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Orbital Perturbation Analysis
In astronomy, perturbation is the complex motion of a massive body subjected to forces other than the gravitational attraction of a single other massive body. The other forces can include a third (fourth, fifth, etc.) body, resistance, as from an atmosphere, and the off-center attraction of an oblate or otherwise misshapen body. Introduction The study of perturbations began with the first attempts to predict planetary motions in the sky. In ancient times the causes were unknown. Isaac Newton, at the time he formulated his laws of motion and of gravitation, applied them to the first analysis of perturbations, recognizing the complex difficulties of their calculation. Many of the great mathematicians since then have given attention to the various problems involved; throughout the 18th and 19th centuries there was demand for accurate tables of the position of the Moon and planets for marine navigation. The complex motions of gravitational perturbations can be broken down. The h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moon Perturbation Diagram
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of Australia). The Moon is a planetary-mass object with a differentiated rocky body, making it a satellite planet under the geophysical definitions of the term and larger than all known dwarf planets of the Solar System. It lacks any significant atmosphere, hydrosphere, or magnetic field. Its surface gravity is about one-sixth of Earth's at , with Jupiter's moon Io being the only satellite in the Solar System known to have a higher surface gravity and density. The Moon orbits Earth at an average distance of , or about 30 times Earth's diameter. Its gravitational influence is the main driver of Earth's tides and very slowly lengthens Earth's day. The Moon's orbit around Earth has a sidereal period of 27.3 days. During each synodic per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-body Problem
In classical mechanics, the two-body problem is to predict the motion of two massive objects which are abstractly viewed as point particles. The problem assumes that the two objects interact only with one another; the only force affecting each object arises from the other one, and all other objects are ignored. The most prominent case of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful insights and predictions. A simpler "one body" model, the " central-force problem", treats one object as the immobile source of a force acting on the other. One then seeks to predict the motion of the single remaining mobile object. Such an approximation can give useful results when one object is much more massive than the other (as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth the mass of the Sun. Jupiter is the List of brightest natural objects in the sky, third brightest natural object in the Earth's night sky after the Moon and Venus, and it has been observed since Pre-history, prehistoric times. It was named after the Jupiter (mythology), Roman god Jupiter, the king of the gods. Jupiter is primarily composed of hydrogen, but helium constitutes one-quarter of its mass and one-tenth of its volume. It probably has a rocky core of heavier elements, but, like the other giant planets in the Solar System, it lacks a well-defined solid surface. The ongoing contraction of Jupiter's interior generates more heat than it receives from the Sun. Because of its rapid rotation, the planet' ... [...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 gravity, gravitationally bound system of the Sun and the objects that orbit it. It Formation and evolution of the Solar System, formed 4.6 billion years ago from the gravitational collapse of a giant interstellar molecular cloud. The solar mass, vast majority (99.86%) of the system's mass is in the Sun, with most of the Jupiter mass, remaining mass contained in the planet Jupiter. The four inner Solar System, inner system planets—Mercury (planet), Mercury, Venus, Earth and Mars—are terrest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celestial Mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data. History Modern analytic celestial mechanics started with Isaac Newton's Principia of 1687. The name "celestial mechanics" is more recent than that. Newton wrote that the field should be called "rational mechanics." The term "dynamics" came in a little later with Gottfried Leibniz, and over a century after Newton, Pierre-Simon Laplace introduced the term "celestial mechanics." Prior to Kepler there was little connection between exact, quantitative prediction of planetary positions, using geometrical or arithmetical techniques, and contemporary discussions of the physical causes of the planets' motion. Johannes Kepler Johannes Kepler (1571–1630) was the first to closely integrate the predictive geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Osculating Orbit
In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. an elliptic or other conic one) that it would have around its central body if perturbations were absent. That is, it is the orbit that coincides with the current orbital state vectors (position and velocity). Etymology The word '' osculate'' is Latin for "kiss". In mathematics, two curves osculate when they just touch, without (necessarily) crossing, at a point, where both have the same position and slope, i.e. the two curves "kiss". Kepler elements An osculating orbit and the object's position upon it can be fully described by the six standard Kepler orbital elements (osculating elements), which are easy to calculate as long as one knows the object's position and velocity relative to the central body. The osculating elements would remain constant in the absence of perturbations. Real astronomical orbits experience pert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variation Of Parameters
