Mekanika Orbit: Bacaan Selanjutnya

Further reading

Many of the options, procedures, and supporting theory are covered in standard works such as:

• Bate, R.R., Mueller, D.D., White, J.E., (1971). Fundamentals of Astrodynamics. Dover Publications, New York. ISBN 978-0486600611.
• Vallado, D. A. (2001). Fundamentals of Astrodynamics and Applications, 2nd Edition. Springer. ISBN 978-0792369035.
• Battin, R.H. (1999). An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics & Ast, Washington, DC. ISBN 978-1563473425.
• Chobotov, V.A. (ed.) (2002). Orbital Mechanics, 3rd Edition. American Institute of Aeronautics & Ast, Washington, DC. ISBN 978-1563475375.
• Herrick, S. (1971). Astrodynamics: Orbit Determination, Space Navigation, Celestial Mechanics, Volume 1. Van Nostrand Reinhold, London. ISBN 978-0442033705.
• Herrick, S. (1972). Astrodynamics: Orbit Correction, Perturbation Theory, Integration, Volume 2. Van Nostrand Reinhold, London. ISBN 978-0442033712.
• Kaplan, M.H. (1976). Modern Spacecraft Dynamics and Controls. Wiley, New York. ISBN 978-0471457039.
• Tom Logsdon (1997). Orbital Mechanics. Wiley-Interscience, New York. ISBN 978-0471146360.
• John E. Prussing and Bruce A. Conway (1993). Orbital Mechanics. Oxford University Press, New York. ISBN 978-0195078343.
• M.J. Sidi (2000). Spacecraft Dynamics and Control. Cambridge University Press, New York. ISBN 978-0521787802.
• W.E. Wiesel (1996). Spaceflight Dynamics, 2nd edition. McGraw-Hill, New York. ISBN 978-0070701106.
• J.P. Vinti (1998). Orbital and Celestial Mechanics. American Institute of Aeronautics & Ast, Reston, VA. ISBN 978-1563472565.
• P. Gurfil (2006). Modern Astrodynamics. Butterworth-Heinemann. ISBN 978-0123735621.

The most elementary but very widely used reference is Bate, Mueller and White. It has several useful graphs off which one can read the rates of change of perigee and node due to earth oblateness, but there are typographical errors in a few equations. For example, in Eq. (9.7.5) the term in (3/2) J2 needs (r_e/r) squared and the term in J3 needs it cubed. The coefficient 315 in the J6 term, Eq.(9.7.6.) should be 245 (but the 315 in the J5 term is just fine). Battin's book may be too mathematical for many users.

[show] v • d • e Orbits

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A Unified Physics By 2050 Part II

 

"Jika kita meninggalkan dunia ini, kita akan baik-baik saja karena kita yakin bahwa 

jiwa kita akan bertemu dengan-Nya"

~Arip~

  A Unified Physics by 2050?

Experiments at CERN and elsewhere should let us complete the Standard Model of particle physics, but a unified theory of all forces will probably require radically new ideas.

By: Prof. Steven Weinberg, Ph.D.

Beyond the Top

The heaviest known particle of the Standard Model is the top quark, with a mass equivalent to an energy of 175 gigaelectron volts (GeV). (One GeV is a little more than the energy contained in a proton mass.) [See "The Discovery of the Top Quark," by Tony M. Liss and Paul L. Tipton; Scientific American, September 1997.] The not yet discovered Higgs particles are expected to have similar masses, from 100 to several hundred GeV. But there is evidence of a much larger scale of masses that will appear in equations of the not yet formulated unified theory. The gluon, W, Z and photon fields of the Standard Model have interactions of rather different strengths with the other fields of this model; that is why the forces produced by exchange of gluons are about 100 times stronger than the others under ordinary conditions. Gravitation is vastly weaker: the gravitational force between the electron and proton in the hydrogen atom is about 10^-39 the strength of the electric force.

To complete the Standard Model, we need to confirm the existence of these scalar fields and find out how many types there are. This is a matter of discovering new elementary particles, often called Higgs particles, that can be recognized as the quanta of these fields. We have every reason to expect that this task will be accomplished before 2020, when the accelerator called the Large Hadron Collider at CERN, the European laboratory for particle physics near Geneva, will have been operating for over a decade.

Profoundest advances in fundamental physics

The profoundest advances in fundamental physics tend to occur when the principles of different types of theories are reconciled within a single new framework. We do not yet know what guiding principle underlies the unification of quantum field theory, as embodied in the Standard Model, with general relativity.

