The distance from the center of a spherical object to its surface or boundary.Radius is the distance from the center of a spherical object to its surface or boundary. In physics, the concept of radius appears in countless contexts: from the radius of an atom (about 0.1 nanometers) to the radius of a black hole's event horizon (the Schwarzschild radius). It is a fundamental geometric parameter that determines properties like volume, surface area, and gravitational pull. In the given titles, no specific use is mentioned, but the concept is ubiquitous in describing the size of particles, orbits, lenses, and detectors.
The concept of radius dates back to ancient geometry, with Euclid defining the circle by its radius around 300 BCE. The Bohr radius was introduced by Niels Bohr in 1913 in his model of the hydrogen atom. The Schwarzschild radius was derived by Karl Schwarzschild in 1916 from Einstein's field equations.
The radius is defined as half the diameter of a sphere or circle. In physics, it often enters formulas through geometric relationships: for a sphere, volume = (4/3)πr³ and surface area = 4πr². In dynamics, the radius of curvature describes how sharply a path bends. In quantum mechanics, the Bohr radius (about 0.053 nm) sets the scale for hydrogen-like atoms. In relativity, the Schwarzschild radius r_s = 2GM/c² defines the size of a black hole for a given mass M.
Radius is used in designing optical lenses, particle accelerators (bending radius of magnets), and in medical imaging to characterize tumors or blood vessels.
The Earth's radius is not constant: it is about 22 kilometers larger at the equator than at the poles due to the planet's rotation, making it an oblate spheroid rather than a perfect sphere.
| G | variable | gravitational constant — gravitational constant cubic metre per kilogram per second squared |
| M | variable | mass of the object — mass kilogram |
| R | variable | radius of the object — radius metre |
| c | variable | speed of light in vacuum — speed of light metre per second |
| v | variable | orbital speed — velocity metre per second |
| M | variable | central mass — mass kilogram |
| r | variable | orbital radius — radius metre |
| G | constant | Universal constant of gravitation, determining the strength of gravitational force. — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| r_H | variable | Accretion horizon radius — radius metre |
| \dot{M} | variable | Mass accretion rate — mass flow rate kilogram per second |
| \rho | variable | Mass density of accreting material — mass density kilogram per cubic metre |
| c_s | variable | Sound speed in accreting material — speed metre per second |
| r | variable | radial coordinate (distance from center) — radius metre |
| M(r) | variable | enclosed mass within radius r — mass kilogram |
| k | variable | constant of motion (related to energy per unit mass) — specific energy metre squared per second squared |
| G | constant | Newtonian constant of gravitation, fundamental strength of gravity — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| ˙ | operator | derivative with respect to time — time derivative |
| r_s | variable | Schwarzschild radius — radius metre |
| M | variable | Mass of the black hole — mass kilogram |
| G | constant | Constant of gravitation in Newton's law — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| \Gamma_1 | variable | First adiabatic index — adiabatic index |
| M | variable | Mass of the star — mass kilogram |
| R | variable | Radius of the star — radius metre |
| c | variable | Speed of light — speed metre per second |
| G | constant | Newtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| k | constant | Numerical constant of order unity depending on stellar structure — structure constant = 1 |
