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Lagrangian point
The Lagrangian points (/ləˈɡrɑːndʒiən/; also Lagrange points, L-points, or libration points) are the five positions in an orbital configuration where a small object affected only by gravity can maintain a stable orbital configuration with respect to two larger objects (such as a satellite with respect to Earth and Moon). The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to orbit with them. A satellite at L1 would have the same angular velocity of Earth with respect to the Sun and hence it would maintain the same position with respect to the Sun as seen from Earth. Without Earth's gravitational influence, a satellite of the Sun, at the distance of L1, would have to move at a higher angular velocity than that of Earth.
Lagrangian points are the constant-pattern solutions of the restricted three-body problem. For example, given two massive bodies in orbits around their common barycenter, there are five positions in space where a third body, of comparatively negligible mass, could be placed so as to maintain its position relative to the two massive bodies. As seen in a rotating reference frame that matches the angular velocity of the two co-orbiting bodies, the gravitational fields of two massive bodies combined with the minor body's acceleration are in balance at the Lagrangian points, allowing the smaller third body to be relatively stationary with respect to the first two.[2]
- 1 History and concepts
- 2 Terminology
- 3 The Lagrangian points
- 4 Stability
- 5 Intuitive explanation
- 6 List of missions to Lagrangian points
- 7 Natural examples
- 8 See also
- 9 Notes
- 10 References
- 11 External links
History and concepts[edit]
The three collinear Lagrange points (L1, L2, L3) were discovered by Leonhard Euler a few years before Lagrange discovered the remaining two.[3][4]
In 1772, Joseph-Louis Lagrange published an "Essay on the three-body problem". In the first chapter he considered the general three-body problem. From that, in the second chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits.[5] Thence, if one mass is made negligible, one immediately gets the five positions now known as the Lagrange Points; but Lagrange himself apparently did not note that.[original research?]
In the more general case of elliptical orbits, there are no longer stationary points in the same sense: it becomes more of a Lagrangian "area". The Lagrangian points constructed at each point in time, as in the circular case, form stationary elliptical orbits that are similar to the orbits of the massive bodies. This is due to Newton's second law (Force = Mass times Acceleration, or ), where p = mv (p the momentum, m the mass, and v the velocity) is invariant if force and position are scaled by the same factor. A body at a Lagrangian point orbits with the same period as the two massive bodies in the circular case, implying that it has the same ratio of gravitational force to radial distance as they do. This fact is independent of the circularity of the orbits, and it implies that the elliptical orbits traced by the Lagrangian points are solutions of the equation of motion of the third body.[citation needed]
Early in the 20th century, Jupiter trojans were discovered at the L4 and L5 Lagrange points of the Sun–Jupiter system.
The five Sun–Earth Lagrangian points may be referred to SEL1–SEL5 and those of the Earth–Moon system EML1–EML5 for short.[6]
The Lagrangian points[edit]
The five Lagrangian points are labeled and defined as follows:
The L1 point lies on the line defined by the two large masses M1 and M2, and between them. It is the most intuitively understood of the Lagrangian points: the one where the gravitational attraction of M2 partially cancels M1's gravitational attraction.
- Example: An object that orbits the Sun more closely than Earth would normally have a shorter orbital period than Earth, but that ignores the effect of Earth's own gravitational pull. If the object is directly between Earth and the Sun, then Earth's gravity weakens the force pulling the object towards the Sun, and therefore increases the orbital period of the object. The closer to Earth the object is, the greater this effect is. At the L1 point, the orbital period of the object becomes exactly equal to Earth's orbital period. L1 is about 1.5 million kilometers from Earth.[7]
The location of L1 is the solution to the following equation balancing gravitation and centrifugal force:
where r is the distance of the L1 point from the smaller object, R is the distance between the two main objects, and M1 and M2 are the masses of the large and small object, respectively. (The quantity in parenthesis on the right is the distance of L1 from the center of mass.) Solving this for r involves solving a quintic function, but if the mass of the smaller object (M2) is much smaller than the mass of the larger object (M1) then L1 and L2 are at approximately equal distances r from the smaller object, equal to the radius of the Hill sphere, given by:
This distance can be described as being such that the orbital period, corresponding to a circular orbit with this distance as radius around M2 in the absence of M1, is that of M2 around M1, divided by :
The Sun–Earth L1 is suited for making observations of the Sun–Earth system. Objects here are never shadowed by Earth or the Moon. The first mission of this type was the International Sun Earth Explorer 3 (ISEE-3) mission used as an interplanetary early warning storm monitor for solar disturbances. The feasibility of this orbit was the result of a PhD thesis by the astrodynamicist Robert W. Farquhar.[8] Subsequently the Solar and Heliospheric Observatory (SOHO) was stationed in a halo orbit at L1, and the Advanced Composition Explorer (ACE) in a Lissajous orbit, also at the L1 point. WIND is also at L1.
The Earth–Moon L1 allows comparatively easy access to Lunar and Earth orbits with minimal change in velocity and has this as an advantage to position a half-way manned space station intended to help transport cargo and personnel to the Moon and back.
In a binary star system, the Roche lobe has its apex located at L1; if a star overflows its Roche lobe, then it will lose matter to its companion star.
The L1 point is also important for scientific research satellites.
Spacecraft at Sun–Earth L1[edit]
International Sun Earth Explorer 3 (ISEE-3) began its mission at the Sun–Earth L1 before leaving to intercept a comet in 1982. The Sun–Earth L1 is also the point to which the Reboot ISEE-3 mission was attempting to return the craft as the first phase of a recovery mission (as September 25, 2014 all eforts have failed and contact was lost).[9] Solar and Heliospheric Observatory (SOHO) was stationed in a halo orbit at L1, and the Advanced Composition Explorer (ACE) in a Lissajous orbit, also at the L1 point. WIND is also at L1.
The L2 point lies on the line through the two large masses, beyond the smaller of the two. Here, the gravitational forces of the two large masses balance the centrifugal effect on a body at L2.
- Example: On the opposite side of Earth from the Sun, the orbital period of an object would normally be greater than that of Earth. The extra pull of Earth's gravity decreases the orbital period of the object, and at the L2 point that orbital period becomes equal to Earth's.
The Sun–Earth L2 is a good spot for space-based observatories. Because an object around L2 will maintain the same relative position with respect to the Sun and Earth, shielding and calibration are much simpler. It is, however, slightly beyond the reach of Earth's umbra,[10] so solar radiation is not completely blocked. Earth–Moon L2 would be a good location for a communications satellite covering the Moon's far side and would be "an ideal location" for a propellant depot as part of the proposed depot-based space transportation architecture.[11]
The location of L2 is the solution to the following equation balancing gravitation and inertia:
with parameters defined as for the L1 case. Again, if the mass of the smaller object (M2) is much smaller than the mass of the larger object (M1) then L2 is at approximately the radius of the Hill sphere, given by:
- Sun and Earth: 1,500,000 km (930,000 mi) from the Earth
- Earth and Moon: 60,000 km (37,000 mi) from the Moon[12]
Spacecraft at Sun–Earth L2[edit]
Spacecraft at the Sun–Earth L2 point are in a Lissajous orbit until decommissioned, when they are sent into a heliocentric graveyard orbit.