The very least new thing that will be discovered is a single electrically neutral scalar particle. It would be a disaster if this were all that were discovered by 2020, though, because it would leave us without a clue to the solution of a formidable puzzle regarding the characteristic energies encountered in physics, known as the hierarchy problem.

The heaviest known particle of the Standard Model is the top quark, with a mass equivalent to an energy of 175 gigaelectron volts (GeV). (One GeV is a little more than the energy contained in a proton mass.) [See "The Discovery of the Top Quark," by Tony M. Liss and Paul L. Tipton; Scientific American,  September 1997.] The not yet discovered Higgs particles are expected to have similar masses, from 100 to several hundred GeV. 

But there is evidence of a much larger scale of masses that will appear in equations of the not yet formulated unified theory. The gluon, W, Z and photon fields of the Standard Model have interactions of rather different strengths with the other fields of this model; that is why the forces produced by exchange of gluons are about 100 times stronger than the others under ordinary conditions. Gravitation is vastly weaker: the gravitational force between the electron and proton in the hydrogen atom is about 10^-39 the strength of the electric force.

But all these interaction strengths depend on the energy at which they are measured [see the "Coupling Strengths" illustration below]. It is striking that when the interactions of the fields of the Standard Model are extrapolated, they all become equal to one another at an energy of a little more than 10¹⁶ GeV, and the force of gravitation has the same strength at an energy not much higher, around 10¹⁸GeV. (Refinements to the theory of gravitation have been suggested that would even bring the strength of gravitation into equality with the other forces at about 10¹⁶ GeV.) We are used to some pretty big mass ratios in particle physics, like the 350,000 to 1 ratio of the top quark to the electron mass, but this is nothing compared with the enormous ratio of the fundamental unification energy scale of 10¹⁶GeV (or perhaps 10¹⁸ GeV) to the energy scale of about 100 GeV that is typical of the Standard Model [see the "Hierarchy Problem" illustration below].

The crux of the hierarchy problem is to understand this huge ratio, this vast jump from one level to the next in the hierarchy of energy scales, and to understand it not just by adjusting the constants in our theories to make the ratio come out right but as a natural consequence of fundamental principles.

Image: Slim Films

THE STANDARD MODEL of particle physics describes each particle of matter and each force with a quantum field. The fundamental particles of matter are fermions and come in three generations (a). Each generation of particles follows the same pattern of properties. The fundamental forces are caused by bosons (b), which are organized according to three closely related symmetries. In addition, one or more Higgs particles or fields (c) generate the masses of the other fields.

Theorists have proposed several interesting ideas for a natural solution to the hierarchy problem, incorporating a new symmetry principle known as supersymmetry (which also improves the accuracy with which the interaction strengths converge at 10¹⁶ GeV), or new strong forces known as technicolor, or both [see the illustration "What Comes Next" below]. All these theories contain additional forces that are unified with the strong, weak and electromagnetic forces at an energy of about 10¹⁶GeV. 

The new forces become strong at some energy far below 10¹⁶GeV, but we cannot observe them directly, because they do not act on the known particles of the Standard Model. Instead they act on other particles that are too massive to be created in our laboratories. These "very heavy" particles are nonetheless much lighter than 10¹⁶ GeV because they acquire their mass from the new forces, which are strong only far below 10¹⁶ GeV.

In this picture, the known particles of the Standard Model would interact with the very heavy particles, and their masses would arise as a secondary effect of this relatively weak interaction. This mechanism would solve the hierarchy problem, making the known particles lighter than the very heavy particles, which are themselves much lighter than 10¹⁶ GeV.

All these ideas share another common feature: they require the existence of a zoo of new particles with masses not much larger than 1,000 GeV. If there is any truth to these ideas, then these particles should be discovered before 2020 at the Large Hadron Collider, and some of them may even show up before then at Fermilab or CERN, although it may take further decades and new accelerators to explore their properties fully. When these particles have been discovered and their properties measured, we will be able to tell whether any of them would have survived the early moments of the big bang and could now furnish the "dark matter" in intergalactic space that is thought to make up most of the present mass of the universe. At any rate, it seems likely that by 2050 we will understand the reason for the enormous ratio of energy scales encountered in nature.

Further Reading:

1. Unified Theories of Elementary-Particle Interaction. Steven Weinberg in Scientific American, Vol. 231, No. 1, pages 50-59; July 1974.

