Oberth effect

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https://en.wikipedia.org/wiki/Oberth_effect

In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed. The resulting maneuver is a more efficient way to gain kinetic energy than applying the same impulse outside of a gravitational well. The gain in efficiency is explained by the Oberth effect, wherein the use of a reaction engine at higher speeds generates a greater change in mechanical energy than its use at lower speeds. In practical terms, this means that the most energy-efficient method for a spacecraft to burn its fuel is at the lowest possible orbital periapsis, when its orbital velocity (and so, its kinetic energy) is greatest. In some cases, it is even worth spending fuel on slowing the spacecraft into a gravity well to take advantage of the efficiencies of the Oberth effect. The maneuver and effect are named after the person who first described them in 1927, Hermann Oberth, an Austro-Hungarian-born German physicist and a founder of modern rocketry.

The Oberth effect is strongest at a point in orbit known as the periapsis, where the gravitational potential is lowest, and the speed is highest. This is because a given firing of a rocket engine at high speed causes a greater change in kinetic energy than when fired otherwise similarly at lower speed.

Because the vehicle remains near periapsis only for a short time, for the Oberth maneuver to be most effective the vehicle must be able to generate as much impulse as possible in the shortest possible time. As a result the Oberth maneuver is much more useful for high-thrust rocket engines like liquid-propellant rockets, and less useful for low-thrust reaction engines such as ion drives, which take a long time to gain speed. The Oberth effect also can be used to understand the behavior of multi-stage rockets: the upper stage can generate much more usable kinetic energy than the total chemical energy of the propellants it carries.

In terms of the energies involved, the Oberth effect is more effective at higher speeds because at high speed the propellant has significant kinetic energy in addition to its chemical potential energy. At higher speed the vehicle is able to employ the greater change (reduction) in kinetic energy of the propellant (as it is exhausted backwards and hence at reduced speed and hence reduced kinetic energy) to generate a greater increase in kinetic energy of the vehicle.

Explanation in terms of momentum and kinetic energy

A rocket works by transferring momentum to its propellant. At a fixed exhaust velocity, this will be a fixed amount of momentum per unit of propellant. For a given mass of rocket (including remaining propellant), this implies a fixed change in velocity per unit of propellant. Because kinetic energy equals mv²/2, this change in velocity imparts a greater increase in kinetic energy at a high velocity than it would at a low velocity. For example, considering a 2 kg rocket:

• at 1 m/s, adding 1 m/s increases the kinetic energy from 1 J to 4 J, for a gain of 3 J;
• at 10 m/s, starting with a kinetic energy of 100 J, the rocket ends with 121 J, for a net gain of 21 J.

This greater change in kinetic energy can then carry the rocket higher in the gravity well than if the propellant were burned at a lower speed.

Description in terms of work

Rocket engines produce the same force regardless of their velocity. A rocket acting on a fixed object, as in a static firing, does no useful work at all; the rocket's stored energy is entirely expended on accelerating its propellant in the form of exhaust. But when the rocket moves, its thrust acts through the distance it moves. Force multiplied by distance is the definition of mechanical energy or work. So the farther the rocket and payload move during the burn (i.e. the faster they move), the greater the kinetic energy imparted to the rocket and its payload and the less to its exhaust.

This is shown as follows. The mechanical work done on the rocket (${\displaystyle W}$) is defined as the dot product of the force of the engine's thrust (${\displaystyle {\vec {F}}}$) and the displacement it travels during the burn (${\displaystyle {\vec {s}}}$):

${\displaystyle W={\vec {F}}\cdot {\vec {s}}.}$

If the burn is made in the prograde direction, ${\displaystyle {\vec {F}}\cdot {\vec {s}}=\|F\|\cdot \|s\|=F\cdot s}$. The work results in a change in kinetic energy

${\displaystyle \Delta E_{k}=F\cdot s.}$

Differentiating with respect to time, we obtain

${\displaystyle {\frac {\mathrm {d} E_{k}}{\mathrm {d} t}}=F\cdot {\frac {\mathrm {d} s}{\mathrm {d} t}},}$

or

${\displaystyle {\frac {\mathrm {d} E_{k}}{\mathrm {d} t}}=F\cdot v,}$

where ${\displaystyle v}$ is the velocity. Dividing by the instantaneous mass ${\displaystyle m}$ to express this in terms of specific energy (${\displaystyle e_{k}}$), we get

${\displaystyle {\frac {\mathrm {d} e_{k}}{\mathrm {d} t}}={\frac {F}{m}}\cdot v=a\cdot v,}$

where ${\displaystyle a}$ is the acceleration vector.

Thus it can be readily seen that the rate of gain of specific energy of every part of the rocket is proportional to speed and, given this, the equation can be integrated (numerically or otherwise) to calculate the overall increase in specific energy of the rocket.

Impulsive burn

Integrating the above energy equation is often unnecessary if the burn duration is short. Short burns of chemical rocket engines close to periapsis or elsewhere are usually mathematically modelled as impulsive burns, where the force of the engine dominates any other forces that might change the vehicle's energy over the burn.