- 1 October 2001 – October 2010 — Wilkinson Microwave Anisotropy Probe[13]
- July 2009 – 29 April 2013 — Herschel Space Observatory [14]
- 3 July 2009 – 21 October 2013 — Space observatory Planck
- 25 August 2011 – April 2012 — Chang'e 2,[15][16] from where it travelled to 4179 Toutatis and then into deep space.
- January 2014 – 2018 — Gaia probe
- 2018 — James Webb Space Telescope will use a halo orbit.
- 2020 — Euclid observatory.
- 2028 — Advanced Telescope for High Energy Astrophysics X-ray telescope will be place on a halo orbit.
The L3 point lies on the line defined by the two large masses, beyond the larger of the two.
- Example: L3 in the Sun–Earth system exists on the opposite side of the Sun, a little outside Earth's orbit but slightly closer to the Sun than Earth is. (This apparent contradiction is because the Sun is also affected by Earth's gravity, and so orbits around the two bodies' barycenter, which is, however, well inside the body of the Sun.) At the L3 point, the combined pull of Earth and Sun again causes the object to orbit with the same period as Earth.
The location of L3 is the solution to the following equation balancing gravitation and centrifugal force:
with parameters defined as for the L1 and L2 cases except that r now indicates how much closer L3 is to the more massive object than the smaller object. If the mass of the smaller object (M2) is much smaller than the mass of the larger object (M1) then:
The Sun–Earth L3 point was a popular place to put a "Counter-Earth" in pulp science fiction and comic books. Once space-based observation became possible via satellites[17] and probes, it was shown to hold no such object. The Sun–Earth L3 is unstable and could not contain an object, large or small, for very long. This is because the gravitational forces of the other planets are stronger than that of Earth (Venus, for example, comes within 0.3 AU of this L3 every 20 months).
A spacecraft orbiting near Sun–Earth L3 would be able to closely monitor the evolution of active sunspot regions before they rotate into a geoeffective position, so that a 7-day early warning could be issued by the NOAA Space Weather Prediction Center. Moreover, a satellite near Sun–Earth L3 would provide very important observations not only for Earth forecasts, but also for deep space support (Mars predictions and for manned mission to near-Earth asteroids). In 2010, spacecraft transfer trajectories to Sun–Earth L3 were studied and several designs were considered.[18]
Scientists at the B612 Foundation are planning to use Venus's L3 point to position their planned Sentinel telescope, which aims to look back towards Earth's orbit and compile a catalogue of near-Earth asteroids.[19]
One example of asteroids that reside in an L3 point is the Hilda family, which have orbits near the Sun–Jupiter L3 point.
L4 and L5[edit]
The L4 and L5 points lie at the third corners of the two equilateral triangles in the plane of orbit whose common base is the line between the centers of the two masses, such that the point lies behind (L5) or ahead (L4) of the smaller mass with regard to its orbit around the larger mass.
The reason these points are in balance is that, at L4 and L5, the distances to the two masses are equal. Accordingly, the gravitational forces from the two massive bodies are in the same ratio as the masses of the two bodies, and so the resultant force acts through the barycenter of the system; additionally, the geometry of the triangle ensures that the resultant acceleration is to the distance from the barycenter in the same ratio as for the two massive bodies. The barycenter being both the center of mass and center of rotation of the three-body system, this resultant force is exactly that required to keep the smaller body at the Lagrange point in orbital equilibrium with the other two larger bodies of system. (Indeed, the third body need not have negligible mass). The general triangular configuration was discovered by Lagrange in work on the three-body problem.
L4 and L5 are sometimes called triangular Lagrange points or Trojan points. The name Trojan points comes from the Jupiter trojans at the Sun–Jupiter L4 and L5 points, named after characters from Homer's Iliad (the legendary siege of Troy). Asteroids at the L4 point, which leads Jupiter, are referred to as the "Greek camp", whereas those at the L5 point are referred to as the "Trojan camp". These asteroids are mostly named after characters from the respective sides of the Trojan War.
- The Sun–Earth L4 and L5 points lie 60° ahead of and 60° behind Earth as it orbits the Sun. The regions around these points contain interplanetary dust and at least one asteroid, 2010 TK7, detected in October 2010 by Wide-field Infrared Survey Explorer (WISE) and announced during July 2011.[20][21]
- The Earth–Moon L4 and L5 points lie 60° ahead of and 60° behind the Moon as it orbits Earth. They may contain interplanetary dust in what is called Kordylewski clouds; however, the Hiten spacecraft's Munich Dust Counter (MDC) detected no increase in dust during its passes through these points.
- The region around the Sun–Jupiter L4 and L5 points are occupied by the Jupiter trojans.
- The region around the Sun–Neptune L4 and L5 points have trojan objects.[22]
- Saturn's moon Tethys has two much smaller satellites at its L4 and L5 points named Telesto and Calypso, respectively.
- Saturn's moon Dione has smaller moons Helene and Polydeuces at its L4 and L5 points, respectively.
- One version of the giant impact hypothesis suggests that an object named Theia formed at the Sun–Earth L4 or L5 points and crashed into Earth after its orbit destabilized, forming the Moon.
Although the L1, L2, and L3 points are nominally unstable, it turns out that it is possible to find (unstable) periodic orbits around these points, at least in the restricted three-body problem. These periodic orbits, referred to as "halo" orbits, do not exist in a full n-body dynamical system such as the Solar System. However, quasi-periodic (i.e. bounded but not precisely repeating) orbits following Lissajous-curve trajectories do exist in the n-body system. These quasi-periodic Lissajous orbits are what most of Lagrangian-point missions to date have used. Although they are not perfectly stable, a relatively modest effort at station keeping can allow a spacecraft to stay in a desired Lissajous orbit for an extended period of time. It also turns out that, at least in the case of Sun–Earth-L1 missions, it is actually preferable to place the spacecraft in a large-amplitude (100,000–200,000 km or 62,000–124,000 mi) Lissajous orbit, instead of having it sit at the Lagrangian point, because this keeps the spacecraft off the direct Sun–Earth line, thereby reducing the impact of solar interference on Earth–spacecraft communications. Another interesting and useful property of the collinear Lagrangian points and their associated Lissajous orbits is that they serve as "gateways" to control the chaotic trajectories of the Interplanetary Transport Network.
