航空航天Right ascension赤经（英文Right ascension；缩写为RA；符号为α）是天文学使用在天球赤道坐标系统内的坐标值之一，通过天球两极并与天赤道垂直，另一个坐标值是赤纬。
In astronomy, right ascension (abbreviated RA; symbol α) is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the (hour circle of the) point in question above the Earth. When paired with declination, these astronomical coordinates specify the location of a point on the celestial sphere in the equatorial coordinate system. An old term, right ascension (Latin: ascensio recta) refers to the ascension, or the point on the celestial equator that rises with any celestial object as seen from Earth's equator, where the celestial equator intersects the horizon at a right angle. It contrasts with oblique ascension, the point on the celestial equator that rises with any celestial object as seen from a given latitude on Earth, where the celestial equator intersects the horizon at an oblique angle.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗在天体力学中，脱离速度、逃逸速度、脱离速率或逃逸速率是物体需要达到的最低速率，以脱离与主体的接触或其轨道，假设： 弹道轨迹——物体上没有其他力作用，包括推进力和摩擦力 没有其他产生重力的物体存在 虽然“逃逸速度”这个术语很常见，但准确而言，它是一个速率，而非速度，因为它与方向无关。由于两个物体之间的引力取决于它们的合并质量，所以逃逸速率也取决于质量。对于人造卫星和小型自然物体，物体的质量对合并质量的贡献可以忽略不计，因此通常忽略不计。 逃逸速率随着距离主体中心的距离而变化，物体在主体的引力影响下运动的速度也会变化。如果物体处于圆形或椭圆轨道上，其速度总是小于当前距离处的逃逸速率。相反，如果它处于双曲线轨迹上，其速度将始终高于当前距离处的逃逸速率。物体在抛物线轨迹上行进时，其速度总是与当前距离处的逃逸速率相同。 逃逸速率的计算通常用于确定物体是否会留在给定天体的引力影响范围内。例如，在太阳系探索中，了解探测器是否会继续绕地球运行或逃逸到日心轨道是有用的。还有助于了解探测器需要减速多少才能被目标天体引力捕获。
In celestial mechanics, escape velocity or escape speed is the minimum speed needed for an object to escape from contact with or orbit of a primary body, assuming: Ballistic trajectory – no other forces are acting on the object, such as propulsion and friction No other gravity-producing objects exist. Although the term escape velocity is common, it is more accurately described as a speed than as a velocity because it is independent of direction. Because gravitational force between two objects depends on their combined mass, the escape speed also depends on mass. For artificial satellites and small natural objects, the mass of the object makes a negligible contribution to the combined mass, and so is often ignored. Escape speed varies with distance from the center of the primary body, as does the velocity of an object traveling under the gravitational influence of the primary. If an object is in a circular or elliptical orbit, its speed is always less than the escape speed at its current distance.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗轨道倾角通常是参考平面和另一个平面或轴的方向之间的夹角。轴倾斜的表示法是行星的自转轴和通过行星的中心垂直于公转轨道平面的线之间所夹的角度。
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth directly above the Equator, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular orbit is that it is tilted, spending half an orbit over the northern hemisphere and half over the southern. If the orbit swung between 20° north latitude and 20° south latitude, then its orbital inclination would be 20°.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗轨道根数（或称轨道要素、轨道元素或轨道参数）是描述在牛顿运动定律和牛顿万有引力定律的作用下的天体或航天器，在其开普勒轨道上运动时，确定其轨道所必要的六个参数。由于运动的方式有许多种的参数表示法，依照选定的测量装置不同，对相同的轨道，有几种不同的方式来定义轨道根数。 这个问题包含三个自由度（轨道上的三个笛卡儿坐标系），所以每个独立的开普勒轨道（未受到摄动）经过解析后，可以由原始的笛卡尔数值以六个参数明确地定义天体的姿态和速度。因此，所有的轨道元素组合都明确的含有这六个元素。在数学上的明确解释和讨论可以参考以下的论述（参见：轨道状态向量）。
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 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. 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 trajectory of the opposite body is apparent; Keplerian elements describe these non-inertial trajectories. An orbit has two sets of Keplerian elements depending on which body is used as the point of reference.