For example, as a vehicle falls towards periapsis in any orbit (closed or escape orbits) the velocity relative to the central body increases. Briefly burning the engine (an “impulsive burn”) prograde at periapsis increases the velocity by the same increment as at any other time (${\displaystyle \Delta v}$). However, since the vehicle's kinetic energy is related to the square of its velocity, this increase in velocity has a non-linear effect on the vehicle's kinetic energy, leaving it with higher energy than if the burn were achieved at any other time.

Oberth calculation for a parabolic orbit

If an impulsive burn of Δv is performed at periapsis in a parabolic orbit, then the velocity at periapsis before the burn is equal to the escape velocity (V_esc), and the specific kinetic energy after the burn is

${\displaystyle {\begin{aligned}e_{k}&={\tfrac {1}{2}}V^{2}\\&={\tfrac {1}{2}}(V_{\text{esc}}+\Delta v)^{2}\\&={\tfrac {1}{2}}V_{\text{esc}}^{2}+\Delta vV_{\text{esc}}+{\tfrac {1}{2}}\Delta v^{2},\end{aligned}}}$

where ${\displaystyle V=V_{\text{esc}}+\Delta v}$.

When the vehicle leaves the gravity field, the loss of specific kinetic energy is

${\displaystyle {\tfrac {1}{2}}V_{\text{esc}}^{2},}$

so it retains the energy

${\displaystyle \Delta vV_{\text{esc}}+{\tfrac {1}{2}}\Delta v^{2},}$

which is larger than the energy from a burn outside the gravitational field (${\displaystyle {\tfrac {1}{2}}\Delta v^{2}}$) by

${\displaystyle \Delta vV_{\text{esc}}.}$

When the vehicle has left the gravity well, it is travelling at a speed

${\displaystyle V=\Delta v{\sqrt {1+{\frac {2V_{\text{esc}}}{\Delta v}}}}.}$

For the case where the added impulse Δv is small compared to escape velocity, the 1 can be ignored, and the effective Δv of the impulsive burn can be seen to be multiplied by a factor of simply

${\displaystyle {\sqrt {\frac {2V_{\text{esc}}}{\Delta v}}}}$

and one get

${\displaystyle V}$ ≈ ${\displaystyle {\sqrt {{2V_{\text{esc}}}{\Delta v}}}.}$

Similar effects happen in closed and hyperbolic orbits.

Parabolic example

If the vehicle travels at velocity v at the start of a burn that changes the velocity by Δv, then the change in specific orbital energy (SOE) due to the new orbit is

${\displaystyle v\,\Delta v+{\tfrac {1}{2}}(\Delta v)^{2}.}$

Once the spacecraft is far from the planet again, the SOE is entirely kinetic, since gravitational potential energy approaches zero. Therefore, the larger the v at the time of the burn, the greater the final kinetic energy, and the higher the final velocity.

The effect becomes more pronounced the closer to the central body, or more generally, the deeper in the gravitational field potential in which the burn occurs, since the velocity is higher there.

So if a spacecraft is on a parabolic flyby of Jupiter with a periapsis velocity of 50 km/s and performs a 5 km/s burn, it turns out that the final velocity change at great distance is 22.9 km/s, giving a multiplication of the burn by 4.58 times.

Paradox

It may seem that the rocket is getting energy for free, which would violate conservation of energy. However, any gain to the rocket's kinetic energy is balanced by a relative decrease in the kinetic energy the exhaust is left with (the kinetic energy of the exhaust may still increase, but it does not increase as much). Contrast this to the situation of static firing, where the speed of the engine is fixed at zero. This means that its kinetic energy does not increase at all, and all the chemical energy released by the fuel is converted to the exhaust's kinetic energy (and heat).

At very high speeds the mechanical power imparted to the rocket can exceed the total power liberated in the combustion of the propellant; this may also seem to violate conservation of energy. But the propellants in a fast-moving rocket carry energy not only chemically, but also in their own kinetic energy, which at speeds above a few kilometres per second exceed the chemical component. When these propellants are burned, some of this kinetic energy is transferred to the rocket along with the chemical energy released by burning.

The Oberth effect can therefore partly make up for what is extremely low efficiency early in the rocket's flight when it is moving only slowly. Most of the work done by a rocket early in flight is "invested" in the kinetic energy of the propellant not yet burned, part of which they will release later when they are burned.

Project Prometheus

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https://en.wikipedia.org/wiki/Project_Prometheus 

 

Nuclear reactors could be used to power ion engines such as this one used on Deep Space 1.

Project Prometheus/Project Promethian was established in 2003 by NASA to develop nuclear-powered systems for long-duration space missions. This was NASA's first serious foray into nuclear spacecraft propulsion since the cancellation of the SNTP project in 1995. The project was planned to design, develop, and fly multiple deep space missions to the outer planets.

The project was cancelled in 2005, due to other demands on NASA's budget. Its budget shrank from $252.6 million in 2005 to only $100 million in 2006, $90 million of which was for closeout costs on cancelled contracts.

