Wednesday, 27 July 2011


"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.

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.


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. 21/5/00, 16/6/00, 22/7/00, 17/1/03, 7/2/03.
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

Saturday, 23 July 2011

Integrating General Relativity and Quantum Mechanics

General relativity typically deals with situations involving large mass objects in fairly large regions of spacetime whereas quantum mechanics is generally reserved for scenarios at the atomic scale (small spacetime regions). 

The two are very rarely used together, and the most common case in which they are combined is in the study of black holes. Having "peak density", or the maximum amount of matter possible in a space, and very small area, the two must be used in synchrony in order to predict conditions in such places; yet, when used together, the equations fall apart, spitting out impossible answers, such as imaginary distances and less than one dimension.

The major problem with their congruence is that, at sub-Planck (an extremely small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, neither of which are anywhere near compatible. 

Superstring theory resolves this issue, replacing the classical idea of point particles with loops. These loops have an average diameter of the Planck length, with extremely small variances, which completely ignores the quantum mechanical predictions of sub-Planck length dimensional warping, there being no matter that is of sub-Planck length.

The Five Superstring Interactions




The five superstring interactions


There are five ways open and closed strings can interact. An interaction in superstring theory is a topology changing event. Since superstring theory has to be a local theory to obey causality the topology change must only occur at a single point. If C represents a closed string and O an open string, then the five interactions are, symbollically:


All open superstring theories also contain closed superstrings since closed superstrings can be seen from the fifth interaction, they are unavoidable. Although all these interactions are possible, in practice the most used superstring model is the closed heterotic E8xE8 superstring which only has closed strings and so only the second interaction (CCC) is needed.



Wednesday, 20 July 2011

Why should we return to the Moon?

"That's one small step for a man, one giant leap for mankind"
~Neil Alden Armstrong~


  1. Human Civilization: Extend human presence to the Moon to enable eventual settlement.
  2. Scientific Knowledge: Pursue scientific activities that address fundamental questions about the history of Earth, the solar system and the universe; and therefore, about our place in them.
  3. Exploration Preparation: Test technologies, systems, flight operations and exploration techniques to reduce the risks and increase the productivity of future missions to Mars and beyond.
  4. Global Partnerships: Provide a challenging, shared and peaceful activity that unites nations in pursuit of common objectives.
  5. Economic Expansion: Expand Earth's economic sphere, and conduct lunar activities with benefits to life on the home planet.
  6. Public Engagement: Use a lively space exploration program to engage the public, encourage students and help develop the high-technology workforce that will be required to address the challenges of tomorrow.

Google Lunar X PRIZE
Google Lunar X Prize logo
Awarded for "land a robot on the surface of the Moon, travel 500 meters over the lunar surface, and send images and data back to the Earth" [1]
Presented by X Prize Foundation (organizer),
Google Inc. (sponsor)
Country Worldwide
Reward US$20 million for the winner,
US$5 million for second place,
US$4 million in technical bonuses,
US$1 million diversity award
Official website

"We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too."
President John F. Kennedy, September 12, 1962, at Rice University, 
Houston, Texas

 Ternyata bulan memiliki sisi magis yang selalu ingin mengundang manusia untuk menjelajahi dan mengeksplorasi. Bulan akan menjadi pijakan dan langkah pertama bagi penjelajahan dan koloni manusia ke luar angkasa. Bukankah seperti kata pepatah, perjalanan jauh selalu dimulai dengan satu langkah ? 

    Monday, 18 July 2011

    A Unified Physics By 2050 Part I

     "Karena aku sedang bahagia, seluruh energi positif kosmis telah memberiku kepercayaan dan kekuatan ajaib." ~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.

    One of the primary goals of physics is to understand the wonderful variety of nature in a unified way. The greatest advances of the past have been steps toward this goal: the unification of terrestrial and celestial mechanics by Newton in the 17th century; of optics with the theories of electricity and magnetism by Maxwell in the 19th century; of space-time geometry and the theory of gravitation by Einstein in the years 1905 to 1916; and of chemistry and atomic physics through the advent of quantum mechanics in the 1920s [see the illustrations titled Unification and Profoundest Advances].

    Einstein devoted the last 30 years of his life to an unsuccessful search for a "unified field theory," which would unite general relativity, his own theory of space-time and gravitation, with Maxwell's theory of electromagnetism. Progress toward unification has been made more recently, but in a different direction. Our current theory of elementary particles and forces, known as the of particle physics, has achieved a unification of electromagnetism with the weak interactions, the forces responsible for the change of neutrons and protons into each other in radioactive processes and in the stars. The Standard Model also gives a separate but similar description of the strong interactions, the forces that hold quarks together inside protons and neutrons and hold protons and neutrons together inside atomic nuclei. 