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查看内容许可 ↗轨道周期（也称为公转周期）是给定的天体完成围绕另一个物体一次的轨道所需的时间。在天文学，它通常适用于围绕太阳运行的行星 或小行星、卫星绕轨道运行的行星、系外行星绕其母恒星运行，或联星的互绕。它也可以指人造卫星绕行星或卫星运行完成一个轨道所需的时间。 对于一般的天体，轨道周期是由轨道天体围绕其母天体公转360°公转决定的，例如地球绕太阳转。 天文学中的周期以时间单位表示，通常是小时、天或年。它的倒数是轨道频率，是一种转动频率，单位为赫兹。
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. It may also refer to the time it takes a satellite orbiting a planet or moon to complete one orbit. For celestial objects in general, the orbital period is determined by a 360° revolution of one body around its primary, e.g. Earth around the Sun. Periods in astronomy are expressed in units of time, usually hours, days, or years. Its reciprocal is the orbital frequency, a kind of revolution frequency, in units of hertz.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗在太空动力学，霍曼转移轨道（或译为郝曼转移轨道，Hohmann transfer orbit）是一种被用于变换太空船轨道的轨道操纵，途中只需两次引擎推进，相对地节省燃料。例如，霍曼转移可用于将卫星的轨道从近地轨道提升到地球静止轨道。在理想情况下，初始轨道和目标轨道都是圆形的且共平面的。该机动是透过将飞行器置于与初始轨道和目标轨道均相切的椭圆转移轨道来完成的。此机动使用两次冲量引擎燃烧：第一次建立转移轨道，第二次调整轨道以匹配目标。 霍曼操纵通常会使用尽可能低的冲力（这会消耗一定比例的ΔV，因此也会消耗一定比例的推进剂）来完成转移，但相较于较高冲力的转移，需要较长的航行时间。在某些情况下，当一个轨道比另一个轨道大很多时，双椭圆转移可以使用更少的冲力，但却需要更长的航行时间。 此种轨道操纵名称来自德国物理学家瓦尔特·霍曼 (Walter Hohmann) 的名字命名，他于1925年出版的著作《天体的可及性》(Die Erreichbarkeit der Himmelskörper) 中对此进行了描述。霍曼在某种程度上受到德国科幻小说作家库尔德·拉斯维茨 (Kurd Lasswitz) 及其1897年著作《在两个行星上》的影响。
In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. For example, a Hohmann transfer could be used to raise a satellite's orbit from low Earth orbit to geostationary orbit. In the idealized case, the initial and target orbits are both circular and coplanar. The maneuver is accomplished by placing the craft into an elliptical transfer orbit that is tangential to both the initial and target orbits. The maneuver uses two impulsive engine burns: the first establishes the transfer orbit, and the second adjusts the orbit to match the target. The Hohmann maneuver often uses the lowest possible amount of impulse (which consumes a proportional amount of delta-v, and hence propellant) to accomplish the transfer, but requires a relatively longer travel time than higher-impulse transfers. In some cases where one orbit is much larger than the other, a bi-elliptic transfer can use even less impulse, at the cost of even greater travel time.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗太空动力学是研究火箭和航天器在飞行中所受的力及其在力作用下的运动的学科，又称轨道力学、天体动力学、航天动力学和星际航行动力学。这些物体的运动通常是根据牛顿运动定律和万有引力定律计算的。 太空动力学是太空任务设计和控制中的核心学科。 太空动力学研究的运动包括航天器的质心运动，称轨道运动；航天器相对于自身质心的运动和各部分的相对运动，称姿态运动；以及与航天器发射、航天器轨道机动飞行有关的火箭运动。航天器的飞行过程一般分为三个阶段。 发射段：航天器由运载器（多级火箭、航天飞机等）携带，从地面起飞达到预定的高度和速度。 运行轨道段：航天器主要在万有引力等自然界外力作用下运动。为了保持预定的轨道，有时需要少量的推力;有时为了轨道机动则需要较大的推力。 降落轨道段：一些航天器需要返回地球表面或者降落在目标天体的表面。这时航天器在火箭推力和介质阻力等作用下，离开运行轨道降落到天体表面。 在以上各个阶段中，航天器的运动都包含了轨道运动和姿态运动两个部分。在运行轨道段，一般可以将两种运动分别求解。而在发射段和降落段，两种运动关系密切，需要联立求解。研究航天器的运动是以牛顿力学和火箭力学为基础的，一般不考虑相对论效应。太空动力学以数学、力学、控制理论为基础。它的研究内容分为轨道运动、姿态运动和火箭运动三个部分。
Orbital mechanics , astrodynamics or space dynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from laws of motion and of universal gravitation derived by Isaac Newton. Astrodynamics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbit dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near the Sun).