Namesake

Originally named the "Nuclear Systems Initiative", Project Prometheus was named for the wisest of the Titans in Greek mythology who gave the gift of fire to humanity. NASA said the name Prometheus indicates its hopes of establishing a new tool for understanding nature and expanding capabilities for the exploration of the Solar System.

Motivations

Due to their distance from the Sun, spacecraft exploring the outer planets are severely limited in that they cannot use solar power as a source of electrical energy for onboard instrumentation or for ion propulsion systems. Previous missions to the outer planets such as Voyager and Galileo probe have relied on radioisotope thermoelectric generators (RTGs) as their primary power source. Unlike RTGs which rely on heat produced by the natural decay of radioactive isotopes, Project Prometheus called for the use of a small nuclear reactor as the primary power source.

The primary advantages of this would have been:

• Increased power generation compared to RTGs, allowing scientists and engineers more flexibility in both mission design and operations.
• Increased spacecraft longevity.
• Increased range and propulsion power.
• Extra power for high speed data transmission.

Missions

Prometheus I (Jupiter Icy Moons Orbiter)

Missions planned to involve Prometheus Nuclear Systems and Technology included:

• Jupiter Icy Moons Orbiter
• Exploration of the Jovian moons Europa, Ganymede, and Callisto. Originally planned to be the first mission of Project Prometheus, it was deemed too complex and expensive, and its funding was cut in the 2006 budget. NASA instead considered a demonstration mission to a target closer to Earth to test out the reactor and heat rejection systems, possibly with a spacecraft scaled down from its original size.

Technology

Project Prometheus was focused on Nuclear electric propulsion:

Development of spacecraft powered by nuclear reactors to generate electricity.

Brayton cycle turboalternators were selected for power generation.

This electricity would then be used to run ion engines. It did not study nor pursue nuclear thermal propulsion (e.g. NERVA)

Collaboration

The project was managed by JPL. Spacecraft design contracts were awarded to Boeing, Lockheed-Martin, and Northrop Grumman.

Project Prometheus would have had substantial involvement of the U.S. Department of Energy (DOE).

Naval Reactors, which oversees the nuclear reactor program of the U.S. Navy, was to participate in the design and construction of the reactors for the Jupiter Icy Moons Orbiter.

Laser propulsion

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Laser_propulsion 

Laser propulsion is a form of beam-powered propulsion where the energy source is a remote (usually ground-based) laser system and separate from the reaction mass. This form of propulsion differs from a conventional chemical rocket where both energy and reaction mass come from the solid or liquid propellants carried on board the vehicle.

A laser launch Heat Exchanger Thruster system

History

The basic concepts underlying a photon-propelled "sail" propulsion system were developed by Eugene Sanger and the Hungarian physicist György Marx. Propulsion concepts using laser-energized rockets were developed in the 1970s by Arthur Kantrowitz and Wolfgang Moekel, with a variant using laser ablation pioneered by Leik Myrabo. An exposition of Kantrowitz's laser propulsion ideas was published in 1988.

Laser propulsion systems may transfer momentum to a spacecraft in two different ways. The first way uses photon radiation pressure to drive momentum transfer and is the principle behind solar sails and laser sails. The second method uses the laser to help expel mass from the spacecraft as in a conventional rocket. Thus, the first uses the laser for both energy and reaction mass, while the second uses the laser for energy, but carries reaction mass. Thus, the second is fundamentally limited in final spacecraft velocities by the rocket equation.

Laser-pushed lightsail

Laser-pushed sails are examples of beam-powered propulsion.

Laser-pushed lightsail

A laser-pushed lightsail is a thin reflective sail similar to a solar sail, in which the sail is being pushed by a laser, rather than the sun. The advantage of lightsail propulsion is that the vehicle does not carry either the energy source or the reaction mass for propulsion, and hence the limitations of the Tsiolkovsky rocket equation to achieving high velocities are avoided. Use of a laser-pushed lightsail was proposed initially by Marx in 1966, as a method of interstellar travel that would avoid extremely high mass ratios by not carrying fuel, and analyzed in detail by physicist Robert L. Forward in 1989. Further analysis of the concept was done by Landis, Mallove and Matloff, Andrews and others.

The beam has to have a large diameter so that only a small portion of the beam misses the sail due to diffraction and the laser or microwave antenna has to have a good pointing stability so that the craft can tilt its sails fast enough to follow the center of the beam. This gets more important when going from interplanetary travel to interstellar travel, and when going from a fly-by mission, to a landing mission, to a return mission. The laser may alternatively be a large phased array of small devices, which get their energy directly from solar radiation.

The laser-pushed sail is proposed as a method of propelling a small interstellar probe by the Breakthrough Starshot project.

Another method of moving a much larger spacecraft to high velocities is by using a laser system to propel a stream of much smaller sails. Each alternative mini sail is slowed down by a laser from the home system so that they collide at ionising velocities. The ionising collisions could then be used to interact with a powerful magnetic field on the spacecraft to provide a force to power and move it. An extension of the idea is to have nuclear materials on the mini sails that undergo fission or fusion to provide a much more powerful force but the collision velocities would have to be much higher.