    We have ideas about how the theory of strong interactions can be unified with the theory of weak and electromagnetic interactions (often called Grand Unification), but this may only work if gravity is included, which presents grave difficulties. We suspect that the apparent differences among these forces have been brought about by events in the very early history of the big bang, but we cannot follow the details of cosmic history at those early times without a better theory of gravitation and the other forces. There is a chance the work of unification will be completed by 2050, but about that we cannot be confident.  

    Image: Alfred T. Kamajian

    THE QUANTUM NATURE of space and time must be dealt with in a unified theory. At the shortest distance scales, space may be replaced by a continually reconnecting structure of strings and membranes--or by something stranger still.  

    Quantum Fields
    The Standard Model is a quantum field theory. Its basic ingredients are fields, including the electric and magnetic fields of 19th-century electrodynamics. Little ripples in these fields carry energy and momentum from place to place, and quantum mechanics tells us that these ripples come in bundles, or quanta, that are recognized in the laboratory as elementary particles. For instance, the quantum of the electromagnetic field is a particle known as the photon.

    The Standard Model includes a field for each type of elementary particle that has been observed in high-energy physics laboratories [see the 'Standard Model' illustration below]. There are the lepton fields: their quanta include the familiar electrons, which make up the outer parts of ordinary atoms, similar heavier particles known as muons and tauons, and related electrically neutral particles known as neutrinos. There are fields for quarks> of various types, some of which are bound together in the protons and neutrons that make up the nuclei of ordinary atoms. Forces between these particles are produced by the exchange of photons and similar elementary particles: the W+, W- and Z0 transmit the weak force, and eight species of gluon produce the strong forces.

    These particles exhibit a wide variety of masses that follow no recognizable pattern, with the electron 350,000 times lighter than the heaviest quark, and neutrinos even lighter. The Standard Model has no mechanism that would account for any of these masses, unless we supplement it by adding additional fields, of a type known as scalar fields. The word "scalar" means that these fields do not carry a sense of direction, unlike the electric and magnetic fields and the other fields of the Standard Model. This opens up the possibility that these scalar fields can pervade all space without contradicting one of the best established principles of physics, that space looks the same in all directions. (In contrast, if, for example, there were a significant magnetic field everywhere in space, then we could identify a preferred direction by using an ordinary compass.) The interaction of the other fields of the Standard Model with the all-pervasive scalar fields is believed to give the particles of the Standard Model their masses.

    UNIFICATION of the forces of nature

    The unification of disparate phenomena within one theory has long been a central theme of physics. The Standard Model of particle physics successfully describes three (electromagnetism, weak and strong interactions) of the four known forces of nature but remains to be united definitively with general relativity, which governs the force of gravity and the nature of space and time.


    Further Reading:

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

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

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

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

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

    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."

    Sunday, 17 July 2011

    Yuks Kita Optimalkan E-Journal Badan Tenaga Nuklir Nasional

    "Diskusi rutin online mengenai pembahasan isi jurnal-jurnal Iptek Nuklir dapat dilakukan dengan menggunakan berbagai media Internet seperti jejaring sosial Facebook dengan berbagai macam grupnya dan Twitter dengan KulTwit-nya [Kuliah Twitter] atau menggunakan media YouTube untuk mengunggah video-video Iptek Nuklir Edukatif dan lain sebagainya."
    *Arip Nurahman*

    Logo Header Halaman


    Jurnal Radioisotop dan Radiofarmaka

    Jurnal Radioisotop dan Radiofarmaka (Journal of Radioisotopes and Radiopharmaceuticals) bertujuan untuk memajukan ilmu pengetahuan dan teknologi di bidang radioisotop, radiofarmaka dan bidang terkait, yang diwujudkan dalam bentuk makalah ilmiah hasil penelitian atau tinjauan dan gagasan.
    Lihat Jurnal | Terbitan Terkini | Daftar

    Logo Header Halaman




    Jurnal Widyanuklida sebagai sarana media informasi ilmiah, diterbitkan oleh Pusat Pendidikan dan Latihan, Badan Tenaga Nuklir Nasional (BATAN).

    Lihat Jurnal | Terbitan Terkini | Daftar

    Bila kita mampu membangun himpunan-himpunan peneliti kecil di tiap sekolah tinggi/kampus di Indonesia mengenai Iptek Nuklir ini, kemungkinan besar percepatan perkembangan ilmu pengetahuan Nuklir di tanah air akan semakin dahsyat dan masyarakat kita di kemudian hari dapat memetik manfaatnya.