In contrast to the collinear Lagrangian points, the triangular points (L4 and L5) are stable equilibria, provided that the ratio of M1/M2 is greater than 24.96.[note 1][23] This is the case for the Sun–Earth system, the Sun–Jupiter system, and, by a smaller margin, the Earth–Moon system. When a body at these points is perturbed, it moves away from the point, but the factor opposite of that which is increased or decreased by the perturbation (either gravity or angular momentum-induced speed) will also increase or decrease, bending the object's path into a stable, kidney-bean-shaped orbit around the point (as seen in the corotating frame of reference). However, in the Earth–Moon case, the problem of stability is greatly complicated by the appreciable solar gravitational influence.[24] In 2008 it was found that the L4 and L5 points in the Earth–Moon system would be stable for 1000 million years, even with perturbations from the sun, but because of smaller perturbations by the planets, orbits around these points can only last a few million years.[25]
Intuitive explanation[edit]
|This section needs additional citations for verification. (January 2013)
|This section may be confusing or unclear to readers. (August 2014)
Lagrangian points can be explained intuitively using the Earth–Moon system.[26]
Lagrangian points L2 through L5 exist only in rotating systems, such as in the monthly orbiting of the Moon around Earth. At these points, the combined attraction from the two masses is equivalent to what would be exerted by a single mass at the barycenter of the system, sufficient to cause a small body to orbit with the same period.
Imagine a person swinging a stone at the end of a string. The string provides a tension force that continuously accelerates the stone toward the center. To an ant standing on the stone, it is only pulled along by the contact forces at its feet. Because the stone seems motionless to the ant and its feet are motionless with respect to the stone, the difference in force between its feet and body seems as if there is an opposite force trying to fling it directly away from the center. This apparent force is called the centrifugal force. It is actually the outward radial component of the stone's inertia caused by its swing. This same effect is present at the Lagrangian points in the Earth–Moon system, where the analogue of the string is the summed (or net) gravitational attraction of the two masses, and the stone is an asteroid or a spacecraft. The Earth–Moon system and the spacecraft all rotate about this combined center of mass, or barycenter. Because Earth is much heavier than the Moon, the barycenter is located within Earth (about 1,700 km or 1,100 mi below the surface). Any object gravitationally held by the rotating Earth–Moon system will be attracted to the barycenter to an equal and opposite degree as its tendency to fly off into space.
L1 is a bit farther from the (less massive) Moon and closer to the (more massive) Earth than the point where total gravity is zero. L1 is slightly unstable (see stability, above) because drifting towards the Moon or Earth increases the gravitational attraction of one body and decreases that of the other, causing more drift.
At Lagrangian points L2, L3, L4, and L5, a spacecraft's inertia to move away from the barycenter is balanced by the attraction of gravity toward the barycenter. L2 and L3 are slightly unstable because small changes in position upset the balance between gravity and inertia, allowing one or the other force to dominate, so that the spacecraft either flies off into space or spirals in toward the barycenter. Stability at L4 and L5 is explained by gravitational equilibrium: if the object were moved into a tighter orbit, it would orbit faster, which would counteract the increase in gravity; if the object moves into a wider orbit, the gravity is lower, but it loses speed. The net result is that the object appears constantly to hover or orbit around the L4 or L5 point.
The easiest way to understand the resulting stability is to say L1, L2, and L3 positions are as stable as a ball balanced on the tip of a wedge would be stable: any disturbance will toss it out of equilibrium. The L4, and L5 positions are stable as a ball at the bottom of a bowl would be stable: small perturbations will move it out of place, but it will drift back toward the center of the bowl.
Note that from the perspective of the smaller-mass object—from the moon, in the preceding example—a spacecraft might appear to orbit in an irregular path about the L4 or L5 point, but from the perspective above the orbital plane, it becomes clear that both the smaller mass and the spacecraft are orbiting the larger mass (or more precisely, all of the objects are in orbit around the barycenter of the system); they simply have overlapping orbital paths. This point of view difference is illustrated clearly by animations in the 3753 Cruithne and Coriolis effect articles.
List of missions to Lagrangian points[edit]
Orbits around Lagrangian points offer unique advantages that have made them a good choice for performing certain spacecraft missions. For example the Sun–Earth L1 point is useful for observations of the Sun, because the Sun is always visible without obstructions by Earth or the Moon. The Sun–Earth L2 point is useful for astronomy missions using space observatories, because from this point the Sun, Earth and Moon are relatively closely positioned together in the sky, and hence leave a large field of view without interference – this is especially helpful for infrared astronomy.
Missions to Lagrangian points generally orbit the points rather than occupy them directly.
Color key:
– Mission at Lagrangian point completed successfully (or partially successfully) – Unflown, cancelled or failed mission – Mission en route or in progress (including mission extensions) – Planned mission
Past and present missions[edit]
|Lagrangian point
|"Lunar Far-Side Communication Satellites"
|Earth–Moon L2
|Proposed in 1968 for communications on the far side of the Moon during the Apollo program, mainly to enable an Apollo landing on the far side—both the satellites and the landing were never realized.[27]
|Space colonization and manufacturing
|Earth–Moon L4 or L5
|Gerard K. O'Neill / L5 Society
|First proposed in 1974 by Gerard K. O'Neill.[28]
|International Sun–Earth Explorer 3 (ISEE-3)
|Sun–Earth L1
|Launched in 1978, it was the first spacecraft to be put into orbit around a libration point, where it operated for four years in a halo orbit about the L1 Sun–Earth point. After the original mission ended, it was commanded to leave L1 in September 1982 in order to investigate comets and the Sun.[29] Now in a heliocentric orbit, an unsuccessful attempt to return to halo orbit was made in 2014 when it made a flyby of the Earth–Moon system.[30][31]
|Advanced Composition Explorer (ACE)
|Sun–Earth L1
|Launched 1997. Has fuel to orbit near the L1 until 2024. As of 2013[update] operational.[32]
|Solar and Heliospheric Observatory (SOHO)
|Sun–Earth L1
|Orbiting near the L1 since 1996. As of 2013[update] operational.[33]
|Sun–Earth L1
|Arrived at L1 in 2004 with fuel for 60 yrs. As of 2013[update] operational.[34]
|Wilkinson Microwave Anisotropy Probe (WMAP)
|Sun–Earth L2
|Arrived at L2 in 2001. Mission ended 2010,[35] then sent to solar orbit outside L2.[36]
|Herschel Space Observatory
|Sun–Earth L2
|Arrived at L2 July 2009. Ceased operation on 29 April 2013 and will be moved to a heliocentric orbit.[37][38]
|Planck Space Observatory
|Sun–Earth L2
|Arrived at L2 July 2009. Mission ended on 23 October 2013, Planck has been moved to a heliocentric parking orbit.[39]
|Chang'e 2
|Sun–Earth L2
|Original mission ended, left L2 point for 4179 Toutatis at April 15, 2012.[40]
|ARTEMIS mission extension of THEMIS
|Earth–Moon L1 and L2
|Mission consists of two spacecraft, which were the first spacecraft to reach Earth–Moon Lagrangian points. Both moved through Earth–Moon Lagrangian points, and are now in lunar orbit.[41][42]
|Sun–Earth L2
|Launched on 19 December 2013.[43][44]
Future and proposed missions[edit]
|Lagrangian point
|Deep Space Climate Observatory (DSCOVR)
|Sun–Earth L1
|Launch planned for January 2015.[45]
|LISA Pathfinder (LPF)
|Sun–Earth L1
|As of 2012[update] launch is scheduled for July 2015.[46]
|Sun–Earth L1
|Possible mission after 2010.[citation needed]
|James Webb Space Telescope (JWST)
|Sun–Earth L2
|As of 2013[update] launch is planned for October 2018.[47]
|Sun–Earth L2
|As of 2013[update] planned for launch in 2020.[48]
|Wide Field Infrared Survey Telescope (WFIRST)
|Sun–Earth L2
|As of 2013[update] in a 'pre-formulation' phase until at least early 2016, possible launch in the early 2020s.[49]
|Exploration Gateway Platform
|Earth–Moon L2[50]
|Proposed in 2011.[51]
|Advanced Telescope for High Energy Astrophysics (ATHENA)
|Sun–Earth L2
|Launch planned for 2028[52]
Natural examples[edit]
In the Sun–Jupiter system several thousand asteroids, collectively referred to as Jupiter trojans or "trojan asteroids", are in orbits around the Sun–Jupiter L4 and L5 points. Recent observations suggest that the Sun–Neptune L4 and L5 points, known as the Neptune trojans, may be very thickly populated, containing large bodies an order of magnitude more numerous than the Jupiter trojans. Mars has three known co-orbital asteroids (5261 Eureka, 1999 UJ7, and 1998 VF31), all at its Lagrangian points. There is one known trojan for Earth as of July 2011. Clouds of dust, called Kordylewski clouds, even fainter than the notoriously weak gegenschein, may also be present in the L4 and L5 of the Earth–Moon system.
