Velocity in the context of "Group velocity"

Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei (/ˌɡælɪˈleɪoʊ ˌɡælɪˈleɪ/ GAL-il-AY-oh GAL-il-AY, US also /ˌɡælɪˈliːoʊ -/ GAL-il-EE-oh -⁠, Italian: [ɡaliˈlɛːo ɡaliˈlɛi]) or mononymously as Galileo, was an Italian astronomer, physicist, and engineer, sometimes described as a polymath. He was born in the city of Pisa, then part of the Duchy of Florence. Galileo has been called the father of observational astronomy, modern-era classical physics, the scientific method, and modern science.

Galileo studied speed and velocity, gravity and free fall, the principle of relativity, inertia, projectile motion, and also worked in applied science and technology, describing the properties of the pendulum and "hydrostatic balances". He was one of the earliest Renaissance developers of the thermoscope and the inventor of various military compasses. With an improved telescope he built, he observed the stars of the Milky Way, the phases of Venus, the four largest satellites of Jupiter, Saturn's rings, lunar craters, and sunspots. He also built an early microscope.

In physics, motion is when an object changes its position with respect to a reference point in a given time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of reference to an observer, measuring the change in position of the body relative to that frame with a change in time. The branch of physics describing the motion of objects without reference to their cause is called kinematics, while the branch studying forces and their effect on motion is called dynamics.

If an object is not in motion relative to a given frame of reference, it is said to be at rest, motionless, immobile, stationary, or to have a constant or time-invariant position with reference to its surroundings. Modern physics holds that, as there is no absolute frame of reference, Isaac Newton's concept of absolute motion cannot be determined. Everything in the universe can be considered to be in motion.

Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in equilibrium with its environment.

If ${\displaystyle {\textbf {F}}}$ is the total of the forces acting on the system, ${\displaystyle m}$ is the mass of the system and ${\displaystyle {\textbf {a}}}$ is the acceleration of the system, Newton's second law states that ${\displaystyle {\textbf {F}}=m{\textbf {a}}\,}$ (the bold font indicates a vector quantity, i.e. one with both magnitude and direction). If ${\displaystyle {\textbf {a}}=0}$, then ${\displaystyle {\textbf {F}}=0}$. As for a system in static equilibrium, the acceleration equals zero, the system is either at rest, or its center of mass moves at constant velocity.

In physics, a force is an action (usually a push or a pull) that can cause an object to change its velocity or its shape, or to resist other forces, or to cause changes of pressure in a fluid. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity (force vector). The SI unit of force is the newton (N), and force is often represented by the symbol F.

Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion. Types of forces often encountered in classical mechanics include elastic, frictional, contact or "normal" forces, and gravitational. The rotational version of force is torque, which produces changes in the rotational speed of an object. In an extended body, each part applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress. In the case of multiple forces, if the net force on an extended body is zero the body is in equilibrium.

Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness (a standard candle), and since objects that are further away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the further away an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.

The accelerated expansion of the universe is thought to have begun since the universe entered its dark-energy-dominated era roughly 5 billion years ago.Within the framework of general relativity, an accelerated expansion can be accounted for by a positive value of the cosmological constant Λ, equivalent to the presence of a positive vacuum energy, dubbed "dark energy". While there are alternative possible explanations, the description assuming dark energy (positive Λ) is used in the standard model of cosmology, which also includes cold dark matter (CDM) and is known as the Lambda-CDM model.

A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field).

Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a 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 weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.