    Sumber: Badan Tenaga Nuklir Nasional

    Kunjungi juga:  (BATAN) (International Atomic Energy Agency)  (Sekolah Sains dan Teknologi Nuklir) (Masyarakat Nuklir Indonesia) (Sekolah Tinggi Teknologi Nuklir BATAN) (Nuclear Engineering OpenCourseWare from MIT) (Jurusan Pendidikan Fisika, FPMIPA Universitas Pendidikan Indonesia)

    Ucapan Terima Kasih Kepada:

    Kak Rezy Pradipta, Ph.D. (Alumni Tim Olimpiade Fisika Indonesia, Belajar di Department of Nuclear Engineering at MIT)

    Dr. Mohamed Mustafa ElBaradei, J.S.D. (Former Director General of IAEA)

    Prof. Mujid S. Kazimi, Ph.D. (Director, Center for Advanced Nuclear Energy Systems MIT)

    Prof.Djarot Sulistio Wisnubroto, M.Sc., D.Sc. (Presiden BATAN)

    Kak Iqbal Robiyana, S.Pd. (Founder Center for Nuclear Education at Indonesia University of Education)

    Dr. Petros Aslanyan, M.Sc. (Joint Institute for Nuclear Research, Rusia & Yerevan State University)

    Semangat Semoga Bermanfaat

    Friday, 15 July 2011

    Nominasi Peraih Nobel

    Nomination forms are sent by the Nobel Committee to about 3,000 individuals, usually in September the year before the prizes are awarded. These individuals are often academics working in a relevant area. For the Peace Prize, inquiries are sent to governments, members of international courts, professors and rectors, former Peace Prize laureates and current or former members of the Norwegian Nobel Committee. 

    The deadline for the return of the nomination forms is 31 January of the year of the award. The Nobel Committee nominates about 300 potential laureates from these forms and additional names. The nominees are not publicly named, nor are they told that they are being considered for the prize. All nomination records for a prize are sealed for 50 years from the awarding of the prize.


    Nobel Prize


    Sunday, 10 July 2011

    Astrobiology and Space Exploration

    "Pencarian akan persahabatan di dunia luar sana, akan membutuhkan kesabaran yang panjang bagi umat manusia"

    2. The Search for other Earths and Life in the Universe

    Stanford University Course

    In the Stanford Astrobiology Course, our lectures follow a more or less linear path from the Big Bang all the way to the development of complex life and, finally, space exploration. It is truly amazing how evolutionary principles have operated at the macro, and micro, level ever since the birth of the universe we reside in today.

    Physics, research, experimentation, astronomy, extraterrestrial life, planets, asteroids, cosmology, measurements, data, innovation, development, history, science, telescopes, observations, theories, predictions, telescopes, instruments, light, expansion.

    Every year Professor Marcy brings new discoveries to his lecture and this year it was 1200 new exoplanets! Read about the Kepler Team’s announcement in the Wall Street Journal or watch their video.
    Save the playlist of Professor Marcy’s latest lecture.
    The first of 6 parts begins here:

    Also listen on Stanford iTunes to Greg Laughlin’s talk on Extrasolar Planets from 2008. With Arbesman Laughlin has tried to predict how soon an Earth-like exoplanet will be found by extrapolating the rate of discovery so far in the search for habitable exoplanets. See the New Scientist, September 21

    A syllabus for the Winter, 2010 Astrobiology Course can be downloaded here.

    Below you will find a list of recommended resources. If you would like to learn more about the Big Bang, check out these books, videos, and articles.

    "There are so many benefits to be derived from space exploration and exploitation; why not take what seems to me the only chance of escaping what is otherwise the sure destruction of all that humanity has struggled to achieve for 50,000 years?"
    ~Isaac Asimov, speech at Rutgers University~

    1. Stanford University
    2. NASA

    Ucapan Terima Kasih:

    1. Bapak. Prof. Dr. Ing. H. B. J. Habibie.

    2. Departemen Pendidikan Nasional

    3. Kementrian Riset dan Teknologi

    4. Lembaga Penerbangan dan Antariksa Nasional

    Disusun Ulang Oleh:

    Arip Nurahman

    Department of Physics, Indonesia University of Education


    Follower Open Course Ware at MIT-Harvard University, Cambridge.USA.

    Semoga Bermanfaat dan Terima Kasih

    Wednesday, 6 July 2011

    Relativitas Umum dan Ke Geniusan Einstein

    Teori Einstein memiliki implikasi astrofisika yang penting. Teori ini memprediksikan adanya keberadaan daerah lubang hitam yang mana ruang dan waktu terdistorsi sedemikiannya tiada satu pun, bahkan cahaya pun, yang dapat lolos darinya. 

    Terdapat bukti bahwa lubang hitam bintang dan jenis-jenis lubang hitam lainnya yang lebih besar bertanggungjawab terhadap radiasi kuat yang dipancarkan oleh objek-objek astronomi tertentu, seperti inti galaksi aktif dan miktrokuasar. 

    Melengkungnya cahaya oleh gravitasi dapat menyebabkan fenomena pelensaan gravitasi. Relativitas umum juga memprediksikan keberadaan gelombang gravitasi. Keberadaan gelombang ini telah diukur secara tidak langsung, dan terdapat pula beberapa usaha yang dilakukan untuk mengukurnya secara langsung. 