The Saturnian moon Tethys has two smaller moons in its L4 and L5 points, Telesto and Calypso. The Saturnian moon Dione also has two Lagrangian co-orbitals, Helene at its L4 point and Polydeuces at L5. The moons wander azimuthally about the Lagrangian points, with Polydeuces describing the largest deviations, moving up to 32 degrees away from the Saturn–Dione L5 point. Tethys and Dione are hundreds of times more massive than their "escorts" (see the moons' articles for exact diameter figures; masses are not known in several cases), and Saturn is far more massive still, which makes the overall system stable.
Other co-orbitals[edit]
2010 TK7 is the first Earth trojan discovered. It was discovered by the Wide-field Infrared Survey Explorer in October, 2010. After evaluation of the collected data the trojan character of its motion was published in July 2011. 2010 TK7 has a diameter of 300 meters. Its path is around the Sun–Earth L4 Lagrangian point.
Earth's companion object 3753 Cruithne is in a relationship with Earth that is somewhat trojan-like, but that is different from a true trojan. Cruithne occupies one of two regular solar orbits, one of them slightly smaller and faster than Earth's, and the other slightly larger and slower. It periodically alternates between these two orbits due to close encounters with Earth. When it is in the smaller, faster orbit and approaches Earth, it gains orbital energy from Earth and moves up into the larger, slower orbit. It then falls farther and farther behind Earth, and eventually Earth approaches it from the other direction. Then Cruithne gives up orbital energy to Earth, and drops back into the smaller orbit, thus beginning the cycle anew. The cycle has no noticeable impact on the length of the year, because Earth's mass is over 20 billion (2×1010) times more than that of 3753 Cruithne.
Epimetheus and Janus, satellites of Saturn, have a similar relationship, though they are of similar masses and so actually exchange orbits with each other periodically. (Janus is roughly 4 times more massive but still light enough for its orbit to be altered.) Another similar configuration is known as orbital resonance, in which orbiting bodies tend to have periods of a simple integer ratio, due to their interaction.
See also[edit]
- Co-orbital configuration
- Euler's three-body problem
- Gegenschein
- Hill sphere
- Home on Lagrange (The L5 Song)
- Horseshoe orbit
- L5 Society
- Lagrange point colonization
- Lagrangian mechanics
- Lissajous orbit
- List of objects at Lagrangian points
- Lunar space elevator
- Trojan asteroids
- Trojan wave packets
- Venus Equilateral
- ^ Actually
- ^ ZF Seidov, "The Roche Problem: Some Analytics", The Astrophysical Journal, 603:283-284, 2004 March 1
- ^ "Lagrange Points" by Enrique Zeleny, Wolfram Demonstrations Project.
- ^ Koon, W. S.; M. W. Lo; J. E. Marsden; S. D. Ross (2006). Dynamical Systems, the Three-Body Problem, and Space Mission Design. p. 9. (16MB)
- ^ Leonhard Euler, De motu rectilineo trium corporum se mutuo attrahentium (1765)
- ^ (French) Lagrange, Joseph-Louis (1867–92). "Tome 6, Chapitre II: Essai sur le problème des trois corps". Oeuvres de Lagrange. Gauthier-Villars. pp. 229–334.
- ^ Forging the Future of Space Science:: The Next 50 Years. National Academies Press. 2010. p. 50. Retrieved 21 October 2014.
- ^ Cornish, Neil J. "The Lagrangian Points". Department of Physics, Bozeman Campus, Montana State University, USA. Retrieved 29 July 2011.
- ^ Farquhar, R. W.: "The Control and Use of Libration-Point Satellites", Ph.D. Dissertation, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, CA, 1968
- ^ "ISEE-3 is in Safe Mode". Space College. 25 September 2014. "The ground stations listening to ISEE-3 have not been able to obtain a signal since Tuesday the 16th"
- ^ Angular size of the Sun at 1 AU + 930000 miles: 31.6', angular size of Earth at 930000 miles: 29.3'
- ^ Zegler, Frank; Bernard Kutter (2010-09-02). "Evolving to a Depot-Based Space Transportation Architecture". AIAA SPACE 2010 Conference & Exposition. AIAA. p. 4. Retrieved 2011-01-25. "L2 is in deep space far away from any planetary surface and hence the thermal, micrometeoroid, and atomic oxygen environments are vastly superior to those in LEO. Thermodynamic stasis and extended hardware life are far easier to obtain without these punishing conditions seen in LEO. L2 is not just a great gateway — it is a great place to store propellants. ... L2 is an ideal location to store propellants and cargos: it is close, high energy, and cold. More importantly, it allows the continuous onward movement of propellants from LEO depots, thus suppressing their size and effectively minimizing the near-Earth boiloff penalties."
- ^ Zegler, Frank; Bernard Kutter (2010-09-02). "Evolving to a Depot-Based Space Transportation Architecture". AIAA SPACE 2010 Conference & Exposition. AIAA. p. 4. Retrieved 2011-08-30. "We can create an energy savings account by moving propellant to the earth-moon Lagrange points—especially L2. Located 60,000 km beyond the Moon, propellant or cargo cached at L2 is very nearly at Earth escape energy. It takes only a small nudge to dislodge it from Earth's gravitational grasp. This has been known for decades and L2 is often called a gateway to the solar system."
- ^ "Mission Complete! WMAP Fires Its Thrusters For The Last Time".
- ^ Toobin, Adam (2013-06-19). "Herschel Space Telescope Shut Down For Good, ESA Announces". Huffington Post.
- ^ Lakdawalla, Emily (14 June 2012). "Chang'E 2 has departed Earth's neighborhood for.....asteroid Toutatis!?". Retrieved 15 June 2012.