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗平近点角（Mean Anomaly）在轨道力学中是轨道上的物体在辅助圆上相对于中心点的运行角度，在测量上不同于其他的近点角，平近点角与时间的关系是线性的。因为与时间是线性的关系，因此要计算在轨道上两点之间移动所需的时间是非常容易的。计算两点之间的平近点角就能得知其间的不同，只要知道，两点之间的移动时间相对于整个轨道 2 π {\displaystyle 2\pi } 的周期是一个简单的比例式（也就是 M 2 − M 1 2 π = t T {\displaystyle {\frac {M_{2}-M_{1}}{2\pi }}={\frac {t}{T}}} ）。
In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed as an angle which can be used in calculating the position of that body in the classical two-body problem. It is the angular distance from the pericenter which a fictitious body would have if it moved in a circular orbit, with constant speed, in the same orbital period as the actual body in its elliptical orbit.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗真近点角 (True Anomaly)（ T {\displaystyle T\,\!} ，也可以写成 ν {\displaystyle \nu \ } ）在天文学是轨道平面上，卫星与近地点之间的椭球焦点角距，如图中的角z-s-p。
In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse (the point around which the object orbits). The true anomaly is usually denoted by the Greek letters ν or θ, or the Latin letter f, and is usually restricted to the range 0–360° (0–2π rad). The true anomaly f is one of three angular parameters (anomalies) that can be used to define a position along an orbit, the other two being the eccentric anomaly and the mean anomaly.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗近点幅角（ω）也做近心点幅角。是描述在轨道上天体在近拱点（最靠近中心的点）时，相对于升交点（由南向北经过参考平面的点）的角度，也是轨道要素之一。这个角度是在轨道平面上量度的，方向则是天体运动的方向（在特定的轨道型式中会换用特定的名词，像日心轨道是"近日点角"，地心轨道是"近地点角"，一般称为"近点幅角"或"近拱点角"）。近点幅角为0度的意义是当天体最靠近中心点时也同时由南向北的通过参考平面；近点幅角为90度的意义则是当天体最靠近中心点时，位于参考平面的最北方。将近点幅角加上升交点经度就得到近心点经度。
The argument of periapsis (also called argument of perifocus or argument of pericenter), symbolized as ω (omega), is one of the orbital elements of an orbiting body. Parametrically, ω is the angle from the body's ascending node to its periapsis, measured in the direction of motion. For specific types of orbits, terms such as argument of perihelion (for heliocentric orbits), argument of perigee (for geocentric orbits), argument of periastron (for orbits around stars), and so on, may be used (see apsis for more information). An argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the orbiting body will reach periapsis at its northmost distance from the plane of reference. Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗活力公式（vis viva equation），又称为轨道能量守恒方程（orbital energy conservation equation），是天体力学中的一个方程，表示二体问题中的总能量守恒，即轨道上任一点的动能与势能之和为常数。 该公式的名称来自拉丁文“活力”（vis viva）一词，其物理意义与动能类似，但现已不再使用。
In astrodynamics, the vis-viva equation is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight which is the gravitational force determined by the product of the mass of the object and the strength of the surrounding gravitational field. Vis viva (Latin for "living force") is a term from the history of mechanics and the name given to the orbital equation originally derived by Isaac Newton. It represents the principle that the difference between the total work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗平均运动， n {\displaystyle n\,\!} 是表征一颗卫星绕其椭圆轨道运行速度的物理量。除了轨道是正圆形外，平均运动都是一个平均值，并不能反映出即时的角速率。 在卫星轨道参数中，平均运动的单位一般为“周期/天”。
In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body. The concept applies equally well to a small body revolving about a large, massive primary body or to two relatively same-sized bodies revolving about a common center of mass. While nominally a mean, and theoretically so in the case of two-body motion, in practice the mean motion is not typically an average over time for the orbits of real bodies, which only approximate the two-body assumption. It is rather the instantaneous value which satisfies the above conditions as calculated from the current gravitational and geometric circumstances of the body's constantly-changing, perturbed orbit. Mean motion is used as an approximation of the actual orbital speed in making an initial calculation of the body's position in its orbit, for instance, from a set of orbital elements.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗与数学更进一步与密切的发展，请参见二体问题和开普勒问题。 开普勒轨道是天体力学描述在三维空间的椭圆、抛物线或双曲线轨道上运动的物体在二维轨道平面上的轨道运动（开普勒轨道也可以是直线）。它只考虑两个点状物体之间的引力作用，而忽略与其它物体之间引力交互作用的摄动、大气拖曳、太阳辐射压、非球面的中心物体等等。因此说它是二体问题，也就是所谓的开普勒问题的一个特殊解。在经典力学中，它也不会考虑到广义相对论的影响。开普勒轨道可以用六个轨道要素呈现出各种不同型式的轨道。 在大多数的应用中，在中心的质量被假设为整个系统的质量中心所在。经过分析，两个质量近似的物体可以用开普勒轨道叙述它们绕质点系的质心（即引力中心）的运动。
In celestial mechanics, a Kepler orbit (or Keplerian orbit, named after the German astronomer Johannes Kepler) is the motion of one body relative to another, in the form of an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space. A Kepler orbit can also tend toward a straight line. It considers only the point-like gravitational attraction of two bodies, neglecting perturbations due to gravitational interactions with other objects, atmospheric drag, solar radiation pressure, a non-spherical central body, and so on. It is thus said to be a solution of a special case of the two-body problem, known as the Kepler problem. As a theory in classical mechanics, it also does not take into account the effects of general relativity. Keplerian orbits can be parameterized into six orbital elements in various ways. In most applications, there is a large central body, the center of mass of which is assumed to be the center of mass of the entire system.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗航空航天工程（英语：Aerospace Engineering 或 Aeronautical and Astronautical Engineering）是航空工程和航天工程的工程学的总称，涉及航空飞行器与航天飞行器有关的工程领域。它包含固体力学、流体力学（特别是空气动力学）、航天动力学、天体力学、热力学、导航、航空电子、自动控制、电机工程学、机械工程、通信工程、材料科学和制造等领域。
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is similar, but deals with the electronics side of aerospace engineering. "Aeronautical engineering" was the original term for the field. As flight technology advanced to include vehicles operating in outer space, the broader term "aerospace engineering" has come into use. Aerospace engineering, particularly the astronautics branch, is often colloquially referred to as "rocket science".
