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The Lagrangian points (IPA: /ləˈgreɪndʒiən/, French pronunciation: [lagʁɑ̃ʒjɑ̃]; also Lagrange point, L-point, or libration point), are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with respect to the 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 rotate with them. They are analogous to geostationary orbits in that they allow an object to be in a "fixed" position in space rather than an orbit in which its relative position changes continuously.

A more precise but technical definition is that the Lagrangian points are the stationary solutions of the circular restricted three-body problem.^[1] For example, given two massive bodies in circular orbits around their common center of mass, there are five positions in space where a third body, of comparatively negligible mass, could be placed which would then maintain its position relative to the two massive bodies. As seen in a rotating reference frame with the same period as the two co-orbiting bodies, the gravitational fields of two massive bodies combined with the centrifugal force are in balance at the Lagrangian points, allowing the third body to be stationary with respect to the first two bodies.^[2]

In astronomy, the adjective 'Trojan' refers to an asteroid or natural satellite (moon) that shares the same orbit as a larger planet or moon, but does not collide with the latter because it orbits around one of the two Lagrangian points of stability, L₄ and L₅, which lie 60° ahead of and behind the larger object.




The term originally referred to asteroids orbiting around Jupiter's Lagrangian points. Subsequently other objects have been found orbiting the Lagrangian points of other planets. In addition, Trojan moons are known to orbit the Lagrangian points of some of Saturn's larger moons.



• The term 'Trojan asteroids' normally refers only to Jupiter Trojans.
• 5261 Eureka, (101429) 1998 VF₃₁, (121514) 1999 UJ₇, and 2007 NS₂ are Mars Trojans^[1].
• Six Neptune Trojans^[2] are known.

A Trojan moon is a natural satellite of a planet occupying the L₄ or L₅ equilateral Lagrangian points of a primary-moon system. They are named by analogy with the Trojan asteroids, which occupy the L₄ and L₅ points of the Sun-Jupiter system.

Four examples are known, all in Saturn's system: Telesto and Calypso bracket Tethys, whilst Helene and the newly discovered Polydeuces bracket Dione. The Earth-Moon points have been repeatedly searched for Trojans, but nothing else than a possible slight overabundance of dust (see Kordylewski clouds) has ever been found.

Astronomers using the National Science Foundation's

Very Long Baseline Array (VLBA) have discovered jets of plasma blasted from
the cores of distant galaxies at speeds within one-tenth of one
percent of the speed of light, placing these plasma jets among
the fastest objects yet seen in the Universe.

"This tells us that the physical processes at the cores of these
galaxies, called blazars, are extremely energetic and are capable
of propelling matter very close to the absolute cosmic speed limit,"

Briefly a blazar, is an object thet have the following
characteristics:

1) It appear optically point-like on the sky, i.e. not appear
widespread like a galaxy or a nebula. Some blazars have nebulae around
them (are fuzzy), but most of the light comes from a point source.

2) Their spectra appear to be smooth (i.e. no strong absorption lines
that a star might have) and flatter than a star. These two properties by
themselves would make them a quasar.

3) Their visible light is often partially polarized.

4) Their output in all wavelength bands varies more rapidly, and by a
larger amount than a classical quasar, with a flare-like behaviour.

5) Many blazar emits a significant fraction of their radiation at energy
above 100 MeV. Their flux is peaked in high bands around 10Mev-1Gev for
the LBL (red-blazar) class, around 1GeV-100GeV for the HBL (blue-blazar)
class and around 200Gev-1TeV for the few TeV-blazar.