, through radioactive decay, making it a useful energy source. It has been used for this purpose on a number of planetary exploration missions. Other elements with very long decay times in their natural state are too weak to use as energy sources.

[This is an old reference and should be updated]

 * Lockwood, A.; Ewell, R.; Wood, C. "Advanced High Temperature Thermo-electrics for Space Power", Proceedings of the 16th Intersociety Energy Conversion Engineering Conference, v 2 pp 1985–1990, 1981.

T. Nuclear Fission
The low natural decay rate of some elements can be increased by artificial means. A Nuclear Reactor is a device for doing this in a controlled way for the production of energy. The two main ways to do this are Nuclear Fission, the splitting of heavy nucleii into smaller parts, and Nuclear Fusion, the merger of lighter nucleii to form a heavier one. The reason for the two types can be found in the Binding Energy per nuclear particle in a nucleus (Figure 1.4-2). A higher binding energy means the particles are more strongly held together and more stable, so energy can be released in forming that nucleus. The binding energy has a peak at Iron-56, so reactions from either the light end (fusion) or heavy end (fission) towards the middle both produce energy. Fission reactors are a significant source of electrical power on Earth. In space, a few small-scale reactors have been used, and work is in progress on developing larger scale versions with higher power demands.

[These are old references and should be updated]

 * El Genk, M.S.; Hoover, M. D. "Space Nuclear Power Systems 1986: Proceedings of the Third Symposium", 1987.
 * Sovie, Ronald J. "SP-100 Advanced Technology Program", NASA Technical Memorandum 89888, 1987.
 * Bloomfield, Harvey S. "Small Space Reactor Power Systems for Unmanned Solar System Exploration Missions", NASA Technical Memorandum 100228, December 1987.
 * Buden, D.; Trapp, T. J. "Space Nuclear Power Plant Technology Development Philosophy for a Ground Engineering Phase", Proceedings of the 20th Intersociety Energy Conversion Engineering Conference vol 1 pp 358-66, 1985.

U. Artificial Nuclear Fusion
Natural fusion occurs in stars, and the resulting light output has been addressed above under beamed power sources. This item is for artificial energy sources. Fusion has been achieved momentarily in nuclear bombs, but steady state operation has proved difficult. The most researched approach uses Tokamaks, which are doughnut shaped magnetic fields which contain a hot plasma. This approach has not yet produced a working device, although various research machines have been built or are under construction. A Tokamak type power reactor would be too massive for a reasonable propulsion system. For stationary projects it would be as reasonable on another planet as on Earth. A number of alternate intermittent and steady state fusion devices are under varying levels of research, but all at much lower funding than the work invested in the Tokamak type devices. Some of those might yield a lightweight enough device for propulsion.

All fusion reactions combine light atomic nuclei into heavier ones. As shown in Figure 1.4-2, the largest energy release is in the first few elements, from Hydrogen to Boron. What is required to achieve fusion is to bring the positively charged nuclei close enough together against their electric repulsion for the nuclear forces to take over. This requires the equivalent of millions of degrees K, or particle kinetic energy in the tens of kilo electron Volts (keV).

[These are old references and should be updated]

 * Miley, G. H. et al "Advanced Fusion Power: A preliminary Assessment, final report 1986-1987". National Academy of Sciences report #AD-A185903, 1987.
 * Eklund, P. M. "Quark-Catalyzed Fusion-Heated Rockets", AIAA paper number 82-1218 presented at AIAA/SAE/ASME 18th Joint Propulsion Conference, Cleveland, Ohio, 21-23 June 1982.

V. Muon-Catalyzed Fusion
Muon-Catalyzed Fusion is a method of catalyzing fusion reactions at temperatures far below the millions of degrees K otherwise required. A beam of muons is directed at a deuterium/tritium mixture, where they cause multiple fusion reactions. This heats the gas, which can then drive a generator for electricity. Although this method and more complicated systems based on it are sound from a physics standpoint, a practical system from an engineering point of view has not been developed yet. It must be considered a possible future energy source at this time.

W. Nuclear Explosions
Unfortunately, explosive Nuclear Weapons are all too well developed. Various concepts have been proposed to use their high energy output for space projects. These include a nuclear-powered launch device, where the explosive heats gas in an underground chamber. This then propels a projectile up a barrel. Another idea is to detonate small nuclear explosions behind a space vehicle, directly pushing it with the blast wave. These concepts are speculative at present, because there is no way to safely test them on Earth, and treaties prohibit nuclear weapons in space.

Matter Conversion Sources
In physics, Mass-Energy Equivalence is the idea that mass is related to energy by the formula E = mc2. Since the speed of light, c, is a large number – 299.8 million m/s, the square is very large: 8.9875 x 1016 Joules/kg. This is equal to the output of a nuclear power plant for 2.85 years for each kg of mass converted to energy. In theory, total matter conversion provides the highest amount of energy per unit mass. In practice, however, this is not so easy.

X. Antimatter
Antimatter is composed of antiparticles, which have the same mass as normal particles, but opposite charge and other properties. When a particle and anti-particle meet, they destroy each other and are converted to other particles or photons, releasing large amounts of energy in the process. Our universe is almost entirely made of matter. So use of this material as an energy source requires making it artificially. This requires at least as much energy as is later released by the annihilation. Antimatter is therefore an extreme type of energy storage. Antimatter is made in small amounts today in particle accelerators, and used for physics research. We do not have practical ways to make and store it in large enough amounts for space projects. Conceptually, a space vehicle would store some amount of antimatter, then use it to produce energy for propulsion. If the storage system is light enough, the energy per mass would then be higher than nuclear fusion or other methods.

[These are old references and should be updated]

 * Hora, H.; Loeb, H. W. "Efficient Production of Antihydrogen by Laser for Space Propulsion", Z. Flugwiss. Weltraumforsch., v. 10 no. 6 pp 393-400, November-December 1986.
 * Forward, R. L., ed. "Mirror Matter Newsletter", self published, all volumes, contains extensive bibliography.

Y. Black Hole
A Black Hole is a region of Spacetime with such strong gravity that nothing can travel from inside to outside it. Two forms of energy extraction are possible for black holes. The first is infall energy, generated as material in an accretion disk around the black hole heats by friction and emits energy. It is essentially converting potential energy into heat. Since the gravitational potential of a black hole is extreme, this can release a lot of energy. The second is Hawking Radiation by quantum tunneling from hypothetical quantum black holes. Black holes can form by the collapse of a large star at the end of it's life, or a sufficiently dense and massive region at the center of a galaxy. Quantum black holes are smaller, and hypothesized to have formed during the creation of the Universe. The nearest known stellar-mass black hole is 2800 light years from Earth, and quantum black holes have not been discovered, nor is there a known way to make them. So use of black holes for space projects is theoretical at present.

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