2. Dreams of a Final Theory. Steven Weinberg. Pantheon Books, 1992.

3. Reflections on the Fate of Spacetime. Edward Witten in Physics Today, Vol. 49, No. 4, pages 24-30; April 1996.

4. Duality, Spacetime and Quantum Mechanics. Edward Witten in Physics Today, Vol. 50, No. 5, pages 28-33; May 1997.

5. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. Brian Greene. W. W. Norton,1999.

http://hera.ph1.uni-koeln.de/~heintzma/Weinberg/Weinberg.htm 

The Author
 

STEVEN WEINBERG is head of the Theory Group at the University of Texas at Austin and a member of its physics and astronomy departments. His work in elementary particle physics has been honored with numerous prizes and awards, including the Nobel Prize for Physics in 1979 and the National Medal of Science in 1991. 

The third volume (Supersymmetry) of his treatise The Quantum Theory of Fields is out from Cambridge University Press. The second volume (Modern Applications) was hailed as being "unmatched by any other book on quantum field theory for its depth, generality and definitive character."

SPACE POWER REACTORS Part II

"Manusia harus segera bekerjasama untuk membangun sebuah alat bertenaga nuklir untuk melintasi tapal batas langit"

~Arip Nurahman~

This EOE article is adapted from an information paper published by the World Nuclear Association (WNA). WNA information papers are frequently updated, so for greater detail or more up to date numbers, please see the latest version on WNA website.

http://www.world-nuclear.org

Radioisotope systems

 

 

So far, radioisotope thermoelectric generators (RTGs) have been the main power source for US space work over more than 40 years, since 1961. The high decay heat of plutonium-238 (²³⁸Pu) (0.56 W/g) enables its use as an electricity source in the RTGs of spacecraft, satellites, navigation beacons, etc. Heat from the oxide fuel is converted to electricity through static thermoelectric elements (solid-state thermocouples), with no moving parts. RTGs are safe, reliable and maintenance-free, and can provide heat or electricity for decades under very harsh conditions, particularly where solar power is not feasible.

Thus far, 45 RTGs have powered 25 US space vehicles including Apollo, Pioneer, Viking, Voyager, Galileo, Ulysses and New Horizons space missions as well as many civil and military satellites. The Cassini spacecraft carries three RTGs providing 870 watts of power en route to Saturn. Voyager spacecraft which have sent back pictures of distant planets have already operated for over 20 years and are expected to send back signals powered by their RTGs for another 15-25 years. The Viking and Rover landers on Mars depended on RTG power sources, as will the Mars Rovers to be launched in 2009.

The latest RTG is a 290 watt system known as the GPHS RTG. The thermal power source for this system is the General Purpose Heat Source (GPHS). Each GPHS contains four iridium-clad ²³⁸Pu fuel pellets, stands 5 cm tall, 10 cm square and weighs 1.44 kg. Eighteen GPHS units power one GPHS RTG. The Multi-Mission RTG (MMRTG), a current research focus, will use 8 GPHS units producing 2 kW that can then be used to generate 100 watts of electricity. 

The Stirling Radioisotope Generator (SRG) is based on a 55-watt electric converter powered by one GPHS unit. The hot end of the Stirling converter reaches 650°C and heated helium drives a free piston reciprocating in a linear alternator, heat being rejected at the cold end of the engine. The AC is then converted to 55 watts direct current (DC). This Stirling engine produces about four times as much electric power from the plutonium fuel than an RTG. Thus each SRG will utilize two Stirling converter units with about 500 watts of thermal power supplied by two GPHS units and will deliver 100-120 watts of electric power. The SRG has been extensively tested but has not yet flown. 

Russia has also developed RTGs using polonium-210—two are still in orbit on 1965 Cosmos navigation satellites. But Russian research was primarily focused on fission reactors for space power systems. In addition to RTGs, Radioactive Heater Units (RHUs) are used on satellites and spacecraft to keep instruments warm enough to function efficiently. Their output is only about one watt and they mostly use ²³⁸Pu—typically about 2.7g. Dimensions are about 3 cm long and 2.5 cm diameter, weighing 40 grams. Some 240 have been used so far by the US and two are in shut-down Russian Lunar Rovers on the moon. There will be eight on each of the US Mars Rovers launched in 2003. 

Both RTGs and RHUs are designed to survive major launch and re-entry accidents intact, as is the SRG.

Fission systems: Heat

 

 

Over 100 kWe, fission systems have a distinct cost advantage over RTGs.

The US SNAP-10A launched in 1965 was a 45 kWt thermal nuclear fission reactor that produced 650 watts using a thermoelectric converter and operated for 43 days; it was shut down due to a satellite (not reactor) malfunction but remains in orbit today. 