- ^ Lakdawalla, Emily (15 June 2012). "Update on yesterday's post about Chang'E 2 going to Toutatis". Planetary Society. Retrieved 26 June 2012.
- ^ STEREO mission description by NASA, http://www.nasa.gov/mission_pages/stereo/main/index.html#.UuG0NxDb-kk
- ^ Tantardini, Marco; Fantino, Elena; Yuan Ren, Pierpaolo Pergola, Gerard Gómez and Josep J. Masdemont (2010). "Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem". Celestial Mechanics and Dynamical Astronomy (Springer).
- ^ The Sentinel Mission, B612 Foundation. Retrieved Feb 2014.
- ^ Space.com: First Asteroid Companion of Earth Discovered at Last
- ^ NASA—NASA's Wise Mission Finds First Trojan Asteroid Sharing Earth's Orbit
- ^ "List Of Neptune Trojans". Minor Planet Center. Archived from the original on 2011-08-23. Retrieved 2010-10-27.
- ^ The Lagrange Points PDF, Neil J. Cornish with input from Jeremy Goodman
- ^ "A Search for Natural or Artificial Objects Located at the Earth–Moon Libration Points" by Robert Freitas and Francisco Valdes, Icarus 42, 442-447 (1980)
- ^ "Solar and planetary destabilization of the Earth–Moon triangular Lagrangian points" by Jack Lissauer and John Chambers, Icarus, vol. 195, issue 1, May 2008, pp. 16-27.
- ^ Tyson, Neil deGrasse (2007-01-16). Death by Black hole: and other cosmic quandaries. W. W. Norton & Company. ISBN 978-0-393-06224-3.
- ^ P. E. Schmid (June 1968). "Lunar Far-Side Communication Satellites" (PDF). NASA. Retrieved 2008-07-16.
- ^ O'Neill, Gerard K. (September 1974). "The Colonization of Space". Physics Today (American Institute of Physics) 27 (9): 32–40. Bibcode:1974PhT....27i..32O. doi:10.1063/1.3128863.
- ^ "Solar System Exploration: ISEE-3/ICE". NASA. Retrieved 2010-09-28.
- ^ Lakdawalla, Emily (October 3, 2008). "It's Alive!". The Planetary Science Weblog.
- ^ Chang, Kenneth (August 8, 2014). "Rudderless Craft to Get Glimpse of Home Before Sinking Into Space's Depths". The New York Times.
- ^ "ACE Mission". Caltech ACE Science Center. Retrieved 2013-03-18.
- ^ "SOHO's Orbit: An Uninterrupted View of the Sun". NASA. Retrieved 2010-09-28.
- ^ "WIND Spacecraft". NASA. Retrieved 2010-09-28.
- ^ "WMAP Facts". NASA. Retrieved 2013-03-18.
- ^ http://map.gsfc.nasa.gov/news/events.html WMAP Ceases Communications
- ^ "Herschel Factsheet". European Space Agency. 17 April 2009. Retrieved 2009-05-12.
- ^ "Herschel space telescope finishes mission". BBC news. 29 April 2013.
- ^ "Last command sent to ESA's Planck space telescope". European Space Agency. October 23, 2013. Retrieved October 23, 2013.
- ^ "嫦娥二号再接新任务预计年底飞掠小行星". 现代快报. Retrieved 2012-06-27.
- ^ Fox, Karen C. "First ARTEMIS Spacecraft Successfully Enters Lunar Orbit". The Sun-Earth Connection: Heliophysics. NASA.
- ^ Hendrix, Susan. "Second ARTEMIS Spacecraft Successfully Enters Lunar Orbit". The Sun-Earth Connection: Heliophysics. NASA.
- ^ "Worldwide launch schedule". Spaceflight Now. 27 November 2013.
- ^ "ESA Gaia home". ESA. Retrieved 23 October 2013.
- ^ "NASA Space Calendar". NASA JPL. June 4, 2014. Retrieved June 4, 2014.
- ^ "LISA Pathfinder factsheet". ESA. 11 June 2012. Retrieved 26 June 2012.
- ^ "JWST factsheet". ESA. 2013-09-04. Retrieved 2013-09-07.
- ^ "NASA Officially Joins ESA's 'Dark Universe' Mission". JPL/NASA. 24 January 2013. Retrieved 12 April 2013.
- ^ Paul Hertz (2013-06-04), NASA Astrophysics presentation to American Astronomical Society, retrieved 2013-09-10
- ^ NASA teams evaluating ISS-built Exploration Platform roadmap
- ^ Bergin, Chris (December 2011). "Exploration Gateway Platform hosting Reusable Lunar Lander proposed". NASA Spaceflight.com. Retrieved 2011-12-05.
- ^ "ESA Science & Technology: Athena to study the hot and energetic Universe". ESA. 27 June 2014. Retrieved 23 August 2014.
External links[edit]
|Wikimedia Commons has media related to Lagrange points.
- Joseph-Louis, Comte Lagrange, from Oeuvres Tome 6, "Essai sur le Problème des Trois Corps"—Essai (PDF); source Tome 6 (Viewer)
- "Essay on the Three-Body Problem" by J-L Lagrange, translated from the above, in http://www.merlyn.demon.co.uk/essai-3c.htm.
- Considerationes de motu corporum coelestium—Leonhard Euler—transcription and translation at http://www.merlyn.demon.co.uk/euler304.htm.
- What are Lagrange points?—European Space Agency page, with good animations
- Explanation of Lagrange points—Prof. Neil J. Cornish
- A NASA explanation—also attributed to Neil J. Cornish
- Explanation of Lagrange points—Prof. John Baez
- Geometry and calculations of Lagrange points—Dr J R Stockton
- Locations of Lagrange points, with approximations—Dr. David Peter Stern
- An online calculator to compute the precise positions of the 5 Lagrange points for any 2-body system—Tony Dunn
- Astronomy cast—Ep. 76: Lagrange Points Fraser Cain and Dr. Pamela Gay
- The Five Points of Lagrange by Neil deGrasse Tyson
- Earth, a lone Trojan discovered


text:
In our globalized world, new forms of colonization are emerging, and popular control over decisions that affect people's freedom and well-being is becoming increasingly weaker.
In the US, UK and Australia, some terrorism investigations appear to be deliberate attempts to stimulate popular support for the war against ISIS.
Marcos Sosa is a senior high school student in San Francisco.

subset: commoncrawl


text:
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Interview with The Chesterfield Palm Beach Assistant General Manager Richard Snyder
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text:
Letters to the editor - Tuesday (9-24-2013)
A gentleman's honesty you could take to the bank
Several weeks ago, in my usual haste, I rushed to my purse to pay a bill and my checkbook was missing. I was on my way to a meeting and had little time to look for it. With my mind half on the meeting, I tried to figure out how I could have misplaced such an important item.
During the meeting, my cell phone rang. It was my dear husband, who said a nice man had just called and had found my checkbook in the Belk's parking lot. I couldn't believe it! I remembered darting into Belk's looking for a last-minute gift, but, finding nothing, I had no reason to open my purse.
