Position (geometry)In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P. In other words, it is the displacement or translation that maps the origin to P: The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.
Four-velocityIn physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space. Physical events correspond to mathematical points in time and space, the set of all of them together forming a mathematical model of physical four-dimensional spacetime. The history of an object traces a curve in spacetime, called its world line.
Angular velocityIn physics, angular velocity (symbol ω, sometimes Ω), also known as angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, , represents the angular speed (or angular frequency), the rate at which the object rotates (spins or revolves).
Software development kitA software development kit (SDK) is a collection of software development tools in one installable package. They facilitate the creation of applications by having a compiler, debugger and sometimes a software framework. They are normally specific to a hardware platform and operating system combination. To create applications with advanced functionalities such as advertisements, push notifications, etc; most application software developers use specific software development kits.
ForceIn physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. It is measured in the SI unit of newton (N) and often represented by the symbol F.
Terrestrial planetA terrestrial planet, telluric planet, or rocky planet, is a planet that is composed primarily of silicate rocks or metals. Within the Solar System, the terrestrial planets accepted by the IAU are the inner planets closest to the Sun: Mercury, Venus, Earth and Mars. Among astronomers who use the geophysical definition of a planet, two or three planetary-mass satellites – Earth's Moon, Io, and sometimes Europa – may also be considered terrestrial planets; and so may be the rocky protoplanet-asteroids Pallas and Vesta.
Planet NinePlanet Nine is a hypothetical ninth planet in the outer region of the Solar System. Its gravitational effects could explain the peculiar clustering of orbits for a group of extreme trans-Neptunian objects (ETNOs), bodies beyond Neptune that orbit the Sun at distances averaging more than 250 times that of the Earth. These ETNOs tend to make their closest approaches to the Sun in one sector, and their orbits are similarly tilted. These alignments suggest that an undiscovered planet may be shepherding the orbits of the most distant known Solar System objects.
Vector-valued functionA vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the dimension of the function's domain has no relation to the dimension of its range. A common example of a vector-valued function is one that depends on a single real parameter t, often representing time, producing a vector v(t) as the result.
Dwarf planetA dwarf planet is a small planetary-mass object that is in direct orbit of the Sun, smaller than any of the eight classical planets but still a world in its own right. The prototypical dwarf planet is Pluto. The interest of dwarf planets to planetary geologists is that they may be geologically active bodies, an expectation that was borne out in 2015 by the Dawn mission to and the New Horizons mission to Pluto. Astronomers are in general agreement that at least the nine largest candidates are dwarf planets: , , , , , , , , and .
Definition of planetThe definition of planet has changed several times since the word was coined by the ancient Greeks. Greek astronomers employed the term ἀστέρες πλανῆται (), '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'.
Four-forceIn the special theory of relativity, four-force is a four-vector that replaces the classical force. The four-force is defined as the rate of change in the four-momentum of a particle with respect to the particle's proper time: For a particle of constant invariant mass , where is the four-velocity, so we can relate the four-force with the four-acceleration as in Newton's second law: Here and where , and are 3-space vectors describing the velocity, the momentum of the particle and the force acting on it respectively.
Vector calculusVector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations.