    Selain itu, relativitas umum adalah dasar dari model kosmologis untuk alam semesta yang terus berkembang. 


    Kunjungi Juga:

    Apa Itu Relativitas Umum Einstein? 


    The University of Cambridge


    To Be Continued

    Monday, 4 July 2011

    Mekanika Orbit: Teknik-Teknik Matematika

    "Teknik-Teknik Mekanika dalam IPTEK Antariksa Sangat Perlu Dikembangkan" 
    *Arip Nurahman*

    Persamaan Kepler

    One approach to calculating orbits (mainly used historically) is to use Kepler's equation:
    M=E-\varepsilon\cdot\sin E.
    where M is the mean anomaly, E is the eccentric anomaly, and \varepsilon is eccentricty.
    With Kepler's formula, finding the time-of-flight to reach an angle (true anomaly) of θ from periapsis is broken into two steps:
    1. Compute the eccentric anomaly E from true anomaly θ
    2. Compute the time-of-flight t from the eccentric anomaly E
    Finding the angle at a given time is harder. Kepler's equation is transcendental in E, meaning it cannot be solved for E analytically, and so numerical approaches must be used. In effect, one must guess a value of E and solve for time-of-flight; then adjust E as necessary to bring the computed time-of-flight closer to the desired value until the required precision is achieved. Usually, Newton's method is used to achieve relatively fast convergence.
    The main difficulty with this approach is that it can take prohibitively long to converge for the extreme elliptical orbits. For near-parabolic orbits, eccentricity e is nearly 1, and plugging e = 1 into the formula for mean anomaly, E − sinE, we find ourselves subtracting two nearly-equal values, and so accuracy suffers. For near-circular orbits, it is hard to find the periapsis in the first place (and truly circular orbits have no periapsis at all). Furthermore, the equation was derived on the assumption of an elliptical orbit, and so it does not hold for parabolic or hyperbolic orbits at all. These difficulties are what led to the development of the universal variable formulation, described below.

    Perturbation theory

    Main article: Perturbation theory
    One can deal with perturbations just by summing the forces and integrating, but that is not always best. Historically, variation of parameters has been used which is easier to mathematically apply with when perturbations are small.

    Conic orbits

    For simple procedures, such as computing the delta-v for coplanar transfer ellipses, traditional approaches[clarification needed] are fairly effective. Others, such as time-of-flight are far more complicated, especially for near-circular and hyperbolic orbits.

    The patched conic approximation

    The transfer orbit alone is a poor approximation for interplanetary trajectories because it neglects the planets' own gravity. Planetary gravity dominates the behaviour of the spacecraft in the vicinity of a planet. It severely underestimates delta-v, and produces highly inaccurate prescriptions for burn timings.
    A relatively simple way to get a first-order approximation of delta-v is based on the patched conic approximation technique. One must choose the one dominant gravitating body in each region of space through which the trajectory will pass, and to model only that body's effects in that region. For instance, on a trajectory from the Earth to Mars, one would begin by considering only the Earth's gravity until the trajectory reaches a distance where the Earth's gravity no longer dominates that of the Sun.

    The spacecraft would be given escape velocity to send it on its way to interplanetary space. Next, one would consider only the Sun's gravity until the trajectory reaches the neighbourhood of Mars. During this stage, the transfer orbit model is appropriate. Finally, only Mars's gravity is considered during the final portion of the trajectory where Mars's gravity dominates the spacecraft's behaviour.

    The spacecraft would approach Mars on a hyperbolic orbit, and a final retrograde burn would slow the spacecraft enough to be captured by Mars.
    The size of the "neighborhoods" (or spheres of influence) vary with radius rSOI:
    r_{SOI} = a_p\left(\frac{m_p}{m_s}\right)^{2/5}
    where ap is the semimajor axis of the planet's orbit relative to the Sun; mp and ms are the masses of the planet and Sun, respectively.
    This simplification is sufficient to compute rough estimates of fuel requirements, and rough time-of-flight estimates, but it is not generally accurate enough to guide a spacecraft to its destination. For that, numerical methods are required.

    The universal variable formulation

    To address the shortcomings of the traditional approaches, the universal variable formulation was developed. It works equally well on circular, elliptical, parabolic, and hyperbolic orbits; and also works well with perturbation theory. The differential equations converge nicely when integrated for any orbit.


    The universal variable formulation works well with the variation of parameters technique, except now, instead of the six Keplerian orbital elements, we use a different set of orbital elements: namely, the satellite's initial position and velocity vectors x0 and v0 at a given epoch t = 0.

    In a two-body simulation, these elements are sufficient to compute the satellite's position and velocity at any time in the future, using the universal variable formulation.