In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations. For first-order inhomogeneous linear differential equations it is usually possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods leverage heuristics that involve guessing and do not work for all inhomogeneous linear differential equations. Variation of parameters extends to linear partial differential equations as well, specifically to inhomogeneous problems for linear evolution equations like the heat equation, wave equation, and vibrating plate equation. In this setting, the method is more often known as Duhamel's principle, named after Jean-Marie Duhamel (1797–1872) who first applied the method to solve the inhomogeneous heat equation. Sometimes variation of parameters itself is called Duhamel's principle and vice versa. History Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Series Expansion
In mathematics, a series expansion is an expansion of a function into a series, or infinite sum. It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division). The resulting so-called ''series'' often can be limited to a finite number of terms, thus yielding an approximation of the function. The fewer terms of the sequence are used, the simpler this approximation will be. Often, the resulting inaccuracy (i.e., the partial sum of the omitted terms) can be described by an equation involving Big O notation (see also asymptotic expansion). The series expansion on an open interval will also be an approximation for non-analytic functions. Types of series expansions There are several kinds of series expansions, listed below. A ''Taylor series'' is a power series based on a function's derivatives at a single point. More specifically, if a function f: U\to\mathbb is infinitely differentiable around ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same orbit, but certain schemes, each consisting of a set of six parameters, are commonly used in astronomy and orbital mechanics. A real orbit and its elements change over time due to gravitational perturbations by other objects and the effects of general relativity. A Kepler orbit is an idealized, mathematical approximation of the orbit at a particular time. Keplerian elements The traditional orbital elements are the six Keplerian elements, after Johannes Kepler and his laws of planetary motion. When viewed from an inertial frame, two orbiting bodies trace out distinct trajectories. Each of these trajectories has its focus at the common center of mass. When viewed from a non-inertial frame centered on one of the bodies, only the traj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satellite
A satellite or artificial satellite is an object intentionally placed into orbit in outer space. Except for passive satellites, most satellites have an electricity generation system for equipment on board, such as solar panels or radioisotope thermoelectric generators (RTGs). Most satellites also have a method of communication to ground stations, called Transponder (satellite communications), transponders. Many satellites use a Satellite bus, standardized bus to save cost and work, the most popular of which is small CubeSats. Similar satellites can work together as a group, forming Satellite constellation, constellations. Because of the high launch cost to space, satellites are designed to be as lightweight and robust as possible. Most communication satellites are radio Broadcast relay station, relay stations in orbit and carry dozens of transponders, each with a bandwidth of tens of megahertz. Satellites are placed from the surface to orbit by launch vehicles, high enough to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sky, night, but their immense distances from Earth make them appear as fixed stars, fixed points of light. The most prominent stars have been categorised into constellations and asterism (astronomy), asterisms, and many of the brightest stars have proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. The observable universe contains an estimated to stars. Only about 4,000 of these stars are visible to the naked eye, all within the Milky Way galaxy. A star's life star formation, begins with the gravitational collapse of a gaseous nebula of material composed primarily of hydrogen, along with helium and trace amounts of heavier elements. Its stellar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mercury Perturbation Comparison
Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Mercury (toy manufacturer), a brand of diecast toy cars manufactured in Italy * Mercury Communications, a British telecommunications firm set up in the 1980s * Mercury Drug, a Philippine pharmacy chain * Mercury Energy, an electricity generation and retail company in New Zealand * Mercury Filmworks, a Canadian independent animation studio * Mercury General, a multiple-line American insurance organization * Mercury Interactive, a software testing tools vendor * Mercury Marine, a manufacturer of marine engines, particularly outboard motors * Mercury Systems, a defense-related information technology company Computing * Mercury (programming language), a functional logic programming language * Mercury (metadata search system), a data search system f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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