Task: Question Answering
Input (English): Context: In the classical physics observed in everyday life, if something has mass and takes up space, it is said to be composed of matter; this includes atoms (and thus molecules) and anything made up of these, but not other energy phenomena or waves such as light or sound. More generally, however, in (modern) physics, matter is not a fundamental concept because a universal definition of it is elusive: elementary constituents of atoms may not take up space individually, and massless particles may be composed to form objects that have mass (even when at rest)., General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the "" is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations., A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. This partial case of a circle of a sphere is opposed to a "small circle", the intersection of the sphere and a plane that does not pass through the center. Any diameter of any great circle coincides with a diameter of the sphere, and therefore all great circles have the same circumference as each other, and have the same center as the sphere. A great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean 3-space is a great circle of exactly one sphere., Physics (from , from "phúsis" "nature") is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental scientific disciplines, the main goal of physics is to understand how the universe behaves., The Einstein field equations (EFE; also known as "Einstein's equations") are the set of 10 equations in Albert Einstein's general theory of relativity that describes the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stressenergy tensor)., In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model., In classical mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta; SI unit kg · m/s) is the product of the mass and velocity of an object, quantified in kilogram-meters per second. It is dimensionally equivalent to impulse, the product of force and time, quantified in newton-seconds. Newton's second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. For example, a heavy truck moving rapidly has a large momentum, and it takes a large or prolonged force to get the truck up to this speed, and would take a similarly large or prolonged force to bring it to a stop. If the truck were lighter, or moving more slowly, then it would have less momentum and therefore require less impulse to start or stop., In mathematics graph theory is the study of "graphs", which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of "vertices", "nodes", or "points" which are connected by "edges", "arcs", or "lines". A graph may be "undirected", meaning that there is no distinction between the two vertices associated with each edge, or its edges may be "directed" from one vertex to another; see Graph (discrete mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered. Graphs are one of the prime objects of study in discrete mathematics., Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and the Sun and the rotation of the Earth., A star is a luminous sphere of plasma held together by its own gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth. Historically, the most prominent stars were grouped into constellations and asterisms, the brightest of which gained proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the stars in the Universe, including all stars outside our galaxy, the Milky Way, are invisible to the naked eye from Earth. Indeed, most are invisible from Earth even through the most powerful telescopes., Newton's law of universal gravitation states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. 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 Naturalis Principia Mathematica" ("the "Principia""), first published on 5 July 1687. (When Newton's book was presented in 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him; see the History section below.), In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as a functions of time and space. Since the field equation is a partial differential equation, there are families of solutions which represent a variety of physical possibilities. Usually, there is not just a single equation, but a set of coupled equations which must be solved simultaneously. Field equations are not ordinary differential equations since a field depends on space and time, which requires at least two variables., The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion (e.g. to the north). Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies., Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect. A closely related term is interconnectivity, which deals with the interactions of interactions within systems: combinations of many simple interactions can lead to surprising emergent phenomena. "Interaction" has different tailored meanings in various sciences. Changes can also involve interaction., Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. , In physics, mass is a property of a physical body. It is the measure of an object's resistance to acceleration (a change in its state of motion) when a net force is applied. It also determines the strength of its mutual gravitational attraction to other bodies. The basic SI unit of mass is the kilogram (kg)., Albert Einstein (14 March 1879  18 April 1955) was a German-born theoretical physicist. He developed the general theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics). Einstein's work is also known for its influence on the philosophy of science. Einstein is best known in popular culture for his massenergy equivalence formula (which has been dubbed "the world's most famous equation"). He received the 1921 Nobel Prize in Physics for his "services to theoretical physics", in particular his discovery of the law of the photoelectric effect, a pivotal step in the evolution of quantum theory., In Newtonian physics , free fall is any motion of a body where gravity is the only force acting upon it . In the context of general relativity , where gravitation is reduced to a space - time curvature , a body in free fall has no force acting on it and moves along a geodesic . The present article only concerns itself with free fall in the Newtonian domain . An object in the technical sense of free fall may not necessarily be falling down in the usual sense of the term . An object moving upwards would not normally be considered to be falling , but if it is subject to the force of gravity only , it is said to be in free fall . The moon is thus in free fall . In a uniform gravitational field , in the absence of any other forces , gravitation acts on each part of the body equally and this is weightlessness , a condition that also occurs when the gravitational field is zero ( such as when far away from any gravitating body ) . A body in free fall experiences `` 0 g '' . The term `` free fall '' is