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Resonant Chain
In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects (binary resonance). The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies (i.e., their ability to alter or constrain each other's orbits). In most cases, this results in an ''unstable'' interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galilean Moon Laplace Resonance Animation 2
Generically, a Galilean (; ; ; ) is a term that was used in classical sources to describe the inhabitants of Galilee, an area of northern Israel and southern Lebanon that extends from the northern coastal plain in the west to the Sea of Galilee and the Jordan Rift Valley to the east. Later the term was used to refer to the early Christians by Roman emperors Julian and Marcus Aurelius, among others. Markus Cromhout describes 1st century Galileans as descendants of Hasmonean-era Judean immigrants. However, they identified as numerous identities, including Galilean, Sepphorean and more broadly, Judean or Israelite. Whilst they all adhered to a 'common Judaism', Galileans 'had a different social, economic and political matrix than Jews living in Judea or the Diaspora'. Other scholars disagree and attribute the conflation between Galileans and Judeans to Hellenistic-Roman culture, which grouped all 1st century Palestinian Jewish groups, and their related diasporas, as "Judean". ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saturn
Saturn is the sixth planet from the Sun and the second largest in the Solar System, after Jupiter. It is a gas giant, with an average radius of about 9 times that of Earth. It has an eighth the average density of Earth, but is over 95 times more massive. Even though Saturn is almost as big as Jupiter, Saturn has less than a third its mass. Saturn orbits the Sun at a distance of , with an orbital period of 29.45 years. Saturn's interior is thought to be composed of a rocky core, surrounded by a deep layer of metallic hydrogen, an intermediate layer of liquid hydrogen and liquid helium, and an outer layer of gas. Saturn has a pale yellow hue, due to ammonia crystals in its upper atmosphere. An electrical current in the metallic hydrogen layer is thought to give rise to Saturn's planetary magnetic field, which is weaker than Earth's, but has a magnetic moment 580 times that of Earth because of Saturn's greater size. Saturn's magnetic field strength is about a twen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonant Interaction
In nonlinear systems a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields. Its most prominent and well-developed forms appear in the study of gravity waves, but also finds numerous applications from astrophysics and biology to engineering and medicine. Theoretical work on partial differential equations provides insights into chaos theory; there are curious links to number theory. Resonant interactions allow waves to (elastically) scatter, diffuse or to become unstable. Diffusion processes are responsible for the eventual thermalization of most nonlinear systems; instabilities offer insight into high-dimensional chaos and turbulence. Discussion The underlying concept is that when the sum total of the energy and momentum of several vibrat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Musica Universalis
The ''musica universalis'' (literally universal music), also called music of the spheres or harmony of the spheres, is a philosophical concept that regards proportions in the movements of celestial bodies—the Sun, Moon, and planets—as a form of music. The theory, originating in ancient Greece, was a tenet of Pythagoreanism, and was later developed by 16th-century astronomer Johannes Kepler. Kepler did not believe this "music" to be audible, but felt that it could nevertheless be heard by the soul. The idea continued to appeal to scholars until the end of the Renaissance, influencing many schools of thought, including humanism. History The concept of the "music of the spheres" incorporates the metaphysical principle that mathematical relationships express qualities or "tones" of energy that manifests in numbers, visual angles, shapes and sounds—all connected within a pattern of proportion. Pythagoras first identified that the pitch of a musical note is an inverse prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galilean Moon
The Galilean moons (), or Galilean satellites, are the four largest moons of Jupiter. They are, in descending-size order, Ganymede, Callisto, Io, and Europa. They are the most readily visible Solar System objects after Saturn, the dimmest of the classical planets; though their closeness to bright Jupiter makes naked-eye observation very difficult, they are readily seen with common binoculars, even under night sky conditions of high light pollution. The invention of the telescope allowed astronomers to discover the moons in 1610. Through this, they became the first Solar System objects discovered since humans have started tracking the classical planets, and the first objects to be found to orbit any planet beyond Earth. They are planetary-mass moons and among the largest objects in the Solar System. All four, along with Titan, Triton, and Earth's Moon, are larger than any of the Solar System's dwarf planets. The largest, Ganymede, is the largest moon in the Solar Syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar System" and "solar system" structures in theinaming guidelines document. The name is commonly rendered in lower case ('solar system'), as, for example, in the ''Oxford English Dictionary'' an''Merriam-Webster's 11th Collegiate Dictionary''. is the gravitationally bound Planetary system, system of the Sun and the objects that orbit it. It Formation and evolution of the Solar System, formed about 4.6 billion years ago when a dense region of a molecular cloud collapsed, forming the Sun and a protoplanetary disc. The Sun is a typical star that maintains a hydrostatic equilibrium, balanced equilibrium by the thermonuclear fusion, fusion of hydrogen into helium at its stellar core, core, releasing this energy from its outer photosphere. As ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-body Problem
In physics, the -body problem is the problem of predicting the individual motions of a group of astronomical object, celestial objects interacting with each other gravitationally.Leimanis and Minorsky: Our interest is with Leimanis, who first discusses some history about the -body problem, especially Ms. Kovalevskaya's 1868–1888 twenty-year complex-variables approach, failure; Section 1: "The Dynamics of Rigid Bodies and Mathematical Exterior Ballistics" (Chapter 1, "The motion of a rigid body about a fixed point (Euler and Poisson equations)"; Chapter 2, "Mathematical Exterior Ballistics"), good precursor background to the -body problem; Section 2: "Celestial Mechanics" (Chapter 1, "The Uniformization of the Three-body Problem (Restricted Three-body Problem)"; Chapter 2, "Capture in the Three-Body Problem"; Chapter 3, "Generalized -body Problem"). Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars. In th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre-Simon Laplace
Pierre-Simon, Marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summarized and extended the work of his predecessors in his five-volume Traité de mécanique céleste, ''Mécanique céleste'' (''Celestial Mechanics'') (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. Laplace also popularized and further confirmed Isaac Newton, Sir Isaac Newton's work. In statistics, the Bayesian probability, Bayesian interpretation of probability was developed mainly by Laplace. Laplace formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplace operator, Laplacian differential operator, widely used in mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stability Of The Solar System
The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have historically been stable as observed, and will be in the "short" term, their weak gravitational effects on one another can add up in ways that are not predictable by any simple means. For this reason (among others), the Solar System is ''chaotic'' in the technical sense defined by mathematical chaos theory, and that chaotic behavior degrades even the most precise long-term numerical or analytic models for the orbital motion in the Solar System, so they cannot be valid beyond more than a few tens of millions of years into the past or future – about 1% its present age. The Solar System is stable on the time-scale of the existence of humans, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years, and that Earth's orbit will be relatively stable. Since Newton's law of gravitation (16 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Law Of Universal Gravitation
Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is Proportionality (mathematics)#Direct proportionality, proportional to the product of their masses and Proportionality (mathematics)#Inverse proportionality, inversely proportional to the square of the distance between their centers of mass. Separated objects attract and are attracted Shell theorem, as if all their mass were concentrated at their centers. The publication of the law has become known as the "Unification (physics)#Unification of gravity and astronomy, first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors. This is a general physical law derived from empirical observations by what Isaac Newton called ''inductive reasoning''. It is a part of classical mechanics and was formulated in Newton's work ''Philosophiæ Natura ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Definition Of Planet
The definition of the term ''planet'' has changed several times since the word was coined by the ancient Greeks. Greek astronomers employed the term (), 'wandering stars', for star-like objects which apparently moved over the sky. Over the millennia, the term has included a variety of different celestial bodies, from the Sun and the Moon to satellites and asteroids. In modern astronomy, there are two primary conceptions of a ''planet''. A ''planet'' can be an astronomical object that ''dynamically dominates'' its region (that is, whether it controls the fate of other smaller bodies in its vicinity) or it is defined to be in ''hydrostatic equilibrium'' (it has become gravitationally rounded and compacted). These may be characterized as the dynamical dominance definition and the geophysical definition. The issue of a clear definition for ''planet'' came to a head in January 2005 with the discovery of the trans-Neptunian object Eris, a body more massive than the smallest t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