    Conversely, at any moment in the satellite's orbit, we can measure its position and velocity, and then use the universal variable approach to determine what its initial position and velocity would have been at the epoch. In perfect two-body motion, these orbital elements would be invariant (just like the Keplerian elements would be).
    However, perturbations cause the orbital elements to change over time. Hence, we write the position element as x0(t) and the velocity element as v0(t), indicating that they vary with time. The technique to compute the effect of perturbations becomes one of finding expressions, either exact or approximate, for the functions x0(t) and v0(t).

    Non-ideal orbits

    The following are some effects which make real orbits differ from the simple models based on a spherical earth. Most of them can be handled on short timescales (perhaps less than a few thousand orbits) by perturbation theory because they are small relative to the corresponding two-body effects.
    • Equatorial bulges cause precession of the node and the perigee
    • Tesseral harmonics of the gravity field introduce additional perturbations
    • lunar and solar gravity perturbations alter the orbits
    • Atmospheric drag reduces the semi-major axis unless make-up thrust is used
    Over very long timescales (perhaps millions of orbits), even small perturbations can dominate, and the behaviour can become chaotic.

    On the other hand, the various perturbations can be orchestrated by clever astrodynamicists to assist with orbit maintenance tasks, such as station-keeping, ground track maintenance or adjustment, or phasing of perigee to cover selected targets at low altitude.



    Friday, 1 July 2011

    High Energy Neutrinos From The Cosmos

    "Now my own suspicion is that the Universe is not only queerer that we suppose, but queerer than we can suppose."
    — J. B. S. Haldane, Possible Worlds, 1927.~

    High Energy Neutrinos from the Cosmos
    by:  Per Olof Hulth

    Edited and Added By:
    Arip Nurahman

    Department of Physics
    Faculty of Science and Mathematics, Indonesian University of Education

    Follower Open Course at MIT-Harvard University, M.A. USA.

    "Energy apa kiranya yang lebih dahsyat dari Cinta dan kasih sayang?"


    Mankind has studied the universe for thousands of years by looking at the fascinating night sky, guided by the visible light emitted from myriads of stars and other phenomena. During the last century new pictures of the night sky have been discovered by scientists using different wavelengths of light which the naked eye cannot see, such as radio waves, infrared light, x-rays and gamma rays.

    Each time new windows in the sky are opened, new unexpected phenomena have been discovered, like the microwave background from Big Bang, neutron stars, active galactic nuclei (AGN), black holes, gamma ray bursts (GRB) and other exciting objects.

    Today, scientists are starting to open up a completely new window by using another elementary particle, the neutrino, instead of the photon, which is the elementary particle of light used to investigate the universe. This new field called neutrino astronomy, will hopefully reveal new unknown phenomena and help us answer several of the questions we have today.


    The neutrino is an elementary particle, which was postulated in 1930 by Wolfgang Pauli, 1945 Nobel Laureate in Physics, in order to solve an energy crisis in nuclear physics. Scientists had difficulty finding energy in radioactive decays and Pauli suggested the existence of a particle which he believed was carrying away the missing energy. But it took some years before the neutrino was discovered. It was Clyde Cowan and Frederick Reines who first detected and identified this particle in 1965. For his contribution, Reines was awarded the 1995 Nobel Prize in Physics.

    The neutrino is an obscure particle with no electric charge and which only interacts with matter via the weak nuclear force. In recent years it has been discovered that neutrinos have a small mass, debunking the earlier assumption that it was massless. In the sun, an enormous number of neutrinos are produced in the fusion process when four hydrogen atoms transform into one helium atom. Despite the large number of neutrinos, an average of only about one of these will interact with a person's body during a lifetime.

    The flux of neutrinos from the sun at the surface of the earth is 6x1010 neutrinos per square centimeter and second. The neutrinos from the fusion process in the sun can pass through several light years of solid lead before being absorbed by matter. The probability for a neutrino to interact with matter increases, however, with the energy of the neutrino.

    Three different kinds of neutrinos have been observed: the electron neutrino , the muon neutrino and the tau neutrino . These neutrinos are related with three electrically charged particles, the electron, the muon and the tau. All six particles are called leptons. When a neutrino interacts with matter, it can either continue as a neutrino after the interaction ("neutral current interaction") or create the corresponding charged particle ("charge current interaction"). The electron neutrino creates an electron, the muon neutrino a muon, and the tau neutrino a tau lepton.

    A muon neutrino interacting with an atom producing a muon and a shower of short-lived particles.

    During a high energy neutrino interaction the charged lepton will continue in almost the same direction as the incoming neutrino. In matter, an electron that is produced during interaction will be stopped by a few meters whilst a muon, with its larger mass, might continue for several kilometers depending on its energy. Determining the direction of the created muon will give the direction of the muon neutrino within a few degrees. This is the key to understanding high energy neutrino astronomy.

    Low and High Energy Neutrinos

    Neutrinos can be divided into two categories, low energy and high energy. This is, of course, a quite arbitrary division but it reflects the production processes and the way in which detectors are built.