often used more loosely than in the strict sense defined above . Thus , falling through an atmosphere without a deployed parachute , or lifting device , is also often referred to as free fall . The aerodynamic drag forces in such situations prevent them from producing full weightlessness , and thus a skydiver 's `` free fall '' after reaching terminal velocity produces the sensation of the body 's weight being supported on a cushion of air ., Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework., In physics, spacetime is any mathematical model that combines space and time into a single interwoven continuum. Since 300 BCE, the spacetime of our universe has historically been interpreted from a Euclidean space perspective, which regards space as consisting of three dimensions, and time as consisting of one dimension, the "fourth dimension". By combining space and time into a single manifold called Minkowski space in 1908, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels., In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates:, A planet is an astronomical body orbiting a star or stellar remnant that
The term "planet" is ancient, with ties to history, astrology, science, mythology, and religion. Several planets in the Solar System can be seen with the naked eye. These were regarded by many early cultures as divine, or as emissaries of deities. As scientific knowledge advanced, human perception of the planets changed, incorporating a number of disparate objects. In 2006, the International Astronomical Union (IAU) officially adopted a resolution defining planets within the Solar System. This definition is controversial because it excludes many objects of planetary mass based on where or what they orbit. Although eight of the planetary bodies discovered before 1950 remain "planets" under the modern definition, some celestial bodies, such as Ceres, Pallas, Juno and Vesta (each an object in the solar asteroid belt), and Pluto (the first trans-Neptunian object discovered), that were once considered planets by the scientific community, are no longer viewed as such., In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". The term "geodesic" comes from "geodesy", the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle. The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph., In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity. Weight is a vector whose magnitude (a scalar quantity), often denoted by an italic letter "W", is the product of the mass "m" of the object and the magnitude of the local gravitational acceleration "g"; thus: . The unit of measurement for weight is that of force, which in the International System of Units (SI) is the newton. For example, an object with a mass of one kilogram has a weight of about 9.8 newtons on the surface of the Earth, and about one-sixth as much on the Moon. In this sense of weight, a body can be weightless only if it is far away (in principle infinitely far away) from any other mass. Although weight and mass are scientifically distinct quantities, the terms are often confused with each other in everyday use (i.e. comparing and converting force weight in pounds to mass in kilograms and vice versa)., Earth, otherwise known as the world, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets., Geodesy,  also known as geodetics, geodetic engineering or geodetics engineering  a branch of applied mathematics and earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth (or any planet), including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal motion, tides, and polar motion. For this they design global and national control networks, using space and terrestrial techniques while relying on datums and coordinate systems., In physics, energy is the property that must be transferred to an object in order to perform work on  or to heat  the object, and can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the mechanical work of moving it a distance of 1 metre against a force of 1 newton., Modern physics is the post-Newtonian conception of physics. It implies that classical descriptions of phenomena are lacking, and that an accurate, "modern", description of nature requires theories to incorporate elements of quantum mechanics or Einsteinian relativity, or both. In general, the term is used to refer to any branch of physics either developed in the early 20th century and onwards, or branches greatly influenced by early 20th century physics., Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward (or "gravitate" toward) one another, including planets, stars and galaxies. Since energy and mass are equivalent, all forms of energy, including light, also cause gravitation and are under the influence of it. On Earth, gravity gives weight to physical objects and causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing, forming stars  and the stars to group together into galaxies  so gravity is responsible for many of the large scale structures in the Universe. Gravity has an infinite range, although its effects become increasingly weaker on farther objects., Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is visible to the human eye and is responsible for the sense of sight. Visible light is usually defined as having wavelengths in the range of 400700 nanometres (nm), or 4.00 × 10 to 7.00 × 10 m, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). This wavelength means a frequency range of roughly 430750 terahertz (THz)., The Universe is all of time and space and its contents. It includes planets, moons, minor planets, stars, galaxies, the contents of intergalactic space, and all matter and energy. The size of the entire Universe is unknown., In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F., In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:, In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that curvature is not necessarily zero., Subject: free fall, Relation: part_of, Options: (A) 18th century (B) albert einstein (C) applied mathematics (D) asteroid belt (E) body (F) book (G) center (H) classical mechanics (I) continuum (J) curve (K) differential calculus (L) discovery (M) discrete mathematics (N) dynamics (O) earth (P) electromagnetic radiation (Q) engineering (R) equation (S) eye (T) frame of reference (U) general relativity (V) geodesy (W) geometry (X) graph (Y) graph theory (Z) gravity ([) hand (\) history (]) human (^) integral calculus (_) international system of units (`) law (a) lead (b) linear algebra (c) mass (d) mathematics (e) may (f) medium (g) moon (h) nature (i) order (j) part (k) phenomenon (l) physics (m) plasma (n) popular culture (o) quantum mechanics (p) radiation (q) reasoning (r) science (s) sea (t) sky (u) solar system (v) spacetime (w) special relativity (x) state (y) system (z) theory ({) uniform (|) universe (}) variety (~) word () work
Output (English): classical mechanics