Lagrange points L4 and L5 can stably contain a maximum mass limit before losing stability
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Retrieved encyclopedia data indicates that objects sharing orbits at Lagrange points L4 and L5 must maintain a mass ratio below a specific instability threshold relative to the central object.
stars, brown dwarfs, or stellar remnants and that have a mass ratio with the central object below the L4/L5 instability (M/Mcentral < 2/(25+√621) are
A planet is a large, rounded astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets by the most restrictive definition of the term: the terrestrial planets Mercury, Venus, Earth, and Mars, and the giant planets Jupiter, Saturn, Uranus, and Neptune. The best available theory of planet form
A planet's defining physical characteristic is that it is massive enough for the force of its own gravity to dominate over the electromagnetic forces binding its physical structure, leading to a state of hydrostatic equilibrium. This effectively means that all planets are spherical or spheroidal. Up to a certain mass, an object can be irregular in shape, but beyond that point, which varies depending on the chemical makeup of the object, gravity begins to pull an object towards its own centre of mass until the object collapses into a sphere.
Mass is the prime attribute by which planets are distinguished from stars. No objects between the masses of the Sun and Jupiter exist in the Solar System, but there are exoplanets of this size. The lower stellar mass limit is estimated to be around 75 to 80 times that of Jupiter (MJ). Some authors advocate that this be used as the upper limit for planethood, on the grounds that the internal physics of objects does not change between approximately one Saturn mass (beginning of significant self-compression) and the onset of hydrogen burning and becoming a red dwarf star. Beyond roughly 13 MJ (at least for objects with solar-type isotopic abundance), an object achieves conditions suitable for nuclear fusion of deuterium: this has sometimes been advocated as a boundary, even though deuterium burning does not last very long and most brown dwarfs have long since finished burning their deuterium. This is not universally agreed upon: the exoplanets Encyclopaedia includes objects up to 60 MJ, and the Exoplanet Data Explorer up to 24 MJ.
The smallest known exoplanet with an accurately known mass is PSR B1257+12A, one of the first exoplanets discovered, which was found in 1992 in orbit around a pulsar. Its mass is roughly half that of the planet Mercury. Even smaller is WD 1145+017 b, orbiting a white dwarf; its mass is roughly that of the dwarf planet Haumea, and it is typically termed a minor planet. The smallest known planet orbiting a main-sequence star other than the Sun is Kepler-37b, with a mass (and radius) that is probably slightly higher than that of the Moon. The smallest object in the Solar System generally agreed to be a…
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Explore This Section What is a Lagrange Point? March 27, 2018
Credit
NASA/WMAP Science Team
Language
english
What are they?: Lagrange Points
Lagrange points are positions in space where objects sent there tend to stay put. At Lagrange points, the gravitational pull of two large masses precisely equals the centripetal force required for a small object to move with them. These points in space can be used by spacecraft to reduce fuel consumption needed to remain in position.
Lagrange Points are positions in space where the gravitational forces of a two body system like the Sun and the Earth produce enhanced regions of attraction and repulsion. These can be used by spacecraft to reduce fuel consumption needed to remain in position.
Lagrange points are named in honor of Italian-French mathematician Josephy-Louis Lagrange.
There are five special points where a small mass can orbit in a constant pattern with two larger masses. The Lagrange Points are positions where the gravitational pull of two large masses precisely equals the centripetal force required for a small object to move with them. This mathematical problem, known as the "General Three-Body Problem" was considered by Lagrange in his prize winning paper ( Essai sur le Problème des Trois Corps , 1772).
Of the five Lagrange points, three are unstable and two are stable. The unstable Lagrange points - labeled L1, L2 and L3 - lie along the line connecting the two large masses. The stable Lagrange points - labeled L4 and L5 - form the apex of two equilateral triangl
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