Photon recycling

Metzgar and Landis proposed a variant on the laser-pushed sail, in which the photons reflected from the sail are re-used by re-reflecting them back to the sail by a stationary mirror; a "multi-bounce laser-based sail." This amplifies the force produced by recycling the photons, resulting in considerably higher force produced from the same laser power. There is also a multi-bounce photonic sail configuration which uses a large Fresnel lens around a laser generating system. In this configuration the laser shines light on a probe sail accelerating it outwards which is then reflected back through the Fresnel lens to be reflected off a larger more massive reflector probe going in the other direction. The laser light is reflected back and forth many times improving the force transmitted but importantly allows the large lens to remain in a more stable position as it is not greatly influenced by the laser lights momentum.

An optical cavity allows greater re-use of photons, but keeping the beam in the cavity becomes much more challenging. An optical cavity can be made with two high-reflectance mirrors, forming a Fabry–Pérot optical resonance cavity in which any small movement of mirrors would destroy the resonance condition and null photonic thrust. Such optical cavities are used for gravitational wave detection as in LIGO, for their extreme sensitivity to the movement of mirror. Bae originally proposed to use photon recycling for use in a nanometer accuracy formation flight of satellites for this reason. Bae, however, discovered that in an active optical cavity formed by two high-reflectance mirrors and a laser gain medium in between, similar to the typical laser cavity, photon recycling becomes less sensitive to the movement of mirrors. Bae named the laser thruster based on the photon recycling in an active optical cavity Photonic Laser Thruster (PLT). In 2015 his team demonstrated the number of photon recycling up to 1,540 over a distance of a few meters and photonic thrusts up to 3.5 mN with the use of a 500 W laser system. In a laboratory demonstration, a Cubesat (0.75 kg in weight) was propelled with PLT.

Laser energized rocket

There are several forms of laser propulsion in which the laser is used as an energy source to provide momentum to propellant that is carried on board the rocket. The use of a laser as the energy source means that the energy provided to the propellant is not limited by the chemical energy of the propellant.

Laser thermal rocket

The laser thermal rocket (heat exchanger (HX) thruster) is a thermal rocket in which the propellant is heated by energy provided by an external laser beam. The beam heats a solid heat exchanger, which in turn heats an inert liquid propellant, converting it to hot gas which is exhausted through a conventional nozzle. This is similar in principle to nuclear thermal and solar thermal propulsion. Using a large flat heat exchanger allows the laser beam to shine directly on the heat exchanger without focusing optics on the vehicle. The HX thruster has the advantage of working equally well with any laser wavelength and both CW and pulsed lasers, and of having an efficiency approaching 100%. The HX thruster is limited by the heat exchanger material and by radiative losses to relatively low gas temperatures, typically 1000 - 2000° C. For a given temperature, the specific impulse is maximized with the minimum molecular weight reaction mass, and with hydrogen propellant, that provides sufficient specific impulse as high as 600 – 800 seconds, high enough in principle to allow single stage vehicles to reach low Earth orbit. The HX laser thruster concept was developed by Jordin Kare in 1991; a similar microwave thermal propulsion concept was developed independently by Kevin L. Parkin at Caltech in 2001.

A variation on this concept was proposed by Prof. John Sinko and Dr. Clifford Schlecht as a redundant safety concept for assets on orbit. Packets of enclosed propellants are attached to the outside of a space suit, and exhaust channels run from each packet to the far side of the astronaut or tool. A laser beam from a space station or shuttle vaporizes the propellant inside the packs. Exhaust is directed behind the astronaut or tool, pulling the target towards the laser source. To brake the approach, a second wavelength is used to ablate the exterior of the propellant packets on the near side.

Ablative laser propulsion

Ablative laser propulsion (ALP) is a form of beam-powered propulsion in which an external pulsed laser is used to burn off a plasma plume from a solid metal propellant, thus producing thrust. The measured specific impulse of small ALP setups is very high at about 5000 s (49 kN·s/kg), and unlike the lightcraft developed by Leik Myrabo which uses air as the propellant, ALP can be used in space.

Material is directly removed from a solid or liquid surface at high velocities by laser ablation by a pulsed laser. Depending on the laser flux and pulse duration, the material can be simply heated and evaporated, or converted to plasma. Ablative propulsion will work in air or vacuum. Specific impulse values from 200 seconds to several thousand seconds are possible by choosing the propellant and laser pulse characteristics. Variations of ablative propulsion include double-pulse propulsion in which one laser pulse ablates material and a second laser pulse further heats the ablated gas, laser micropropulsion in which a small laser on board a spacecraft ablates very small amounts of propellant for attitude control or maneuvering, and space debris removal, in which the laser ablates material from debris particles in low Earth orbit, changing their orbits and causing them to reenter.

University of Alabama Huntsville Propulsion Research Center has researched ALP.

Pulsed plasma propulsion

A high energy pulse focused in a gas or on a solid surface surrounded by gas produces breakdown of the gas (usually air). This causes an expanding shock wave which absorbs laser energy at the shock front (a laser sustained detonation wave or LSD wave); expansion of the hot plasma behind the shock front during and after the pulse transmits momentum to the craft. Pulsed plasma propulsion using air as the working fluid is the simplest form of air-breathing laser propulsion. The record-breaking lightcraft, developed by Leik Myrabo of RPI (Rensselaer Polytechnic Institute) and Frank Mead, works on this principle.