    The low energy neutrinos are mainly produced in nuclear processes, like the fusion reactions in the sun or in the center of an exploding Supernova. The high energy neutrinos are mainly produced in high energy particle collisions producing short lived mesons, decaying to neutrinos and other particles.

    In a particle physics scale the low energy neutrinos have energies in the 10th of MeV (Mega electron Volts), whilst the high energy neutrinos have energies above 10th of GeV (Giga electron Volts).

    Sources of Neutrinos

    Solar Neutrinos

    So far, only two sources of extraterrestrial neutrinos have been observed. Both are low energy neutrino sources. The first source is the sun from which Raymond Davis Jr., 2002 Nobel Laureate in Physics, managed to catch an average of half an electron neutrino interaction per day in his detector during 20 years.

    Supernova Neutrinos

    The second source of extraterrestrial neutrinos was observed during 10 seconds in 1987 when a star in the Large Magellanic Cloud exploded as a supernova, which was later named SN1987. The neutrinos from the inner part of the collapse reached the earth after a journey of 170,000 years, a few hours before the arrival of light. The neutrinos were able to travel more or less directly from the central collapse in the inner part of the star, but the effect of the explosion was not visible at the star surface until later. About 25 neutrino interactions were observed by the detectors at Kamiokande (Japan), Baksan (Sovjet union) and IMB (USA) during 10 seconds. This observation of neutrinos from the sun and the supernova represented a new kind of astronomy since the neutrinos give us information from processes deep inside objects hidden from visible light or photons in general.

    The crab nebula is the remnant from a supernova explosion 1054. In the enormous explosion 99% of the energy was released in invisible neutrinos.
    Copyright © NASA/CXC/SAO

    Neutrinos from the Unknown Sources of Cosmic Rays

    A strong argument for the existence of high energy neutrinos from the cosmos is the observation of high energy cosmic rays.

    Nuclear particles, which have propagated through deep space for many millions of years, are continuously bombarding the atmosphere of the earth. When colliding with the earth's atmosphere the particles create showers with many short-lived particles. At the surface of the earth we observe the remnants of the showers in the form of about 100 muons per square meters and second. Very large surface detectors are today measuring the intensity and the energies of the cosmic rays.

    Despite the discovery of the cosmic rays as early as 1912 by Victor Hess, 1936 Nobel Laureate in Physics, we still do not know where they come from. We expect that most of the particles are created in supernova explosions in our local galaxy but the cosmic ray particles that have the highest observed energies are assumed to come from unknown sources outside our galaxy. The highest observed cosmic rays have energies of 50 joules. The acceleration process giving the particles these extreme high energies is not known. Neither are the sources of these particles.

    The energy of the highest cosmic ray particles is ten million times higher than what the world's most powerful particle accelerator LHC (Large Hadron Collider) will be able to reach when it starts in 2007 at CERN, Geneva. If one would "build" an accelerator for protons with the same energy as the highest cosmic rays based on the LHC superconducting magnets, the size of the accelerator should be larger than the earth's trajectory around the sun (LHC has a circumference of 27 kilometers). Since the cosmic rays are electrically charged they will be deflected by the magnetic field in space. That means that the direction of the cosmic rays is not pointing back to the source. To detect the source one needs an electrically neutral particle like the neutrino that is not influenced by the magnetic field. The cosmic rays with more than 10% of the maximum observed energies will interact with the microwave background from the Big Bang and will not be able to travel long distances in the universe.

    The sources have to be "close," not further away than 50 million light years, which is a very "short" distance in the cosmos. The existence of these extreme high energy cosmic rays is a real mystery. When the protons collide with the microwave background photons, mesons are created which in their decays will produce high energy neutrinos. These are called GZK-neutrinos (after Greisen, Zatseptin and Kuzmin) and are a guaranteed source of extraterrestrial high energy neutrinos.

    The photons have an even larger probability than protons to be absorbed by the microwave background photons, which implies that the universe is not transparent for very high energy photons.

    The Centaurus A shown in x-ray by the Chandra satellite. What is special with this object is the black hole in the center and the jet pointing towards the upper left corner in the picture. A possible source of high energy neutrinos?

    There are several possible candidates for the sources of the highest energy cosmic rays. The active galaxy nuclei (AGN) is a galaxy that has a super heavy black hole in the center. The black hole can have a mass of up to a thousand million solar masses. From the center of these galaxies a jet structure is observed ranging tens of thousands of light years out, emitting large amounts of energy. The jet is produced when matter in the galaxy falls into the black hole. High energy photons have been observed from these objects and protons might be accelerated, too. Another possible source are the gamma ray bursts (GRB) which are strange events emitting a short pulse of gamma rays during a fraction of a second and up to 100 seconds.

    They are the most energetic events observed in the universe. About two of these events happen every day. They are very far away, with distances of up to 1010 light years. Possible explanations of these events are that of super heavy stars collapsing to black holes or two neutron stars falling into each other.