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗多普勒效应（英语：Doppler effect）是波源与观察者有相对运动时，“观察者接受到的波频率”与“波源发出的波频率”并不相同的现象。多普勒效应属于一种运动学效应，也属于一种频移效应，任何波都具有这一效应。频移（frequency shift）即“频率偏移”，又称频差，也就是波在传播过程中频率发生变化的现象。 波源与观察者相对接近或相向运动时，波被压缩，观察者接收到（感受到）的频率变高（声调变尖，光波发生蓝移）；两者相对远离或相背运动时，波被拉伸，观察者接收到（感受到）的频率变低（声调变沉，光波发生“红移”）。频移的程度（频差）与相对运动速度成正比。 多普勒效应的例子如：远方急驶过来的火车鸣笛声变得尖细（即频率变高，波长变短），而离我们而去的火车鸣笛声变得低沉（即频率变低，波长变长），就是多普勒效应的现象，同样现象也发生在汽车鸣响与火车的敲钟声。 这一现象最初由奥地利物理学家克里斯蒂安·多普勒于1842年发现。荷兰气象学家拜斯·巴洛特在1845年让一队喇叭手站在一辆从乌得勒支附近疾驶而过的敞篷火车上吹奏，他在站台上测到了音调的改变。 多普勒效应从19世纪下半叶起就被天文学家用来测量恒星的视向速度。现已被广泛用来佐证观测天体和人造卫星的运动。
The Doppler effect (also Doppler shift) is the change in the frequency or, equivalently, the period of a wave in relation to an observer who is moving relative to the source of the wave. It is named after the physicist Christian Doppler, who described the phenomenon in 1842. A common example of a Doppler shift is the change of pitch heard when a vehicle approaches and recedes from an observer. Compared to the emitted sound, the received sound has a higher pitch during the approach, identical at the instant of passing by, and lower pitch during the recession. When the source of the sound wave is moving towards the observer, each successive cycle of the wave is emitted from a position closer to the observer than the previous cycle. Hence, from the observer's perspective, the period or time between cycles is reduced, meaning the frequency is increased.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗辐射压（英语：Radiation pressure），亦称光压，是电磁辐射对所有暴露在其下的物体表面所施加的压力。如果被吸收，压力是流量密度除以光速；如果完全被反射，辐射压将会加倍。例如，太阳辐射的能量在地球的流量密度是 1367 W / m 2 {\displaystyle 1367W/m^{2}} ，所以吸收状态下的辐射压是 4.6 μ P a {\displaystyle 4.6\mu Pa} （参考气候模型）。
Radiation pressure (also known as light pressure) is mechanical pressure exerted upon a surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is absorbed, reflected, or otherwise emitted (e.g. black-body radiation) by matter on any scale (from macroscopic objects to dust particles to gas molecules). The associated force is called the radiation pressure force, or sometimes just the force of light. The forces generated by radiation pressure are generally too small to be noticed under everyday circumstances; however, they are important in some physical processes and technologies. This particularly includes objects in outer space, where it is usually the main force acting on objects besides gravity, and where the net effect of a tiny force may have a large cumulative effect over long periods of time.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗四元数（英语：Quaternion）是由爱尔兰数学家威廉·卢云·哈密顿在1843年创立出的数学概念。通常记为H，或 H {\displaystyle \mathbb {H} } 。 从明确地角度而言，四元数是复数的不可交换延伸。如把四元数的集合考虑成多维实数空间的话，四元数则代表着一个四维空间，相对于复数为二维空间。 作为用于描述现实空间的坐标表示方式，人们在复数的基础上创造了四元数并以a+bi+cj+dk的形式说明空间点所在位置。 i、j、k作为一种特殊的虚数单位参与运算，并有以下运算规则：i0=j0=k0=1，i2=j2=k2=-1 对于i、j、k本身的几何意义可以理解为一种旋转，其中i旋转代表X轴与Y轴相交平面中X轴正向向Y轴正向的旋转，j旋转代表Z轴与X轴相交平面中Z轴正向向X轴正向的旋转，k旋转代表Y轴与Z轴相交平面中Y轴正向向Z轴正向的旋转，-i、-j、-k分别代表i、j、k旋转的反向旋转。
In mathematics, the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of addition, subtraction, multiplication, and division, but with four real-number components instead of two. Unlike with the complex numbers, quaternion multiplication is not commutative, meaning that the result of multiplying two quaternions depends on their order. Quaternions can be used to represent vectors in three-dimensional space, which provides a definition of the quotient of two vectors. Quaternions were first described by the Irish mathematician and physicist William Rowan Hamilton in 1843, and in his honor the set of all quaternions is conventionally denoted by H {\displaystyle \mathbb {H} } or H.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗在航天动力学和宇宙空间动力学中，所谓的重力助推（gravity assist；也被称为重力弹弓效应或绕行星变轨）是利用行星或其他天体的相对运动和引力改变飞行器的轨道和速度，以此来节省燃料、时间和计划成本。重力助推既可用于加速飞行器，也能用于降低飞行器速度。