Another concept of pulsed plasma propulsion is being investigated by Prof. Hideyuki Horisawa.

CW plasma propulsion

A continuous laser beam focused in a flowing stream of gas creates a stable laser sustained plasma which heats the gas; the hot gas is then expanded through a conventional nozzle to produce thrust. Because the plasma does not touch the walls of the engine, very high gas temperatures are possible, as in gas core nuclear thermal propulsion. However, to achieve high specific impulse, the propellant must have low molecular weight; hydrogen is usually assumed for actual use, at specific impulses around 1,000 seconds. CW plasma propulsion has the disadvantage that the laser beam must be precisely focused into the absorption chamber, either through a window or by using a specially-shaped nozzle. CW plasma thruster experiments were performed in the 1970s and 1980s, primarily by Dr. Dennis Keefer of UTSI and Prof. Herman Krier of the University of Illinois at Urbana–Champaign.

Laser electric propulsion

A general class of propulsion techniques in which the laser beam power is converted to electricity, which then powers some type of electric propulsion thruster.

A small quadcopter has flown for 12 hours and 26 minutes charged by a 2.25 kW laser (powered at less than half of its normal operating current), using 170 watt photovoltaic arrays as the power receiver, and a laser has been demonstrated to charge the batteries of an unmanned aerial vehicle in flight for 48 hours.

For spacecraft, laser electric propulsion is considered as a competitor to solar electric or nuclear electric propulsion for low-thrust propulsion in space. However, Leik Myrabo has proposed high-thrust laser electric propulsion, using magnetohydrodynamics to convert laser energy to electricity and to electrically accelerate air around a vehicle for thrust.

Photon rocket

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Photon_rocket

A photon rocket is a rocket that uses thrust from the momentum of emitted photons (radiation pressure by emission) for its propulsion. Photon rockets have been discussed as a propulsion system that could make interstellar flight possible, which requires the ability to propel spacecraft to speeds at least 10% of the speed of light, v ≈ 0.1c = 30,000 km/s. Photon propulsion has been considered to be one of the best available interstellar propulsion concepts, because it is founded on established physics and technologies. Traditional photon rockets are proposed to be powered by onboard generators, as in the nuclear photonic rocket. The standard textbook case of such a rocket is the ideal case where all of the fuel is converted to photons which are radiated in the same direction. In more realistic treatments, one takes into account that the beam of photons is not perfectly collimated, that not all of the fuel is converted to photons, and so on. A large amount of fuel would be required and the rocket would be a huge vessel.

The limitations posed by the rocket equation can be overcome, as long as the reaction mass is not carried by the spacecraft. In the Beamed Laser Propulsion (BLP), the photon generators and the spacecraft are physically separated and the photons are beamed from the photon source to the spacecraft using lasers. However, BLP is limited because of the extremely low thrust generation efficiency of photon reflection. One of the best ways to overcome the inherent inefficiency in producing thrust of the photon thruster is by amplifying the momentum transfer of photons by recycling photons between two high reflectance mirrors, one being stationary, or on a thruster, the other being the "sail".

Speed

The speed an ideal photon rocket will reach, in the absence of external forces, depends on the ratio of its initial and final mass:

${\displaystyle v=c{\frac {\left({\frac {m_{\text{i}}}{m_{\text{f}}}}\right)^{2}-1}{\left({\frac {m_{\text{i}}}{m_{\text{f}}}}\right)^{2}+1}}}$

where ${\displaystyle m_{\text{i}}}$ is the initial mass and ${\displaystyle m_{\text{f}}}$ is the final mass.

The gamma factor corresponding to this speed has the simple expression:

${\displaystyle \gamma ={\frac {1}{2}}\left({\frac {m_{\text{i}}}{m_{\text{f}}}}+{\frac {m_{\text{f}}}{m_{\text{i}}}}\right)}$.

At 10% the speed of light, the gamma factor is about 1.005, implying ${\displaystyle {\frac {m_{\text{f}}}{m_{\text{i}}}}}$is very nearly 0.9.

Derivation

We denote the four-momentum of the rocket at rest as ${\displaystyle P_{\text{i}}}$, the rocket after it has burned its fuel as ${\displaystyle P_{\text{f}}}$, and the four-momentum of the emitted photons as ${\displaystyle P_{\text{ph}}}$. Conservation of four-momentum implies:

${\displaystyle P_{\text{ph}}=P_{\text{i}}-P_{\text{f}}}$

squaring both sides (i.e. taking the Lorentz inner product of both sides with themselves) gives:

${\displaystyle P_{\text{ph}}^{2}=P_{\text{i}}^{2}+P_{\text{f}}^{2}-2P_{\text{i}}\cdot P_{\text{f}}.}$

According to the energy-momentum relation ${\displaystyle E^{2}-(pc)^{2}=(mc^{2})^{2}}$, the square of the four-momentum equals the square of the mass, and ${\displaystyle P_{\text{ph}}^{2}=0}$ because photons have zero mass.