    The unknown sources of the high-energy cosmic rays will produce neutrinos when the accelerated high-energy protons collide with the photon gas around the sources, in the same way as with the microwave background. The collisions will produce mesons, which decay to muons and neutrinos and the muons will decay to electrons (positrons) and two neutrinos. These neutrinos will travel, unaffected by the magnetic field in space and if detected on earth, they will point back to the sources of the cosmic rays.

    The flux of cosmic neutrinos can be estimated from the observation of the rate of high energy cosmic rays and one will find that one needs detectors the size of cubic kilometers in order to catch the neutrinos!

    Neutrinos from "Dark Matter"

    High energy neutrinos, though not as high as those mentioned in the previous section, might be produced in connection with another strange observation. One of the main mysteries in physics and astronomy today is the "dark matter" in the universe. Galaxies and groups of galaxies rotate as if they contain more matter than what we can observe with our standard astronomical instruments.

    With only the observed visible matter, the galaxies should eject stars and matter out in the empty space due to the fast rotation. But this is not happening, which indicates that there is more matter in the objects than what we can observe. It is only the gravitational force, which feels the unknown hidden matter.

    This matter is called the "dark matter." About 30% of the energy in the universe is in matter and the rest is in the form of an unknown "dark energy," which we will not be discussed in this article. Recent measurements by the WMAP satellite has shown that only 4% of the energy of the universe is made of ordinary matter in the form of atoms building up the stars and planets. The rest, 25% of the total energy, is a new yet unknown kind of matter.

    The galaxy cluster NGC 2300 with three galaxies and a gas cloud. In order to keep the system gravitationally stable about 20 times more mass than the observed one is needed.
    Copyright © NASA/CXC/SAO

    One popular explanation of the dark matter is that the large part of this different kind of matter consists of weakly interacting massive particles (WIMPs) that were created in the Big Bang at the same time as our ordinary matter. Today, these particles flow around us and build up the dominating part of the matter in our galaxies. When they pass through the sun and the earth they might become gravitationally trapped in the center of these objects.

    The dark matter particles in the centers of the earth and the sun will destroy or annihilate each other when two of them meet and produce ordinary matter with, among other particles, high energy neutrinos. The typical energy of these neutrinos is much higher than that of the electron neutrinos produced by the fusion process in the sun. By observing high energy neutrinos from the center of the earth and/or the sun one could get information about the dark matter. At the same time, this should be a very important discovery for particle physics.

    Atmospheric Neutrinos

    When the cosmic rays hit the atmosphere, short-lived particles are produced which decay to, among others, muons and muon neutrinos. The muons spray the surface of the earth and are absorbed a few tens of kilometers into the earth. The neutrinos, however, can easily pass through the entire earth and they correspond to a neutrino background for cosmic neutrinos. At the same time, they can be used for testing the neutrino telescopes. Since the cosmic neutrinos are expected to have, on average, higher energies than the atmospheric neutrinos, this background can be handled.

    Detection of High Energy Neutrinos

    How Are Neutrinos Detected?

    To detect high energy neutrinos from the cosmos, one is forced to compensate the extremely small chance that the neutrinos will interact with matter. The only way to do that is to use a very large amount of matter in the detection. The more matter used (in the detector) the more neutrinos will interact. Since the cost of a detector has to be limited, one chooses matter existing in nature, like water and ice, as detector material. One equips the detector volumes with light sensors placed in large geometrical patterns and uses the fact that charged particles moving faster than the speed of light in the matter emits Cherenkov light (named after the work of Pavel A. Cherenkov, Il' ja M. Frank and Igor Y. Tamm, 1958 Nobel Laureates in Physics) in a cone around the moving particles. Since the neutrinos are electrically neutral they will not emit Cherenkov light, but the charged particles produced by the interaction will emit light. The material chosen for the detector medium has to be very transparent for light.

    The light sensors in the detector volume will observe the arrival time and the intensity of the emitted Cherenkov light from the muon. Using this information, it is possible to determine the direction of the neutrino within a few degrees. A problem with this kind of telescopes is that the flux of muons from the cosmic ray interactions in the sky above the telescopes is by far larger than the expected amount of muons from neutrino interactions. In order to reduce this background, the telescopes are placed deep in water or ice sheet, with the detector elements looking down through the earth. The earth is used as a filter absorbing the atmospheric muons. Only muons coming up through the earth are accepted as muons from neutrino interactions below the telescopes.

    The demands of large volumes of very transparent medium and low rate of atmospheric muon flux leads to the fact that the neutrino telescopes can be built only in very special places; deep in lakes or oceans, as deep as 4,000 meters or deep in the gigantic ice sheet in Antarctica.

    High Energy Neutrino Telescopes

    There are two high energy neutrino telescopes taking data today - the Baikal detector in Lake Baikal and Antarctic Muon and Neutrino Detector Array (AMANDA), the largest neutrino telescope located at the South Pole.