A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense. Gravity assistance can be used to accelerate a spacecraft, that is, to increase or decrease its speed or redirect its path. The "assist" is provided by the motion of the gravitating body as it pulls on the spacecraft. Any gain or loss of kinetic energy and linear momentum by a passing spacecraft is correspondingly lost or gained by the gravitational body, in accordance with Newton's Third Law. The gravity assist maneuver was first used in 1959 when the Soviet probe Luna 3 photographed the far side of Earth's Moon, and it was used by interplanetary probes from Mariner 10 onward, including the two Voyager probes' notable flybys of Jupiter and Saturn.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗在概率论与统计学中，协方差（英语：Covariance）用于衡量随机变量间的相关程度。
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. The sign of the covariance shows the tendency in the linear relationship between the variables. Covariance is positive when variables tend to show similar behavior and negative when variables tend to show opposite behavior. The magnitude of the covariance is the geometric mean of the variances that are shared for the two random variables, where a larger magnitude means two variables more strongly depend on each other. Covariance has units of measurement, and the magnitude of the covariance is affected by said units. This means changing the units (e.g., from meters to millimeters) changes the covariance value proportionally, making it difficult to assess the strength of the relationship from the covariance alone. In some situations, it is desirable to compare the strength of the joint association between different pairs of random variables that do not necessarily have the same units.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗卡尔曼滤波（英语：Kalman filter）是一种高效率的递归滤波器（自回归滤波器），它能够从一系列的不完全及包含噪声的测量中，估计动态系统的状态。卡尔曼滤波会根据各测量量在不同时间下的值，考虑各时间下的联合分布，再产生对未知变量的估计，因此会比只以单一测量量为基础的估计方式要准。卡尔曼滤波得名自主要贡献者之一的鲁道夫·卡尔曼。 卡尔曼滤波在技术领域有许多的应用。常见的有飞机及太空船的导引、导航及控制。卡尔曼滤波也广为使用在时间序列的分析中，例如信号处理及计量经济学中。卡尔曼滤波也是机器人运动规划及控制的重要主题之一，有时也包括在轨迹优化。卡尔曼滤波也用在中轴神经系统运动控制的建模中。因为从给与运动命令到收到感觉神经的回授之间有时间差，使用卡尔曼滤波有助于建立符合实际的系统，估计运动系统的目前状态，并且更新命令。 卡尔曼滤波的算法是二步骤的程序。在估计步骤中，卡尔曼滤波会产生有关目前状态的估计，其中也包括不确定性。只要观察到下一个量测（其中一定含有某种程度的误差，包括随机噪声）。会通过加权平均来更新估计值，而确定性越高的量测加权比重也越高。算法是迭代的，可以在实时控制系统中执行，只需要目前的输入量测、以往的计算值以及其不确定性矩阵，不需要其他以往的信息。 使用卡尔曼滤波不用假设误差是正态分布，不过若所有的误差都是正态分布，卡尔曼滤波可以得到正确的条件概率估计。 也发展了一些扩展或是广义的卡尔曼滤波，例如运作在非线性系统的扩展卡尔曼滤波及无迹卡尔曼滤波（英语：unscented Kalman filter）。底层的模型类似隐马尔可夫模型，不过潜在变量的状态空间是连续的，而且所有潜在变量及可观测变量都是正态分布。
In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but also relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán. Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. Kalman filtering is also important for robotic motion planning and control, and can be used for trajectory optimization.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗在天文动力学中，ΔV字面上的意思是“方向和速度的变化”。但ΔV也有其他含义，即一个用来测量轨迹变换需要多少“作用力”的标量单位，比如在改物质的轨道。
Delta-v (also known as "change in velocity"), symbolized as Δ v {\textstyle {\Delta v}} and pronounced /dɛltə viː/, as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as launching from or landing on a planet or moon, or an in-space orbital maneuver. It is a scalar that has the units of speed. As used in this context, it is not the same as the physical change in velocity of said spacecraft. A simple example might be the case of a conventional rocket-propelled spacecraft, which achieves thrust by burning fuel. Such a spacecraft's delta-v, then, would be the change in velocity that spacecraft can achieve by burning its entire fuel load. Delta-v is produced by reaction engines, such as rocket engines, and is proportional to the thrust per unit mass and the burn time. It is used to determine the mass of propellant required for the given maneuver through the Tsiolkovsky rocket equation.