The kind man told my husband I could retrieve the checkbook if I would come to his address the next morning. My husband was assured that the man was "on the level, honest and upright," so a few minutes after 7 a.m. I rang his doorbell.
A nice-looking gentleman came to the door with my checkbook and $6 in his hand. He told me that when he got out of his car (parked next to mine) he found a dollar bill. When he leaned over to pick up the dollar, he saw a $5 bill and then spotted my checkbook. He insisted on giving all of this back to me. After much insistence, I was able to give him only a token reward! He also told me he was a retired veteran and his wife was not well.
I write this to honor Mr. Harvey Dezern! Thank you from the bottom of my heart for your honesty and integrity. I want all of Rowan and the world to know there are still honest folks around. I heard a sermon once by Dr. Bob Lewis stating that one could learn pretty much who a person really is by seeing three of his possessions — his checkbook, his address book and his holy book. It's pretty obvious which one Mr. Dezern goes by!
— Dellene L. Gudger


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Why wait 3 years and 8 months?
Firecat 400
year 1.new roof
year 2.add 8-12' to the liveing room
year 3.build up my garage with tools and neat stuff so i can do a compleet tare down and rebuild on my 4runner into how i want it.
month 8.my wife and i get around 50-80k to invest,and to buy some things we want.
i have a strick spending grid i make my self follow.so many things i want but i have to take care of the family befor i take care of me.my wife wants to buy my oldest daughter a bedroom set,my wife wants a banchee.we will be doing many small and large up grades on the houe over this time.so i made my self a time line for when i will buy my self a few new toys.that way i have it planed years in advance and my wife cant say squat.lol
A man with a plan!
Firecat 400
not to many side jobs for a grave digger so no real extra income to off set and save for things i really want,like the 30-30 i have been dreaming about for years and years.it takes me a good 6 months to a year to talk my self into buying something over $50 for myself.lol
Just signed up over there too, also with the same username.
2011 Martin Firecat 400/NAP Apache Dropaway/Truglo Xtreme Sight/Custom 8" Stabilizer/Victory V6 Arrows
2007 Martin Jaguar /Trophy Taker Dropaway/Extreme Sight/Custom 21" Stabilizer/Victory V6 Arrows
Bow String Depot, Custom String Builders email us @ email@example.com
18 beers a month, now thats a tight budget
2011 Firecat 400, sword twilight hunter, apa twister, lots of arrows


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Cancer Health Center
8 Ways to Help Your Doctor Make the Right Diagnosis
5. Describe Your Symptoms, but Don't Conclude
Abruzese says she coaches her patients to illustrate the experience they're having. "If you have ear pain and tell your doctor, 'I have an ear infection,' you're excluding other causes of ear pain, such as TMJ or tooth abscess, and your doctor may do that as well," she says. Better to keep a wider path and let the doctor entertain all the possibilities. "Accurate but incomplete information is better than definitive but potentially wrong," says Abruzese.
6. Be Specific About Your Symptoms
Try to get as precise as you can about what you're feeling. If you've got a pain, is it a shooting, sharp pain or a dull ache? Does it come and go after eating? How long does it last? A few seconds? A few minutes? How long have you had it? A week? A month? A year? Does anything decrease the pain?
Also, turn subjective data into objective. If you feel feverish, for example, take your temperature for a week nightly and write down all the information.
This way when you see your doctor you can say, "I've had six headaches in one month, they weren't relieved by Tylenol, they lasted four hours, and I had nausea with them." Then give your doctor time to ask questions.
7. Ask Your Doctor What to Expect
If your doctor does make a diagnosis, ask what you should expect and any red flags you should be looking for, says Gordon Schiff, MD, associate director of the Center for Patient Safety Research and Practice at Brigham and Women's Hospital in Boston. In other words, if you have a viral respiratory infection you should be better in seven days. If you suddenly develop a high fever or feel neck pain, that's a tip-off that something isn't right, says Schiff.
8. Question, Question, Question
Don't be afraid to ask the doctor what he needs to make the diagnosis. Ask point blank: What data do you need to get to the bottom of this? What's your differential diagnosis? (the list of diagnoses it could be) Are there other specialists, procedures, or tests that would help you make the diagnosis? When do you want me to make the next appointment and what information can I bring to help make the diagnosis? Is there a specialist I should see?
Once you have a diagnosis, don't be afraid to second guess your doctor. Are you sure this is what I have? What makes you think that?
And don't be afraid to ask for a second opinion. "I'm not perfect and to go to another doctor and get another opinion doesn't threaten me in any way," says Cutler. Nature, science, and biology are unpredictable, he says. "Good doctors are not threatened by a second opinion. In fact, they're strengthened by it."


text:
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Tesla Live!
September 25th, 2009 at The Backyard Beamont Club in Kansas City, MO.
by John Kindred
Staff Writer
With autumn at our doorstep, Tesla stopped in Kansas City to play the Backyard at the Beaumont Club. The outdoor venue is an intimate setting that could probably hold a little more than 1,000 people. With a stage set up on a flat-bed, 18-wheel trailer, the venue truly is standing room only as there are no seats; just concrete, grass and dirt.
Battling the possible threat of a down pour of rain, Tesla took the stage to perform what felt like an accelerated set. Touring in support of their latest studio album Forever More, the band took the stage and opened with the self-titled song the also opens the new record.
Jeff Keith and company; drummer Troy Luccketta, bassist Brian Wheat and guitarists Frank Hannon and Dave Rude, brought their A-game and served up their signature roots-laden, '70s-inspired hard rock upon the crowd. Tesla performed for nearly and hour and half and beat the ominous, suspected down pour of rain. That really turned out to be a light rain shower beginning three songs before the end of their set.
The band played several songs from the new album "Forever More," "I Wanna Live," "Breaking Free" and "So What!" The music fit in amongst their hits and fan favorites; "Love Song," "Modern Day Cowboy," "Hang Tuff" and, of course, their cover of "Signs."
The showmanship and musicianship of Tesla is not lacking on any front. Guitarist Rave Rudd appears to not only fill the role left by Tommy Skoech, but now after recording and touring, he has become an integral part of the band. Together, Hannon and Rudd play off each others riffs and rhythms with ease and fluidity. They performed harmony solos to perfection. Also impressive was their acoustic guitar work that opens up "Love Song." With Rudd playing a bluesy lead and Hannon playing a classical arrangement underneath, they showcased the melodic softer side of the band.
Keith's voice may not be as sharp as it was in the '80s, but he still had enough edge to deliver the new and older material with purpose. Luccketta's drumming is loud and powerful, and he and Wheat provide the bottom end and pulse of the band.
Obvious crowd favorites included "Modern Day Cowboy," "Paradise" and "Love Song." The new material appeared to be known to the audience as they sang along in a spirited frenzy. The set never seemed to hit a lull as the band rocked whether doing their hard, faster songs or slower mid-tempo songs.