    A muon from a neutrino interaction in the AMANDA neutrino telescope at the South Pole.
    Copyright © Antarctic Moun and Neutrino Detector Array (AMANDA)

    AMANDA consists of 677 light detectors deployed in 19 holes deep in the ice sheet at the Amundsen-Scott base at the South Pole. The reasons for choosing this very strange place are the three kilometers thick ice sheet with the most optical transparent ice on earth and the USA base Amundsen-Scott, which is manned around the year. The light detectors have been deployed by melting holes in the ice, 60 centimeters in diameter and more than 2,000 meters deep. When the water filled hole was ready the drill was removed and the light detectors deployed before the water refreezed (which took about a week). The effective size of the telescope is 400 meters in height and 200 meters in diameter. The AMANDA telescope detects 3-4 neutrinos per day, which is in agreement with the expected number of atmospheric neutrinos.

    Cubic Kilometer-sized Neutrino Telescopes
    By detecting atmospheric neutrinos, the Baikal and the AMANDA neutrino telescopes have proven that the technique of large Cherenkov detectors is mature and ready to be used to search for high energy neutrinos from the cosmos. AMANDA, the largest telescope running today, has a possibility to observe cosmic neutrinos the coming years but might not be large enough.

    Several projects to build neutrino telescopes of the needed size are going on. The most advanced project is IceCube, which has started to be deployed at the same site as AMANDA at the South Pole. IceCube will consist of 80 strings of light detectors (in total 4,800) between 1,450 and 2,450 meters deep at the same site as AMANDA. The detector volume will be one cubic kilometer and the first string was successfully deployed in January, 2005. The deployment of the detector will take six years but data will be recorded together with the AMANDA telescope already from the first years.

    In the Mediterranean there are three projects, Astronomy with a Neutrino Telescope and Abyss Environmental Research (ANTARES) outside Toulon in France, Neutrino Extended Submarine Telescope with Oceanographic Research (NESTOR) outside Pylos in Greece and Neutrino Mediterranean Observatory (NEMO) outside Sicily in Italy. The ANTARES and NESTOR detectors are, with the first versions, aimed to reach the same size as the AMANDA telescope at the South Pole. One large neutrino telescope on the northern hemisphere would be a very nice complement to the one cubic kilometer neutrino telescope IceCube at the South Pole.

    The ANTARES neutrino telescope in the Mediterranean.
    Copyright © F. Montanet, CNRS/IN2P3 for the ANTARES collaboration

    Even Larger-Sized Neutrino Detectors

    There are other projects going on to detect high neutrino interactions in even larger detector volumes than one cubic kilometer. The main goal is to detect many of the GZK neutrinos that are produced when the highest energy cosmic rays are colliding with the microwave background from Big Bang. These detectors are recording the radio waves emitted in the neutrino interactions. The reason for using radio waves instead of optical Cherenkov light is that the radio waves can travel much longer in matter without being absorbed, allowing larger detector volumes. The neutrino energy threshold for this technique is, however, much higher than for the previous discussed telescopes, and they are mainly sensitive to the interactions of high energy electron neutrinos.

    The Radio Ice Cerenkov Experiment (RICE) project has investigated the technique of radio waves at the South Pole in the AMANDA site. Another interesting project is Antarctic Impulse Transient Array (ANITA) that is a balloon experiment in Antarctica. The balloon with the ANITA radio receivers will circulate at 37 kilometers altitude in several turns (30 days) over the ice sheets and look for high energy neutrino interactions in the ice. The "detector volume" will be thousands of cubic kilometers.

    Looking for high energy neutrino interactions in the ice with the Antarctic Impulse Transient Array (ANITA) balloon experiment.

    Copyright © Peter Gorham (Hawaii)

    An even larger detector volume is used in the GLUE project that is looking for radio waves from neutrino interactions in the lunar surface. Finally there are two satellite projects, Extreme Universe Space Observatory (EUSO) and Orbiting Wide-angle Light-collectors (OWL), which are proposed to look for neutrino interactions in the atmosphere with detector volumes of several 1,000 cubic kilometers.

    The hunt for high energy neutrinos from the cosmos has just started and, in the near future, we will hopefully learn new interesting facts about our fascinating universe.

    J. Bahcall, "How the Sun Shines,"


    The Sudbury Neutrino Observatory (SNO)


    Antarctic Moun and Neutriono Detector Array (AMANDA)

    IceCube High Energy Neutrino Observatory

    Astronomy with a Neutrino Telescope and Abyss Environmental Research (ANTARES)

    Neutrino Mediterranean Observatory (NEMO)

    Neutrino Extended Submarine Telescope with Oceanographic Research (NESTOR)

    Radio Ice Cerenkov Experiment (RICE)

    Antarctic Impulse Transient Array (ANITA)

    Extreme Universe Space Observatory (EUSO)

    Orbiting Wide-angle Light-collectors (OWL)