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗地面站（英语：Ground station）、又称地球站或地球终端站，是航天器通信系统地面部分的一个重要组成部分。地面站的基本作用是与航天器进行行星外通信或接收来自外太空的无线电波，亦可用于接收由其它地面站经卫星转发来的信号。地面站可能位于地球表面或地球的大气层之中。地面站与太空船经由发送或接收超高频率（SHF）或极高频率（EHF）的频段（如微波）的无线电波来达成与航天器通信的目的。 当地面站成功地发送无线电波到太空船上时，便形成了一个电波通信链接（反之亦然）。抛物线天线是一个地面站的主要电波通信设备。 地面站有固定式与移动式两种类型。 ITU 无线电规则第一条之第三款描述了多种形式的固定式与移动式地面站，以及它们与卫星之间的关系。 专门的卫星地面站或卫星跟踪站能与通信卫星为主的人造卫星进行远程电波通信；其他的地面站则与载人太空站或无人太空探测器进行通信。另有一类主要接收遥测数据或跟踪空间任务，或不运行于地球静止轨道上的卫星的地面站，它们被称为地面跟踪站（英语：Ground tracking station）或空间跟踪站，简称跟踪站。 当一个人造卫星或航天器进入地面站的视野中，便称其为可视卫星（参见轨道通过（英语：Orbital pass））。人造卫星可同时与多个的地面站进行通信。而当一颗卫星同时位于两个地面站的视野中时，便称其具有共同视野。
A ground station, Earth station, or Earth terminal is a terrestrial radio station designed for extraplanetary telecommunication with spacecraft (constituting part of the ground segment of the spacecraft system), or reception of radio waves from astronomical radio sources. Ground stations may be located either on the surface of the Earth, or in its atmosphere. Earth stations communicate with spacecraft by transmitting and receiving radio waves in the super high frequency (SHF) or extremely high frequency (EHF) bands (e.g. microwaves), or in the optical bands for laser communication (then called Optical Ground Station, OGS). When a ground station successfully transmits radio waves to a spacecraft (or vice versa), it establishes a telecommunications link. A principal telecommunications device of the ground station is the parabolic antenna. Ground stations may have either a fixed or itinerant position. Article 1 § III of the International Telecommunication Union (ITU) Radio Regulations describes various types of stationary and mobile ground stations, and their interrelationships.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗阻力（英语：Drag），又称后曳力或流体阻力，是物体在流体动力学中相对运动所产生与运动方向相反的力。 对于一个在流体中移动的物体，阻力为周围流体对物体施力，在移动方向的反方向上分量的总和。而施力和移动方向垂直的分量一般则视为升力。因此阻力和物体移动方向恰好相反，像飞机前进时会产生推力来克服阻力的影响。 在航天动力学中，大气阻力可以视为太空飞行器在发射时的低效率，其影响则是在发射时需要额外的能量，不过在返回轨道时大气阻力有助于太空飞行器减速，可减少减速额外需要的能量，不过大气阻力产生的热量甚至可以将物体熔化。
In fluid dynamics, drag, sometimes referred to as fluid resistance, and also known as viscous force, is a force acting opposite to the direction of motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers, or between a fluid and a solid surface. Drag forces tend to decrease fluid velocity relative to the solid object in the fluid's path. Unlike other resistive forces, drag force depends on velocity. Drag force is proportional to the relative velocity for low-speed flow and is proportional to the velocity squared for high-speed flow. This distinction between low and high-speed flow is measured by the Reynolds number.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗轨道测定（Orbit Determination，亦称轨道确定或轨道决定）是估算行星、小行星、彗星、月球、行星卫星、人造卫星、和太空船等天体绕行其引力源的轨道的技术。透过确定天体的轨道元素，不仅可以推测天体未来的位置，并透过观测来验证；也可以知道还未被发现前的位置。太空船进行星际旅行时，需要不断变换轨道，也需要确定变换后的轨道，以便准确航向目的地。 观测是取得一系列资料以送入轨道测定的算法。通常一位地基的观测者的观测资料包括时间标记、方位角、高度角、斜距和/或范围率值。因为肉眼的观测不能满足精密定轨的需求，所以都要使用望远镜或雷达装置。 轨道测定之后，数学的推演技术可以用于预测物体未来的轨道位置。随着时间的推移，物体的实际轨道路径往往会偏离预期的路径（尤其是天体的摄动是很难预测的，像是大气阻力等）；新的轨道测定使用新的观测，并有助于重新角准轨道的知识。 美国和做伙的国家，范围广泛的光学、和雷达的资源，允许联合太空作战中心观测与搜集地球轨道上所有的物体。这些观测用于新的轨道计算和测定，以及维护卫星目录的总体精度。防撞计算可以使用这些资料来计算一个轨道上的物体与另一个轨道上的物体碰撞的概率。如果在目前轨道上的碰撞风险是不能接受的，卫星的营运单位可能会决定调整轨道（如果碰撞的概率很低，它是不可能调整轨道的。因为这样做将会导致卫星的推进剂迅速耗尽）。当观测的数量和品质提高，轨道测定技术的准确性也会提高，就会减少提醒卫星营运单位注意的假警报。其它国家，包括俄罗斯和中国，都有类似的追踪资源。