As we start in the rest frame (i.e. the zero-momentum frame) of the rocket, the initial four-momentum of the rocket is:

${\displaystyle {P}_{\text{i}}={\begin{pmatrix}{\frac {{m}_{\text{i}}c^{2}}{c}}\\0\\0\\0\end{pmatrix}},}$

while the final four-momentum is:

${\displaystyle {P}_{\text{f}}={\begin{pmatrix}\ {\gamma }{m}_{\text{f}}c\\{\gamma }{m}_{\text{f}}{v}_{\text{f}}\\0\\0\end{pmatrix}}.}$

Therefore, taking the Minkowski inner product (see four-vector), we get:

${\displaystyle 0=m_{\text{i}}^{2}+m_{\text{f}}^{2}-2m_{\text{i}}m_{\text{f}}\gamma .}$

We can now solve for the gamma factor, obtaining:

${\displaystyle \gamma ={\frac {1}{2}}\left({\frac {m_{\text{i}}}{m_{\text{f}}}}+{\frac {m_{\text{f}}}{m_{\text{i}}}}\right).}$

Maximum speed limit

Standard theory says that the theoretical speed limit of a photon rocket is below the speed of light. Haug has recently, in Acta Astronautica, suggested a maximum speed limit for an ideal photon rockets that is just below the speed of light. However, his claims have been contested by Daniele Tommasini et.al., because such velocity is formulated for the relativistic mass and is therefore frame-dependent.

Regardless of the photon generator characteristics, onboard photon rockets powered with nuclear fission and fusion have speed limits from the efficiency of these processes. Here it is assumed that the propulsion system has a single stage. Suppose the total mass of the photon rocket/spacecraft is M that includes fuels with a mass of αM with α < 1.  Assuming the fuel mass to propulsion-system energy conversion efficiency γ and the propulsion-system energy to photon energy conversion efficiency δ ≪ 1, the maximum total photon energy generated for propulsion, E_p, is given by

${\displaystyle E_{\text{p}}=\alpha \gamma \delta Mc^{2}}$

If the total photon flux can be directed at 100% efficiency to generate thrust, the total photon thrust, T_p, is given by

${\displaystyle T_{\text{p}}={\frac {E_{\text{p}}}{c}}=\alpha \gamma \delta Mc}$

The maximum attainable spacecraft velocity, V_max, of the photon propulsion system for V_max ≪ c, is given by

${\displaystyle V_{\text{max}}={\frac {T_{\text{p}}}{M}}=\alpha \gamma \delta c}$

For example, the approximate maximum velocities achievable by onboard nuclear powered photon rockets with assumed parameters are given in Table 1. The maximum velocity limits by such nuclear powered rockets are less than 0.02% of the light velocity (60 km/s). Therefore, onboard nuclear photon rockets are unsuitable for interstellar missions.

Table 1  The maximum velocity obtainable by photon rockets with onboard nuclear photon generators with exemplary parameters.

Energy Source	α	γ	δ	Vmax/c
Fission	0.1	10−3	0.5	5 × 10−5
Fusion	0.1	4 × 10−3	0.5	2 × 10−4

The Beamed Laser Propulsion, such as Photonic Laser Thruster, however, can provide the maximum spacecraft velocity approaching the speed of light, c, in principle.

Robotic spacecraft

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Robotic_spacecraft 

 

An artist's interpretation of the MESSENGER spacecraft at Mercury

A robotic spacecraft is an uncrewed spacecraft, usually under telerobotic control. A robotic spacecraft designed to make scientific research measurements is often called a space probe. Many space missions are more suited to telerobotic rather than crewed operation, due to lower cost and lower risk factors. In addition, some planetary destinations such as Venus or the vicinity of Jupiter are too hostile for human survival, given current technology. Outer planets such as Saturn, Uranus, and Neptune are too distant to reach with current crewed spacecraft technology, so telerobotic probes are the only way to explore them.

Many artificial satellites are robotic spacecraft, as are many landers and rovers.

History

A replica of Sputnik 1 at the U.S. National Air and Space Museum

 

A replica of Explorer 1

The first robotic spacecraft was launched by the Soviet Union (USSR) on 22 July 1951, a suborbital flight carrying two dogs Dezik and Tsygan. Four other such flights were made through the fall of 1951.

The first artificial satellite, Sputnik 1, was put into a 215-by-939-kilometer (116 by 507 nmi) Earth orbit by the USSR on 4 October 1957. On 3 November 1957, the USSR orbited Sputnik 2. Weighing 113 kilograms (249 lb), Sputnik 2 carried the first living animal into orbit, the dog Laika. Since the satellite was not designed to detach from its launch vehicle's upper stage, the total mass in orbit was 508.3 kilograms (1,121 lb).

