An Etymological Dictionary of Astronomy and Astrophysics
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1) In theories of magnetized → accretion disks, the distance from a non-rotating star where the → free fall of a spherical accretion flow is stopped, which occurs where the → ram pressure of the infalling matter equals the → magnetic pressure of the star.
2) The distance from an accreting or wind-blowing star where the → Alfvén Mach number of the flow (→ inflow or → outflow) is unity.

→ Alfvén wave; → radius.

1) In theories of magnetized → accretion disks, the distance from a non-rotating star where the → free fall of a spherical accretion flow is stopped, which occurs where the → ram pressure of the infalling matter equals the → magnetic pressure of the star.
2) More generally, the distance from an accreting or wind-blowing star where the → Alfvén Mach number of the flow (→ inflow or → outflow) is unity.

→ Alfvén wave; → radius.

The radius of the orbit of the hydrogen electron in its ground state (0.529 Å).

→ Bohr; → radius.

In the → Bondi-Hoyle accretion process, the radius where the gravitational energy owing to star is larger than the kinetic energy and, therefore, at which material is bound to star. The Bondi-Hoyle accretion radius is given by R_BH = 2 GM / (v² + c_s²) where G is the gravitational constant, M is the stellar mass, v the gas/star relative velocity, and c_s is the sound speed.

→ Bondi-Hoyle accretion; → radius.

1) In the → X-wind model of → accretion, the distance from the star where the → centrifugal force on a particle corotating with the star balances the → gravitational attraction; in other words, where the → accretion disk rotates at the same → angular velocity as the star.
2) In a → spiral galaxy, the place where the spiral → pattern speed has the same velocity as the → rotation curve of the → galactic disk. In the frame rotating with the wave, particles inside this radius will appear to revolve in the direction of the frame rotation (prograde) while outside this corotation radius, they will be retrograde.

→ corotation; → radius.

Same as → Larmor radius.

→ cyclotron; → radius.

An → isophotal radius of a galaxy, where the → surface brightness in the B band falls to 25 mag arcsec^-2.

After the French-born American astronomer Gérard de Vaucouleurs (1918-1995); → radius.

The distance from the Earth's center to its surface, about 6,371 km.

→ earth; → radius.

Of a galaxy, the distance from its center within which half of the total luminosity is included.

→ effective; → radius.

In gravitational lens phenomenon, the critical distance from the → lensing object for which the light ray from the source is deflected to the observer, provided that the source, the lens, and the observer are exactly aligned. Consider a massive object (the lens) situated exactly on the line of sight from Earth to a background source. The light rays from the source passing the lens at different distances are bent toward the lens. Since the bending angle for a light ray increases with decreasing distance from the lens, there is a critical distance such that the ray will be deflected just enough to hit the Earth. This distance is called the Einstein radius. By rotational symmetry about the Earth-source axis, an observer on Earth with perfect resolution would see the source lensed into an annulus, called Einstein ring, centered on its position. The size of an Einstein ring is given by the Einstein radius: θ_E = (4GM/c²)^0.5 (d_LS/(d_L.d_S)^0.5, where G is the → gravitational constant, M is the mass of the lens, c is the → speed of light, d_L is the angular diameter distance to the lens, d_S is the angular diameter distance to the source, and d_LS is the angular diameter distance between the lens and the source. The equation can be simplified to: θ_E = (0''.9) (M/10¹¹Msun)^0.5 (D/Gpc)^-0.5. Hence, for a dense cluster with mass M ~ 10 × 10¹⁵ Msun at a distance of 1 Gigaparsec (1 Gpc) this radius is about 100 arcsec. For a gravitational → microlensing event (with masses of order 1 Msun) at galactic distances (say D ~ 3 kpc), the typical Einstein radius would be of order milli-arcseconds.

→ Einstein; → radius.

The classical size of the electron given by r_e = e²/m_ec² = 2.81794 × 10^-13 cm, where e and m_e are the → electron charge and → electron mass, respectively, and c is the → speed of light.

→ electron; → radius.

Of a planet, the distance from the center to the equator. For Earth it is 6,378.1370 km. Jupiter has an equatorial radius 11.2 times Earth's value.

→ equatorial; → radius.

Same as → Larmor radius.

→ gyro-; → radius.

The size of the observable Universe as derived from the ratio c/H₀, where H₀ is the → Hubble-Lemaitre constant and c the → speed of light. Same as → Hubble distance, → Hubble length, and → cosmic horizon.

→ Hubble; → radius.

The size attributed to a galaxy corresponding to a particular level of → surface brightness. The reason is that galaxies do not have sharp edges.

→ isophotal; → radius.

The radius of the circular motion of a → charged particle moving in a → uniform magnetic field. Same as → gyroradius, → radius of gyration, → cyclotron radius. The Larmor radius (r_L) is obtained by equating the → Lorentz force with the → centripetal force: qvB = mv²/r_L, which leads to r_L = p/(ZeB), where p is → momentum, Z is → atomic number, e is the → electron charge, and B is → magnetic induction. The frequency of this circular motion is known as the → gyrofrequency.

→ Larmor frequency; → radius.

Of a circle, any straight line segment extending from the center to a point on the circumference.
Of a sphere, any straight line segment extending from the center to a point on the surface.
Of a regular polygon, the radius of the circle circumscribed about the polygon.

From L. radius "staff, spoke of a wheel, beam of light," of unknown origin.

Šo'â', loan from Ar.

Same as → Larmor radius.

→ radius; → gyration.

Math.: In a system of polar or spherical coordinates, a line joining a point to the origin.
Astro.: A line drawn from a central body to a satellite object in any position in its orbit.

→ radius; → vector.

The critical radius at which a massive body becomes a → black hole, i.e., at which light is unable to escape to infinity: R_s = 2GM / c², where G is the → gravitational constant, M is the mass, and c the → speed of light. The fomula can be approximated to R_s≅ 3 x (M/Msun), in km. Therefore, the Schwarzschild radius for Sun is about 3 km and for Earth about 1 cm.

→ Schwarzschild black hole; → radius.