Orbit determination is the estimation of orbits of objects such as moons, planets, and spacecraft. One major application is to allow tracking newly observed asteroids and verify that they have not been previously discovered. The basic methods were discovered in the 17th century and have been continuously refined. Observations are the raw data fed into orbit determination algorithms. Observations made by a ground-based observer typically consist of time-tagged azimuth, elevation, range, and/or range rate values. Telescopes or radar apparatus are used, because naked-eye observations are inadequate for precise orbit determination. With more or better observations, the accuracy of the orbit determination process also improves, and fewer "false alarms" result. After orbits are determined, mathematical propagation techniques can be used to predict the future positions of orbiting objects.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗宽高比（英语：Aspect ratio，也称为纵横比）是几何形状在不同尺寸的比值。举个例子，当矩形方向为横向时的宽高比值，是其长边与短边的比率。 宽高比的书写方式通常是以冒号分隔两个整数（ x : y {\displaystyle x:y} ），在少数情况也会写成简易的分数或十进制小数；x值和y值并不代表实际的宽度和高度，而是代表宽度和高度之间的比例。例如， 8 : 5 {\displaystyle 8:5} 、 16 : 10 {\displaystyle 16:10} 、 1.6 : 1 {\displaystyle 1.6:1} 、 8 / 5 {\displaystyle 8/5} 、 1.6 {\displaystyle 1.6} 都是表示相同宽高比的方式。 在超矩形等具有二维以上的对象中，宽高比仍然可以定义为长边与短边之比。
The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, 8⁄5 and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗马赫（M或Ma，英语：Mach number）是流体力学中的无量纲数，表示通过边界的流速与局部音速之比。 M = u c {\displaystyle \mathrm {M} ={\frac {u}{c}}} ， 其中： M为局部马赫数， u为相对于边界的局部流速， c为介质中的音速。 马赫数的命名是为了纪念奥地利学者恩斯特·马赫（德语：Ernst Mach）。 马赫一般用于飞机、火箭等航空航天飞行器。由于声音在空气中的传播速度随着不同的条件而不同，因此马赫也只是一个相对的单位，每“一马赫”的具体速度并不固定。在低温下声音的传播速度低些，一马赫对应的具体速度也就低一些。因此相对来说，在高空比在低空更容易达到较高的马赫数。 1947年10月14日，查克·叶格驾驶X-1试验飞机在加州南部上空脱离B-29母机，上升到一万二千米高空，并在此高度上达到每小时1078公里的速度，首次突破音障，超过了一马赫。 当马赫数Ma<0.3时，流体所受的压力不足以压缩流体，仅会造成流体的流动。在此状况下，流体密度不会随压力而改变，此种流场称为亚音速流（Subsonic flow），流场可视为不可压缩流场。一般的水流及大气中空气的流动，譬如湍急的河流、台风风场和汽车的运动等，皆属于不可压缩流场。但流体在高速运动（流速接近音速或大于音速）时，流体密度会随压力而改变，此时气体之流动称为可压缩流场（Compressible flow）。当马赫数Ma>1.0，称为超音速流（Supersonic flow），此类流况在航空动力学中才会遇到。 任何超过音速移动的物体会从头部向后产生锥状的能量激波（速度越高锥角越小），其力量可能会破坏接触物体，而且会摩擦制造高温，因此其体型设计必须尽量限制在锥状激波的范围内，同时要采用高抗热性的材料。 在地表的速度换算相当于一马赫≈1235km/h，340m/s。飞行物在相同的速度下，其马赫会因所在高度空气的音速不同而有差异；高度越高，音速越低，而使得马赫越高，因此高空飞行的速度会降低以免产生冲击。
The Mach number (M or Ma), often only Mach (; German: [max]), is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after Austrian physicist and philosopher Ernst Mach. M = u c , {\displaystyle \mathrm {M} ={\frac {u}{c}},} where: M is the local Mach number, u is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel), and c is the speed of sound in the medium, which in air varies with the square root of the thermodynamic temperature. By definition, at Mach 1, the local flow velocity u is equal to the speed of sound. At Mach 0.65, u is 65% of the speed of sound (subsonic), and, at Mach 1.35, u is 35% faster than the speed of sound (supersonic). The local speed of sound, and hence the Mach number, depends on the temperature of the surrounding gas.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗高超声速（英语：hypersonic），也称高超声速或超高音速，为空气动力学名词，意指速度较超声速还高出许多的状态。在1970年代，这个词通常指5马赫（5倍音速，约1700m/s）或更高的速度。高超声速流态（hypersonic regime）是超声速流态的分支。 高超声速气流与亚音速气流性质迥异。当一飞行器加速到高超声速，路径中几乎所有的空气特性剧烈地改变。不过尽管有如此明显的界线，对于“高超声速”的定义仍有一些争议。其中一个定义是整架飞行器各部分速度皆在1马赫或之上。更技术性地定义指出：整架飞行器周遭的所有气流速度皆是高超声速才能称作是高超声速，这样的情形对寻常设计的飞行器来说，通常是出现在1.2马赫上下。0.8到1.2马赫的范围因此称作跨音速。 考虑到连高超声速的简单定义都有争议，就不会对“定义高超声速更加困难”这件事感到意外，因为成为“高超声速”并不会有任何气流的物理性质改变。一般来说，在5马赫附近，一些效应的组合整体来说变得重要。高超声速流态常定义为冲压发动机（ramjet）无法产生净推力的速度。这是一个模糊的定义，因为存在有一些改装提议，使得喷气发动机在这样的速度范围仍可操作，例如高超声速燃烧冲压发动机（Scramjet）。