In a close race with the Soviets, the United States launched its first artificial satellite, Explorer 1, into a 357-by-2,543-kilometre (193 by 1,373 nmi) orbit on 31 January 1958. Explorer I was an 205-centimetre (80.75 in) long by 15.2-centimetre (6.00 in) diameter cylinder weighing 14.0 kilograms (30.8 lb), compared to Sputnik 1, a 58-centimeter (23 in) sphere which weighed 83.6 kilograms (184 lb). Explorer 1 carried sensors which confirmed the existence of the Van Allen belts, a major scientific discovery at the time, while Sputnik 1 carried no scientific sensors. On 17 March 1958, the US orbited its second satellite, Vanguard 1, which was about the size of a grapefruit, and remains in a 670-by-3,850-kilometre (360 by 2,080 nmi) orbit as of 2016.

Nine other countries have successfully launched satellites using their own launch vehicles: France (1965), Japan and China (1970), the United Kingdom (1971), India (1980), Israel (1988), Iran (2009), North Korea (2012), and New Zealand (2018).

Design

In spacecraft design, the United States Air Force considers a vehicle to consist of the mission payload and the bus (or platform). The bus provides physical structure, thermal control, electrical power, attitude control and telemetry, tracking and commanding.

JPL divides the "flight system" of a spacecraft into subsystems. These include:

Structure

An illustration's of NASA's planned Orion spacecraft approaching a robotic asteroid capture vehicle

This is the physical backbone structure. It:

• provides overall mechanical integrity of the spacecraft
• ensures spacecraft components are supported and can withstand launch loads

Data handling

This is sometimes referred to as the command and data subsystem. It is often responsible for:

• command sequence storage
• maintaining the spacecraft clock
• collecting and reporting spacecraft telemetry data (e.g. spacecraft health)
• collecting and reporting mission data (e.g. photographic images)

Attitude determination and control

See also: Attitude control system

This system is mainly responsible for the correct spacecraft's orientation in space (attitude) despite external disturbance-gravity gradient effects, magnetic-field torques, solar radiation and aerodynamic drag; in addition it may be required to reposition movable parts, such as antennas and solar arrays.

Landing on hazardous terrain

In planetary exploration missions involving robotic spacecraft, there are three key parts in the processes of landing on the surface of the planet to ensure a safe and successful landing. This process includes an entry into the planetary gravity field and atmosphere, a descent through that atmosphere towards an intended/targeted region of scientific value, and a safe landing that guarantees the integrity of the instrumentation on the craft is preserved. While the robotic spacecraft is going through those parts, it must also be capable of estimating its position compared to the surface in order to ensure reliable control of itself and its ability to maneuver well. The robotic spacecraft must also efficiently perform hazard assessment and trajectory adjustments in real time to avoid hazards. To achieve this, the robotic spacecraft requires accurate knowledge of where the spacecraft is located relative to the surface (localization), what may pose as hazards from the terrain (hazard assessment), and where the spacecraft should presently be headed (hazard avoidance). Without the capability for operations for localization, hazard assessment, and avoidance, the robotic spacecraft becomes unsafe and can easily enter dangerous situations such as surface collisions, undesirable fuel consumption levels, and/or unsafe maneuvers.

Entry, descent, and landing

Integrated sensing incorporates an image transformation algorithm to interpret the immediate imagery land data, perform a real-time detection and avoidance of terrain hazards that may impede safe landing, and increase the accuracy of landing at a desired site of interest using landmark localization techniques. Integrated sensing completes these tasks by relying on pre-recorded information and cameras to understand its location and determine its position and whether it is correct or needs to make any corrections (localization). The cameras are also used to detect any possible hazards whether it is increased fuel consumption or it is a physical hazard such as a poor landing spot in a crater or cliff side that would make landing very not ideal (hazard assessment).

Telecommunications

Components in the telecommunications subsystem include radio antennas, transmitters and receivers. These may be used to communicate with ground stations on Earth, or with other spacecraft.

Electrical power

The supply of electric power on spacecraft generally come from photovoltaic (solar) cells or from a radioisotope thermoelectric generator. Other components of the subsystem include batteries for storing power and distribution circuitry that connects components to the power sources.

Temperature control and protection from the environment

Main article: Spacecraft thermal control

Spacecraft are often protected from temperature fluctuations with insulation. Some spacecraft use mirrors and sunshades for additional protection from solar heating. They also often need shielding from micrometeoroids and orbital debris.

Propulsion

Main article: Spacecraft propulsion

Spacecraft propulsion is a method that allows a spacecraft to travel through space by generating thrust to push it forward. However, there is not one universally used propulsion system: monopropellant, bipropellant, ion propulsion, etc. Each propulsion system generates thrust in slightly different ways with each system having its own advantages and disadvantages. But, most spacecraft propulsion today is based on rocket engines. The general idea behind rocket engines is that when an oxidizer meets the fuel source, there is explosive release of energy and heat at high speeds, which propels the spacecraft forward. This happens due to one basic principle known as Newton's Third Law. According to Newton, "to every action there is an equal and opposite reaction." As the energy and heat is being released from the back of the spacecraft, gas particles are being pushed around to allow the spacecraft to propel forward. The main reason behind the usage of rocket engine today is because rockets are the most powerful form of propulsion there is.