Fans probably wanted more music, but considering the venue and the weather, all in all, the fans got their money's worth.
Set List:
Forever More
I Wanna Live
Modern Day Cowboy
Breaking Free
Hang Tough
Heaven's Trail
So What!
Mama's Fool
Love Song
Edison's Medicine
Into The Now
Comin' Atcha Live


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School of Education Dean Edward A. Silver has been appointed to the National Research Councils committee on Defining Deeper Learning and 21st Century Skills
March 30, 2011
DEARBORN / March 30, 2011---Edward A. Silver, dean of the School of Education, has been appointed to the National Research Councils (NRC) committee on Defining Deeper Learning and 21st Century Skills.
The current context of education in states like Michigan is a focus on college and career readiness with the 21st century skills prominently featured in the rationale for higher expectations in K-12 education. The Defining Deeper Learning and 21st Century Skills committee is charged with clarifying the public discussion around these skills by helping policymakers and educational researchers define these terms and lessen their subjectivity and ambiguity.
The five key questions for the Committee are: (a) Define a set of key skills that reflects the constructs referenced by such labels as deeper learning, 21st century skills, college and career readiness, student centered learning, next generation learning, new basic skills, and higher order thinking. (b) Describe how these skills relate to each other and how students can master them in the context of core academic disciplines such as English language arts, mathematics, and science. (c) Summarize the findings of the research that investigates the importance of such skills to success in education, work, and other areas of adult responsibility and that demonstrates the importance of developing these skills in K-16 education (d) Summarize what is known and what research is needed about how these skills can be learned, taught, and assessed; and (e) Identify features of educational interventions that research suggests could be used as indicators that an intervention is likely to develop the key skills in a substantial and meaningful way.
The Committee will generate a consensus report based on their findings, which will be publicly released in fall 2011, with final publication in late 2011. To generate the report, the Committee will participate in a public discussion with the sponsors about the project goals and the evidence available that can provide the basis for the reports conclusions and recommendations. This initial discussion will allow the sponsors and committee to exchange ideas about the issues to be addressed. The committee and NRC staff will prepare for the first meeting by drafting an initial outline of existing research that the committee can use to develop its report.
The work of the committee will be overseen by the Board on Testing and Assessment (BOTA) and the Board on Science Education (BOSE), which are the two NRC boards that have overseen the prior NRC work related to 21st century skills. Silvers term with the committee, effective immediately, will run through Sept. 3, 2012 with a focus on deeper learning in mathematics.
In addition to serving as dean of the School of Education, Silver is William A. Brownell collegiate professor in education at U-M Ann Arbor. His research interests focus on the teaching, learning and assessment of mathematics, particularly mathematical problem solving. He is also actively involved in efforts to promote high-quality mathematics education for all students, particularly Hispanic and African-American students.
Silvers service with the NRC includes the Mathematical Sciences Education Board, the study group on Guidelines for Mathematics Assessment, the committee on the Foundations of Assessment, and the committee on the Study of Teacher Preparation Programs in the United States.
Also of note, Silver has been selected for the Senior Scholar award from the American Educational Research Association Special Interest Group for Research in Mathematics Education. The award is presented in recognition of the research of a single scholar within the field whose programmatic work has been essential in mathematics education.
The National Research Council (NRC) functions under the auspices of the National Academy of Sciences (NAS), the National Academy of Engineering (NAE), and the Institute of Medicine (IOM). The NAS, NAE, IOM, and NRC are part of a private, nonprofit institution that provides science, technology and health policy advice under a congressional charter signed by President Abraham Lincoln that was originally granted to the NAS in 1863. Under this charter, the NRC was established in 1916, the NAE in 1964, and the IOM in 1970. The four organizations are collectively referred to as the National Academies.
The mission of the NRC is to improve government decision making and public policy, increase public education and understanding, and promote the acquisition and dissemination of knowledge in matters involving science, engineering, technology, and health. The institution takes this charge seriously and works to inform policies and actions that have the power to improve the lives of people in the U.S. and around the world.
Founded in 1959 with a gift of just over 200 acres of land and $6.5 million from the Ford Motor Company, University of Michigan-Dearborn is a metropolitan university serving southeastern Michigan, committed to excellence rooted in strong academics, innovative research and programming and civic engagement. The University has nearly 8,900 students pursuing more than 90 bachelor's, masters, doctoral and professional degrees in liberal arts and sciences, engineering, business and education. A top-ranked university with a faculty devoted to teaching, and students committed to achievement, UM-Dearborn has been shaped by its history of partnering with local leaders and communities, and is committed to finding solutions for the challenges that face the region.
Beth Marmarelli


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Main Content
You're not just the king of the world; you're the king of the sea. Arrive to your favorite shore in the Squash rashguard by HIC. The chest and back yoke both feature custom HIC brand graphics, perfect for labeling you as a chill guy who digs an early-morning sesh. This snug guard also has contrast color flatlock topstitching and a super stretchy nylon/spandex material. You'll definitely remain comfy and content with your beachin' style.
- 80% Nylon/20% Spandex
- Made in the USA
- Screen print graphics
- Tagless collar
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Special event items are produced by manufacturers only after the outcome of a game or event. These are advanced sale items and will ship immediately after they are received in our warehouse.
Manufacturer direct items are shipped directly from the manufacturer. These items are not available for international or expedited shipping.
Customized items can be personalized with options such as your name, your favorite number, and/or designs. Some options may be limited by league rules.


text:
Haves :
Edge of Tomorrow 3D Disc - $15 shipped, DVD $8 (disc only, brand new generic case)
- Art of Bioshock Infinite (sealed) (http://www.amazon.co...s/dp/1595829946) - Make an offer/trade.
-The Sky : Art of Final Fantasy (sealed) (http://www.amazon.co...d/dp/1616551607) - Make an offer/trade.
-Sealed Hyrule Historia LE - $120 shipped.
-Skyrim Lithograph , measures 24 x 36. Has some damage as most of these do, due to negligence of shippers from Bethesda Store. Not so much visible on front side of litho(which is where it counts) and only when looking.
The numbered portion (bottom right corner) was cut out. If you have white backing in your frame, it won't even look too bad from normal viewing distance. $45 shipped.
Dead Space : Ishumura Lithograph - 18x24, but missing a chunk where signature should be. Came un-numbered so had to cut and take picture for replacement. If you could care less about the signature, the art itself is untouched(about 18 x 12) and could be framed itself. - Make an offer
See pic -
-Got some empty 4-disc DVD cases. These are the same size as single 1-disc cases width wise, but hold 4. Great for consolidating!
-Have Original Xbox Cases. Green and Grey varities.
-Empty non-pc RE:4 case with cover art , but no manual or game. Let me know if you are interested in it.
