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Dynamic Method
The dynamic method is a procedure for the determination of the masses of asteroids. The procedure gets its name from its use of the Newtonian laws of the ''dynamics,'' or motion, of asteroids as they move around the Solar System. The procedure works by taking multiple position measurements to determine the gravitational deflection caused when two or more asteroids move past each other. The method relies on the fact that the large number of known asteroids means they will occasionally move past one another at very close distances. If at least one of the two interacting bodies is large enough, its gravitational influence on the other can reveal its mass. The accuracy of the determined mass is limited by the precision and timing of the appropriate astrometric observations being made to determine the gravitational deflection caused by a given interaction. Because the method relies on detecting the amount of gravitational deflection induced during an interaction, the procedure work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asteroid
An asteroid is a minor planet of the Solar System#Inner solar system, inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. Of the roughly one million known asteroids the greatest number are located between the orbits of Mars and Jupiter, approximately 2 to 4 astronomical unit, AU from the Sun, in the main asteroid belt. Asteroids are generally classified to be of three types: C-type asteroid, C-type, M-type asteroid, M-type, and S-type asteroid, S-type. These were named after and are generally identified with carbonaceous, metallic, and silicaceous compositions, respectively. The size of asteroids varies greatly; the largest, Ceres (dwarf planet), Ceres, is almost across and qualifies as a dwarf planet. The total mass of all the asteroids combined is only 3% that of Earth's Moon. The majority of main belt asteroids follow slig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrometry
Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. History The history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis and Aristillus to discover Earth's precession. In doing so, he also developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions. Hipparchus's successor, Ptolemy, included a catalogue of 1,022 stars in his work the ''Almagest'', giving their location, coordinates, and brightness. In the 10th century, Abd al-Rahman al-Sufi carried out observations on the stars and described their positions, magn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orbital Resonance
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] |
Rutherford Scattering
In particle physics, Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model of the atom and eventually the Bohr model. Rutherford scattering was first referred to as Coulomb scattering because it relies only upon the static electricity, static electric (Coulomb) potential, and the minimum distance between particles is set entirely by this potential. The classical Rutherford scattering process of alpha particles against gold atomic nucleus, nuclei is an example of "elastic scattering" because neither the alpha particles nor the gold nuclei are internally excited. The Rutherford formula (see below) further neglects the recoil kinetic energy of the massive target nucleus. The initial discovery was made by Hans Geiger and Ernest Marsden in 1909 when they performed the Geiger–Marsden experiment, gold foil experime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McGraw-Hill
McGraw Hill is an American educational publishing company and one of the "big three" educational publishers that publishes educational content, software, and services for pre-K through postgraduate education. The company also publishes reference and trade publications for the medical, business, and engineering professions. McGraw Hill operates in 28 countries, has about 4,000 employees globally, and offers products and services to about 140 countries in about 60 languages. Formerly a division of The McGraw Hill Companies (later renamed McGraw Hill Financial, now S&P Global), McGraw Hill Education was divested and acquired by Apollo Global Management in March 2013 for $2.4 billion in cash. McGraw Hill was sold in 2021 to Platinum Equity for $4.5 billion. Corporate History McGraw Hill was founded in 1888 when James H. McGraw, co-founder of the company, purchased the ''American Journal of Railway Appliances''. He continued to add further publications, eventually establishin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptote
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. The word asymptote is derived from the Greek ἀσύμπτωτος (''asumptōtos'') which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve. There are three kinds of asymptotes: ''horizontal'', ''vertical'' and ''oblique''. For curves given by the graph of a function , horizontal asymptotes are horizontal lines that the graph of the function approaches as ''x'' tends to Vertical asymptotes are vertical lines near which t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Orbit
In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one. Under simplistic assumptions a body traveling along this trajectory will coast towards infinity, settling to a final excess velocity relative to the central body. Similarly to parabolic trajectories, all hyperbolic trajectories are also escape trajectories. The specific energy of a hyperbolic trajectory orbit is positive. Planetary flybys, used for gravitational slingshots, can be described within the planet's sphere of influence using hyperbolic trajectories. Parameters describing a hyperbolic trajectory Like an elliptical orbit, a hyperb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asteroids
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. Of the roughly one million known asteroids the greatest number are located between the orbits of Mars and Jupiter, approximately 2 to 4 AU from the Sun, in the main asteroid belt. Asteroids are generally classified to be of three types: C-type, M-type, and S-type. These were named after and are generally identified with carbonaceous, metallic, and silicaceous compositions, respectively. The size of asteroids varies greatly; the largest, Ceres, is almost across and qualifies as a dwarf planet. The total mass of all the asteroids combined is only 3% that of Earth's Moon. The majority of main belt asteroids follow slightly elliptical, stable orbits, revolving in the same direction as the Earth and taking from three to six years to com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrometry
Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. History The history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis and Aristillus to discover Earth's precession. In doing so, he also developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions. Hipparchus's successor, Ptolemy, included a catalogue of 1,022 stars in his work the ''Almagest'', giving their location, coordinates, and brightness. In the 10th century, Abd al-Rahman al-Sufi carried out observations on the stars and described their positions, magn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