The last US space reactor initiative was a joint NASA-DOE-Defence Department program developing the SP-100 reactor—a 2 MWt fast reactor unit and thermoelectric system delivering up to 100 kWe as a multi-use power supply for orbiting missions or as a lunar/Martian surface power station. This was terminated in the early 1990s after absorbing nearly US$1 billion. The design used uranium nitride fuel and was lithium-cooled. 

There was also a Timberwind pebble bed reactor (PBR) concept under the Defence Department Multi-Megawatt (MMW) space power program during the late 1980s, in collaboration with Department of Energy (DOE). This had power requirements well beyond any civil space program. 

Between 1967 and 1988, the former Soviet Union launched 31 low-powered fission reactors in Radar Ocean Reconnaissance Satellites (RORSATs) on Cosmos missions. They utilized thermoelectric converters to produce electricity, as with the RTGs. Romashka reactors were their initial nuclear power source, a fast spectrum graphite reactor with 90%-enriched uranium carbide fuel operating at high temperature. The Bouk fast reactor then produced 3 kW for up to 4 months. Later reactors, such as on Cosmos-954 that re-entered over Canada in 1978, had uranium-molybdenum fuel rods and a layout similar to the US heatpipe reactors described below. 

These designs were followed by the Topaz reactors with thermionic conversion systems, generating about 5 kWe of electricity for on-board uses. This was a US idea developed during the 1960s in Russia. In Topaz-2, each fuel pin (96% enriched uranium dioxide (UO₂)), sheathed in an emitter, is surrounded by a collector that form the 37 fuel elements which penetrate the cylindrical ZrH moderator. This in turn is surrounded by a beryllium neutron reflector containing 12 rotating control drums. NaK (a sodium-potassium alloy) coolant surrounds each fuel element. 

Topaz-1 was flown in 1987 on Cosmos 1818 and 1867. It was capable of delivering power for 3-5 years for ocean surveillance. Later Topaz designs were aiming for 40 kWe via an international project, undertaken largely in the USA starting in 1990. Two Topaz-2 reactors (without fuel) were sold to the USA in 1992. Budget restrictions in 1993 forced cancellation of a Nuclear Electric Propulsion Spaceflight Test Program associated with this reactor design.

Fission systems: propulsion

 

 

For spacecraft propulsion, once launched, some experience has been gained with nuclear thermal propulsion systems (NTR), that are said to be well-developed and proven. Nuclear fission heats a hydrogen propellant that is stored as liquid in cooled tanks. The hot gas (about 2500°C) is expelled through a nozzle to give thrust that may be augmented by injection of liquid oxygen into the supersonic hydrogen exhaust; this is more efficient than chemical reactions. Bimodal versions will run electrical systems on board a spacecraft, including powerful radars, as well as provide propulsion. Compared with nuclear electric plasma systems, these have much more thrust for shorter periods and can be used for launches and landings. 

However, attention is now turning to nuclear electric systems, where nuclear reactors are a heat source for electric ion drives, expelling plasma out of a nozzle to propel spacecraft already in space. Superconducting magnetic cells ionize hydrogen or xenon, heat it to extremely high temperatures (millions °C), accelerate it and expel it at very high velocity (e.g., 30 km/sec) to provide thrust. Research on one version, the Variable Specific Impulse Magnetoplasma Rocket (VASIMR), draws on that for magnetically-confined fusion power (tokamak) for electricity generation, but here the plasma is deliberately leaked to give thrust. The system works most efficiently at low thrust (that can be sustained), with small plasma flow, but high thrust operation is possible. The design is very efficient, with 99% conversion of electric to kinetic energy.

Sources:

1. Poston, D.I. 2002, Nuclear design of SAFE-400 space fission reactor, Nuclear News, Dec 2001.
2. Poston, D.I. 2002, Nuclear design of HOMER-15 Mars surface fission reactor, Nuclear News, Dec 2001.
3. Vrillon et al, 1990, ERATO article, Nuclear Europe Worldscan 11-12, 1990.
4. US DOE web site- space applications.
5. space.com 21/5/00, 16/6/00, 22/7/00, 17/1/03, 7/2/03.
6. www.nuclearspace.com
7. Delovy Mir 8/12/95.
8. G. Kulcinski, University of Wisconsin material on web.
9. Kleiner K. 2003, Fission Control, New Scientist 12/4/03.

10. OECD 1990, Emergency Preparedness for Nuclear-Powered Satellites.
11. NASA web site