Payments - Amazon GC , Amazon Payments, Paypal (pref. in that order )
Wants :(But always open to check lists)
Mass Effect 2 CE
Valkyrie DS
Star Ocean PSP
Fallout 3 GOTY CE
World of Disgaea (Broccoli Books)
Half Life 2 : Raising the Bar
Shadow Hearts : Covenant
Haunting Grounds
Resident Evil 4 : Wii
World Ends With You, The
Lego Star Wars Complete Saga
N/A for now (will see lists)
N/A for Now (will see lists)
N/A for Now (will see lists)
Edited by Pookymeister, 08 October 2014 - 04:08 PM.


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NATO's Mediterranean Dialogue
NATO's Mediterranean Dialogue was initiated in 1994 by the North Atlantic Council. It currently involves seven non-NATO countries of the Mediterranean region: Algeria, Egypt, Israel, Jordan, Mauritania, Morocco and Tunisia.more
Visit to NATO Headquarters of High-Level Opinion Leaders from Morocco27 May. 2014
A group of high-level Opinion Leaders from Morocco visited the NATO Headquarters on 27 May 2014, in the context of the 20th Anniversary of the Mediterranean Dialogue.more
Mauritanian Officers visit NATO HQ26 May. 2014
On 26 May 2014, a group of officers from the Mauritanian military academy visited NATO Headquarters for a series of briefings and discussions with officials from the Alliance's International Staff and International Military Staff.more
Responding to security challenges in Morocco19 May. 2014
Cyber defence and other global security issues such as chemical, biological, radiological and nuclear (CBRN) resilience and civil emergency were the focus of a NATO Science for Peace and Security information day held in Rabat, Morocco on 19 May.more
NATO's Mediterranean Dialogue & Istanbul Cooperation Initiative - Questions & Answers
What is the difference between NATO's Mediterranean Dialogue and the Istanbul Cooperation Initiative?more
History - Landmarks
- 02 Dec. 2008
- 06 Nov. 2008
- 07 Dec. 2007
- 03 Dec. 2007
Newspaper articles
The following articles, in pdf, have been graciously provided by their authors


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Hi all. I have wanted to get a decent camera for a while and it is a big birthday soon so i thought I would ask people to donate to my camera fund. I want to be able to take quality photos and not have to lug a massive camera around. I want to advance from a simple compact camera though. I would take pictures of outdoorsy type things and even photos of family etc.
I am torn between getting a simple bridge camera (it seems simple - has one lens etc) or a DSLR (could get a decent lens and take higher quality photos.
I am perhaps looking to pay up to or around £400 so not spending mega bucks.
Please could you help me!


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| hotels Rome | hotel Rome | three 3 star hotel Rome | hotel in Rome Italy
Intimate and elegant, in via Merulana, near Termini Station, just a short walk from the piazza and the Basilica of Santa Maria Maggiore, Hotel Amalfi stands out for its class and comfort among the 3-star hotels in the historic center of Rome. With 22 very comfortable, welcoming and functional rooms for vacations or business trips, a complimentary breakfast and numerous other services, an unforgettable vacation awaits you at this hotel in Rome.
Special offers
From April 18 2014 to April 12 2015
The hotel can provide gluten ...
Events in Rome and surroundings
From June 29 2014 to January 06 2015
Retrospective of Henri Cartier-Bresson


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Other titles in the Song of Ice and Fire series:
A Clash of Kings (A Song of Ice and Fire #2)by George R. R. Martin
Synopses & Reviews
Publisher Comments:
In this eagerly awaited sequel to A Game of Thrones, George R. R. Martin has created a work of unsurpassed vision, power, and imagination. A Clash of Kings transports us to a world of revelry and revenge, wizardry and warfare unlike any you have ever experienced.
A comet the color of blood and flame cuts across the sky. And from the ancient citadel of Dragonstone to the forbidding shores of Winterfell, chaos reigns. Six factions struggle for control of a divided land and the Iron Throne of the Seven Kingdoms, preparing to stake their claims through tempest, turmoil, and war. It is a tale in which brother plots against brother and the dead rise to walk in the night. Here a princess masquerades as an orphan boy; a knight of the mind prepares a poison for a treacherous sorceress; and wild men descend from the Mountains of the Moon to ravage the countryside. Against a backdrop of incest and fratricide, alchemy and murder, victory may go to the men and women possessed of the coldest steel...and the coldest hearts. For when kings clash, the whole land trembles.
"[Martin] provides a banquet for fantasy lovers with large appetites — and this is only the second course of a repast with no end in sight." Publishers Weekly
"The rewards are considerable: a backdrop of convincing depth and texture; intricate, flawless plotting; fully realized characters; and restrained, inventive magical/occult elements." Kirkus Reviews
"Aided by an appendix of kings and their courts, Clash can be enjoyed on its own, though many then may retreat to Game, reread Clash, and impatiently await more of Westeros." Roberta Johnson, Booklist
"Martin has created a rich world filled with characters whose desires for love and power drive them to extremes of nobility and betrayal. Fans of epic fantasy should appreciate this lavishly detailed sequel to A Game of Thrones." Library Journal
"This work of superior world building inhabited by fully-developed characters is for a mature audience because of the violence, strong language, and sexual encounters. Great cover and a great read!" VOYA
"A classic work of fantasy." Cleveland Plain-Dealer
This second novel of Martin's "New York Times" bestselling fantasy series, the sequel to "A Game of Thrones", transports readers to a world of revelry and revenge, wizardry and warfare--where six factions struggle for control of a divided land and the Iron Throne of the Seven Kingdoms. Includes 16-page preview of the upcoming hardcover, "A Storm of Swords".
About the Author
George R. R. Martin is the award-winning author of six novels, including Fevre Dream and The Armageddon Rag. For the last ten years, he has been a screenwriter for feature films and television and was a writer-producer of the TV series Beauty and the Beast as well as a story editor for The Twilight Zone. He lives in Santa Fe, New Mexico, with the lovely Parris, a big white dog called Mischa, and two cats named Augustus and Caligula who think they run the place.
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When you look back on your Arizona State game day memories, you won't remember what the food tasted like or what the exact scores were. You'll always remember who you were with – and thanks to today's technology, you'll always remember what you were wearing via the photos your friends are always snapping, no matter how embarrassing that could be. Prove that your impressive game day style will live on for years to come with this Jersey hat from Zephyr. Made from the same jersey material that your team wears on the field, this hat features an embroidered Arizona State wordmark on the crown, an embroidered team name on the back, and a contrast color flat bill. Throw it on the next time you head out to a Sun Devils game and save yourself from years of long-lasting embarrassment. S fits 7 - 7 1/8. M/L fits 7 1/4 - 7 3/8. XL fits 7 1/2 - 7 3/4. Sizes are approximate.
- 100% Polyester fabric
- Contrast color flat bill
- Imported
- Mesh body
- Officially licensed Sun Devils hat
- Quality embroidery
- Six panels with eyelets
- Stretch-fit
- Structured fit
Special event items are produced by manufacturers only after the outcome of a game or event. These are advanced sale items and will ship immediately after they are received in our warehouse.
Manufacturer direct items are shipped directly from the manufacturer. These items are not available for international or expedited shipping.
Customized items can be personalized with options such as your name, your favorite number, and/or designs. Some options may be limited by league rules.