biologia: Lagrange point

Evidence: 100 • authority: 72

In celestial mechanics, the Lagrange points (), also called the Lagrangian points or libration points, are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. Mathematically, this involves the solution of the restricted three-body problem. Normally, the two massive bodies exert an unbalanced gravitational force at a point, altering the orbit of any other celestial body at that point. At the Lagrange points, the gravitational forces of the two large bodies and the centrifugal pseudo-force balance each other. This can make Lagrange points an excellent location for satellites, as orbit corrections, and hence fuel requirements, needed t…

Evidence: 82 • authority: 72

The Jupiter trojans, commonly called trojan asteroids or simply trojans, are a large group of asteroids that share the planet Jupiter's orbit around the Sun. Relative to Jupiter, each trojan librates around one of Jupiter's stable Lagrange points: either L4, existing 60° ahead of the planet in its orbit, or L5, 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average semi-major axis of about 5.2 AU. The first Jupiter trojan discovered, 588 Achilles, was spotted in 1906 by German astronomer Max Wolf. More than 15,300 Jupiter trojans have been found as of October 2025. By convention, they are each named from Greek mythology af…

Evidence: 82 • authority: 72

In astronomy, a trojan is a small celestial body (mostly asteroids) that shares the orbit of a larger body, remaining in a stable orbit approximately 60° ahead of or behind the main body near one of its Lagrangian points L4 and L5. Trojans can share the orbits of planets or of large moons. Trojans are one type of co-orbital object. In this arrangement, a star and a planet orbit about their common barycenter, which is close to the center of the star because it is usually much more massive than the orbiting planet. In turn, a much smaller mass than both the star and the planet, located at one of the Lagrangian points of the star–planet system, is subject to a combined gravitational force that…

Evidence: 68 • authority: 92

NASA'S <i>Lucy</i> Mission to Trojan Asteroids: Unraveling the History of the Outer Solar System.. Lucy is a NASA Discovery-class mission to send a highly capable and robust spacecraft to investigate primitive bodies near both the L 4 and L 5 Lagrange points with Jupiter; the Jupiter Trojan asteroids. This heretofore unexplored population of planetesimals from the outer planetary system holds vital clues to deciphering the history of the Solar System. Due to an unusual and fortuitous orbital configuration, Lucy will perform a comprehensive investigation that visits eight Trojans, including all the recognized taxonomic classes, a collisional family member and a near equal-mass bi…

Evidence: 68 • authority: 90

Origin and Evolution of Jupiter’s Trojan Asteroids. Abstract The origin of the Jupiter Trojan asteroids has long been a mystery. Dynamically, the population, which is considerably smaller than the main asteroid belt, librates around Jupiter’s stable L4 and L5 Lagrange points, 60 deg ahead and behind Jupiter. It is thought that these bodies were captured into these orbits early in solar system history, but any capture mechanism must also explain why the Trojans have an excited inclination distribution, with some objects reaching inclinations of 35°. The Trojans themselves, individually and in aggregate, also have spectral and physical properties that appear consistent with many small bodies…

Evidence: 68 • authority: 90

Origin and Evolution of Trojan Asteroids. The regions around the L4 and L5 Lagrangian points of Jupiter are populated by two large swarms of asteroids called the Trojans. They may be as numerous as the main-belt asteroids and their dynamics is peculiar, involving a 1:1 resonance with Jupiter. Their origin probably dates back to the formation of Jupiter: the Trojan precursors were planetesimals orbiting close to the growing planet. Different mechanisms, including the mass growth of Jupiter, collisional diffusion, and gas drag friction, contributed to the capture of planetesimals in stable Trojan orbits before the final dispersal. The subsequent evolution of Trojan asteroids is the outcome of…

Evidence: 61 • authority: 92

Search for L5 Earth Trojans with DECam.. Most of the major planets in the Solar System support populations of co-orbiting bodies, known as Trojans, at their L4 and L5 Lagrange points. In contrast, Earth has only one known co-orbiting companion. This paper presents the results from a search for Earth Trojans using the DECam instrument on the Blanco Telescope at CTIO. This search found no additional Trojans in spite of greater coverage compared to previous surveys of the L5 point. Therefore, the main result of this work is to place the most stringent constraints to date on the population of Earth Trojans. These constraints depend on assumptions regarding the underlying population properties,…

Evidence: 61 • authority: 90

Manifolds in the Solar System and application to L4-L5 asymmetry of Trojan asteroids. The arches of chaos (Todorović et al. 2020) consist in an ornamental structure of manifolds generated by all planets connected in a series of arches that spread throughout the whole Solar System. In this work we propose to investigate the nature of the strongest ones, stemming from Jupiter, and their implications for small body dynamics in the various regions of the phase-space. As a pivotal case, we consider the well-known open problem in our solar system concerning the observed asymmetry in the number and phase-space distribution of Trojan asteroids around Jupiter's equilateral equilibrium points L4 and…

Evidence: 61 • authority: 72

In astronomy, a co-orbital configuration is a configuration of two or more astronomical objects (such as asteroids, moons, or planets) orbiting at the same, or very similar, distance from their primary; i.e., they are in a 1:1 mean-motion resonance. (Or 1:−1 if orbiting in opposite directions.) There are several classes of co-orbital objects, depending on their point of libration. The most common and best-known class is the trojan, which librates around one of the two stable Lagrangian points (Trojan points), L4 and L5, 60° ahead of and behind the larger body respectively. Another class is the horseshoe orbit, in which objects librate around 180° from the larger body. Objects librating arou…

Evidence: 61 • authority: 72

The Mars trojans are a group of trojan objects that share the orbit of the planet Mars around the Sun. They can be found around the two Lagrangian points 60° ahead of and behind Mars. The origin of the Mars trojans is not well understood. One hypothesis suggests that they were primordial objects left over from the formation of Mars that were captured in its Lagrangian points as the Solar System was forming. However, spectral studies of the Mars trojans indicate this may not be the case. Another explanation involves asteroids chaotically wandering into the Mars Lagrangian points later in the Solar System's formation. This is also questionable considering the short dynamical lifetimes of thes…

Evidence: 54 • authority: 90

Investigating Trojan Asteroids at the L4/L5 Sun-Earth Lagrange Points. Investigations of Earth's Trojan asteroids will have benefits for science, exploration, and resource utilization. By sending a small spacecraft to the Sun-Earth L4 or L5 Lagrange points to investigate near-Earth objects, Earth's Trojan population can be better understood. This could lead to future missions for larger precursor spacecraft as well as human missions. The presence of objects in the Sun-Earth L4 and L5 Lagrange points has long been suspected, and in 2010 NASA's Wide-field Infrared Survey Explorer (WISE) detected a 300 m object. To investigate these Earth Trojan asteroid objects, it is both essential and feasi…

Evidence: 47 • authority: 92

Orbital stability analysis and photometric characterization of the second Earth Trojan asteroid 2020 XL<sub>5</sub>.. Trojan asteroids are small bodies orbiting around the L 4 or L 5 Lagrangian points of a Sun-planet system. Due to their peculiar orbits, they provide key constraints to the Solar System evolution models. Despite numerous dedicated observational efforts in the last decade, asteroid 2010 TK 7 has been the only known Earth Trojan thus far. Here we confirm that the recently discovered 2020 XL 5 is the second transient Earth Trojan known. To study its orbit, we used archival data from 2012 to 2019 and observed the object in 2021 from three ground-based observatories.…