Monopropellant

For a propulsion system to work, there is usually an oxidizer line and a fuel line. This way, the spacecraft propulsion is controlled. But in a monopropellant propulsion, there is no need for an oxidizer line and only requires the fuel line. This works due to the oxidizer being chemically bonded into the fuel molecule itself. But for the propulsion system to be controlled, the combustion of the fuel can only occur due to a presence of a catalyst. This is quite advantageous due to making the rocket engine lighter and cheaper, easy to control, and more reliable. But, the downfall is that the chemical is very dangerous to manufacture, store, and transport.

Bipropellant

A bipropellant propulsion system is a rocket engine that uses a liquid propellent. This means both the oxidizer and fuel line are in liquid states. This system is unique because it requires no ignition system, the two liquids would spontaneously combust as soon as they come into contact with each other and produces the propulsion to push the spacecraft forward. The main benefit for having this technology is because that these kinds of liquids have relatively high density, which allows the volume of the propellent tank to be small, therefore increasing space efficacy. The downside is the same as that of monopropellant propulsion system: very dangerous to manufacture, store, and transport.

Ion

An ion propulsion system is a type of engine that generates thrust by the means of electron bombardment or the acceleration of ions. By shooting high-energy electrons to a propellant atom (neutrally charge), it removes electrons from the propellant atom and this results the propellant atom becoming a positively charged atom. The positively charged ions are guided to pass through positively charged grids that contains thousands of precise aligned holes are running at high voltages. Then, the aligned positively charged ions accelerates through a negative charged accelerator grid that further increases the speed of the ions up to 40 kilometres per second (90,000 mph). The momentum of these positively charged ions provides the thrust to propel the spacecraft forward. The advantage of having this kind of propulsion is that it is incredibly efficient in maintaining constant velocity, which is needed for deep-space travel. However, the amount of thrust produced is extremely low and that it needs a lot of electrical power to operate.

Mechanical devices

Mechanical components often need to be moved for deployment after launch or prior to landing. In addition to the use of motors, many one-time movements are controlled by pyrotechnic devices.

Robotic vs. uncrewed spacecraft

Robotic spacecraft are specifically designed system for a specific hostile environment. Due to their specification for a particular environment, it varies greatly in complexity and capabilities. While an uncrewed spacecraft is a spacecraft without personnel or crew and is operated by automatic (proceeds with an action without human intervention) or remote control (with human intervention). The term 'uncrewed spacecraft' does not imply that the spacecraft is robotic.

Control

Robotic spacecraft use telemetry to radio back to Earth acquired data and vehicle status information. Although generally referred to as "remotely controlled" or "telerobotic", the earliest orbital spacecraft – such as Sputnik 1 and Explorer 1 – did not receive control signals from Earth. Soon after these first spacecraft, command systems were developed to allow remote control from the ground. Increased autonomy is important for distant probes where the light travel time prevents rapid decision and control from Earth. Newer probes such as Cassini–Huygens and the Mars Exploration Rovers are highly autonomous and use on-board computers to operate independently for extended periods of time.

Space probes

Main article: Space probe

A space probe is a robotic spacecraft that does not orbit Earth, but instead, explores further into outer space.[1] A space probe may approach the Moon; travel through interplanetary space; flyby, orbit, or land on other planetary bodies; or enter interstellar space.

SpaceX Dragon

Main article: SpaceX Dragon

This file is an excerpt from SpaceX Dragon.

 

An example of a fully robotic spacecraft in the modern world would be SpaceX Dragon. The SpaceX Dragon was a robotic spacecraft designed to send 6,000 kg (13,000 lb) of cargo to the International Space Station. The SpaceX Dragon's total height was 7.2 m (24 ft) with a diameter of 3.7 m (12 ft). The maximum launch payload mass was 6,000 kg (13,000 lb) with a maximum return mass of 3,000 kg (6,600 lb), along with a maximum launch payload volume of 25 m³ (880 cu ft) and a maximum return payload volume of 11 m³ (390 cu ft). The maximum endurance of the Dragon in space was two years.

In 2012 the SpaceX Dragon made history by becoming the first commercial robotic spacecraft to deliver cargo to the International Space Station and to safely return cargo to Earth in the same trip, something previously achieved only by governments. Since then, it performed 22 cargo flights, and its last flight was SpaceX CRS-20. The Dragon spacecraft is being replaced by the cargo variant of SpaceX Dragon 2 as of 2020.

Robotic spacecraft service vehicles

AERCam Sprint released from the Space Shuttle Columbia payload bay

• MDA Space Infrastructure Servicing vehicle — an in-space refueling depot and service spacecraft for communication satellites in geosynchronous orbit. Launch planned for 2015.

• Mission Extension Vehicle is an alternative approach that does not utilize in-space RCS fuel transfer. Rather, it would connect to the target satellite in the same way as MDA SIS, and then use "its own thrusters to supply attitude control for the target."
• OSAM-1 is NASA's Servicing, Assembly and Manufacturing engineering test mission. The vehicle has two robotic payloads with a total of three robot arms and performs multiple tasks: refueling an older Earth Observation satellite (Landsat 7) , constructing a communications antenna from segments, and manufacturing a structural beam.