In aerodynamics, hypersonic speed refers to speeds much faster than the speed of sound, usually more than approximately Mach 5. The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since individual physical changes in the airflow (like molecular dissociation and ionization) occur at different speeds; these effects collectively become important around Mach 5–10. The hypersonic regime can also be alternatively defined as speeds where specific heat capacity changes with the temperature of the flow as the kinetic energy of the moving object is converted into heat. Hypersonic weapons are typically boost-glide vehicles or cruise missiles designed for aerodynamic flight and maneuvering above Mach 5. High hypersonic speeds are experienced during atmospheric entry. Spaceplanes are designed to be capable of flight in this regime. The North American X-15 and the Space Shuttle orbiter are the only crewed spaceplanes to fly faster than Mach 5.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗大气制动，或称空气制动，是指一种透过将航天器环绕轨道的最低点（近拱点）降低到天体的大气层之内，透过空气阻力来减速，以降低轨道最高点（远拱点）的轨道机动。大气制动通常用于进入一个拥有大气层的天体之低轨道的任务之中，由于通常航天器抵达一天体时，与天体的相对速度非常快，因此使用大气制动相对于直接使用火箭发动机，所需的燃料更少。
Aerobraking is a spaceflight maneuver that reduces the high point of an elliptical orbit (apoapsis) by flying the vehicle through the atmosphere at the low point of the orbit (periapsis). The resulting drag slows the spacecraft. Aerobraking is used when a spacecraft requires a low orbit after arriving at a body with an atmosphere, as it requires less fuel than using propulsion to slow down. A more extreme maneuver is aerocapture, where a spacecraft uses an atmosphere to perform orbit insertion, decelerating from a flyby trajectory.
来源、授权与使用说明
维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗激波（英语：Shock Wave），又译作冲击波、骇波或激波，属于紊流的一种传播形式。如同其他通常形式下的波动，激波也可以通过介质传输能量。在某些不存在物理介质的特殊情况下，激波可以通过场，如电磁场来传输能量。激波的主要特点表现为介质特性（如压力、温度、或速度）在激波前后发生了一个像正的阶梯函数般的突然变化。与此相应的负的阶跃则为膨胀波。声学激波其速度一般高于通常波速（在空气中即音速）。 激波随距离的增加耗散很快，与孤波（另一种形式的非线性波）不同。而且，膨胀波总是伴随着激波，并最终与激波合并。这部分抵消了激波的影响。声爆，一种超音速飞机通过时产生的声学现象，即是由激波——膨胀波对激波的耗散和湮灭所产生的。
In mechanics, specifically acoustics, a shock wave, shockwave, or shock is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium, but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium. For the purpose of comparison, in supersonic flows, additional increased expansion may be achieved through an expansion fan, also known as a Prandtl–Meyer expansion fan. The accompanying expansion wave may approach and eventually collide and recombine with the shock wave, creating a process of destructive interference. The sonic boom associated with the passage of a supersonic aircraft is a type of sound wave produced by constructive interference. Unlike solitons (another kind of nonlinear wave), the energy and speed of a shock wave alone dissipates relatively quickly with distance. When a shock wave passes through matter, energy is preserved but entropy increases.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗质心为多质点系统的质量中心。若对该点施力，系统会沿着力的方向运动、不会旋转。质点位置对质量加权取平均值，可得质心位置。以质心的概念计算力学通常比较简单。质心对应的英文有 center of mass 与 barycenter（或 barycentre，源自古希腊的 βαρύς heavy + κέντρον centre）。后者指两个或多个物体互绕物体的质量中心。 Barycenter 在天文学和天文物理上是很重要的一个观念。从一个物体的质心转移一个距离至彼此的质心，可以简化成二体问题来进行计算。在两个天体当中，有一个比另一个大许多的情况下（在相对封闭的环境），质心通常会位于质量较大的天体之内。因而较小的天体会在轨道上绕着共同的质心运动，而较大的仅仅只会略微"抖动"。地月系统就是这样的状况，俩者的质心距离地球的中心4,671公里，而地球的半径是6,378公里。当两个天体的质量差异不大时，质心通常会介于两者之间，而这两个天体会呈现互绕的现象。冥王星和它的卫星夏戎，还有许多双小行星和联星，都是这种情况的例子。木星和太阳的质量相差虽然超过1,000倍，但因为它们之间的距离较大，也是这一类型的例子。 在天文学，质心坐标是非转动坐标，其原点是两个或多个天体的质心所在。国际天球参考系统是质心坐标之一，它的原点是太阳系的质心所在之处。 在几何学，质心不等同于重心，是二维形状的几何中心。
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For a rigid body containing its center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for the application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
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