An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

The instantaneous action of a body on another body independently of the distance separating them. The description of → gravity by → Newton's law and → electrostatics by → Coulomb's law are examples of action at a distance. According to Newton, → gravitation acts directly and instantaneously between two objects. For example, if the Sun should suddenly break apart, the Earth's orbit would be affected instantaneously. However, action at a distance violates the → principle of relativistic causality. According to → general relativity, gravitational effects travel at the → speed of light. For modern physics there is no instantaneous action at a distance.

→ action; → distance.

1) The ratio of an object's → linear size (l) to its → angular size (δθ, in → radians), that is D_A = l/δθ. It is used to convert observed angular separations into proper separations at the source.

2) In cosmology, a distance defined as the ratio of an object's physical transverse size (l) to its angular size (δθ). It is used to convert angular separations in telescope images into proper separations at the source. The angular diameter distance is defined by: D_A = l / δθ. Consider a light source of size l at r = r₁ and t = t₁ subtending an angle δθ at the origin (r = 0, t = t₀). The proper distance between the two ends of the object is related to δθ by: δθ = l / [a(t₁). r₁], where a(t₁) is the → scale factor at the present epoch. Therefore, D_A = r₁ / (1 + z). The angular diameter distance has the particularity that it does not increase infinitely with z→ ∞. It gets its maximum value at a → redshift of ~ 1 and then decreases for higher z. Therefore, more distant objects appear larger in angular size. This is explained by considering the size of the Universe when the light of the object was emitted. At that time the Universe was smaller and therefore the object occupied a larger fraction of the size of the Universe. In other words, objects appear larger because the entire Universe acts as a → gravitational lense.

→ angular; → diameter; → distance.

Between two points A and B, the angle → subtended by lines drawn from an observing point O to A and B. Same as → angular separation.

→ angular; → distance.

Same as → angular diameter distance.

→ angular; → size; → distance.

The distance between the → Sun and an → object in orbit around it when they are at their farthest approach.

→ perihelion; → distance.

The angular distance between two celestial bodies (e.g. the components of a binary star system), expressed in degrees, minutes and seconds of arc.

→ apparent; → distance.

1) A distance in → comoving coordinates between two points in space at a given cosmological time. In other words, the distance between two nearby objects in the Universe which remains constant with epoch if the two objects are moving with the → Hubble flow. More specifically, it is the → proper distance divided by the ratio of the → scale factor of the Universe between then, a(t)_em, and now, a(t)_obs: D_C = D_proper . [a(t)_obs/a(t)_em]. In terms of → redshift (z), it is the proper distance multiplied by (1 + z). At the present epoch, i.e. a = a(t_obs) = 1, D_C = D_proper. If the objects have no peculiar velocity their comoving distance at any time is the same as their distance today.
The comoving distance of the → cosmic horizon is about 48 × 10⁹→ light-years.

2) Transverse comoving distance: In a non-flat Universe, the comoving distance between two events at the same → redshift but separated on the sky by some angle. It is expressed by trigonometric functions of → curvature, → comoving distance, and the → Hubble distance accounting for the curvature of space. In a flat universe (Ω_k) it is the same as the → comoving distance.

3) Line-of-sight comoving distance: The total line-of-sight comoving distance from us to a distant object computed by integrating the infinitesimal comoving distance contributions between nearby events along the radial ray from the time t_emit, when the light from the object was emitted, to the time t_obs, when the object is observed.

→ comoving; → distance.

Measurement of the distances to the farthest objects in the Universe based on a bootstrapping series of methods, each applicable to more distant objects, and each dependent on the previous methods.

→ cosmic; → distance; → scale.

The distance to a remote galaxy based on its redshift assuming that the redshift is caused by the → Doppler effect and reflects the general expansion of the Universe.

→ cosmological; → distance .

1) The separation/length in space/time between two things/events.
2) The state of being apart in space or time.
3) In cosmology four main distance definitions are used: → luminosity distance, → angular diameter distance, → comoving distance, and → light-travel distance. In a → flat Universe these four approaches give the same result for the present epoch for distances below 100 Mpc. In a non-flat Universe with the → Robertson-Walker metric they give different but related values.
See also:
→ apparent distance, → cosmic distance scale, → cosmological distance, → distance function, → distance modulus, → distance to the horizon, → focal distance, → Hubble distance, → perihelion distance, → polar distance, → proper distance, → redshift-distance relation, → velocity-distance relation, → zenith distance.

M.E., from O.Fr., from L. distantia "a standing apart," from distantem (nominative distans) "standing apart, separate, distant," pr.p. of distare "to stand apart," from → dis- "apart, off" + stare "to stand," (cf. Mod.Pers. istâdan "to stand," O.Pers./Av. sta- "to stand, stand still; set," Skt. sthâ- "to stand," Gk. histemi "put, place, weigh," stasis "a standing still").

Apest, literally "standing apart," from apa- prefix denoting "separation, away, off," → dis-, + est variant of ist, present stem of istâdan, to stand," as above;" cf. Choresmian bst "to stand apart," from *apa- + st- "to stand," → stand.
Durâ, duri, noun from dur "far, distant, remote," Mid.Pers. dur, O.Pers. dūra- "far (in time or space)," Av. dūra-, from dav- "to move away," cf. Skt. dūrá- "distant, far."

Same as → metric.

→ distance + → function.

The difference between the → apparent magnitude (m) of a star or galaxy and its → absolute magnitude (M). It is given by m - M = 5 log d - 5, where d is the distance in → parsecs. For an object that is 10 pc away, the distance modulus is zero.

→ distance; → modulus.

The distance separating an observer and the → apparent horizon of the place. Neglecting the → atmospheric refraction, it is given by: d = (2Rh)^1/2, where R is the radius of the Earth and h is the observer's height. This can be approximated to: d (km) = 3.57(h)^1/2 for a typical value of R = 6378 km. The atmospheric refraction, however, makes the thing more complex, depending on the temperature and density variations along the line of sight. Generally, refraction pushes the apparent horizon about 10% farther.

→ distance; → horizon.

same as → focal length.

→ focal; → distance.

The distance from the center of a galaxy.

→ galactocentric; → distance.

The distance from the Earth to the → cosmic horizon which marks the edge of the → observable Universe. Same as → Hubble radius, → Hubble length, and → cosmic horizon.

→ Hubble; → distance.

The distance traversed by a photon between the time it is emitted and the time it reaches the observer. It is also referred to as the → look-back time.

→ light; → travel; → distance.

1) Distance derived by comparison of → observed and → intrinsic luminosities. If an object has a known luminosity L, and the observed flux is S, the luminosity distance is defined by D_L = (L/4πS)^1/2.

2) In cosmology, the → expansion of the Universe results in a diminution of the photon flux and the above equation fails. The reason is that for a homogeneous and isotropic Universe (→ Robertson-Walker metric), the luminosity decreases by a factor (1 + z)⁴. Therefore, the luminosity distance is related to the → angular diameter distance (D_A) by: D_L = (1 + z)².D_A.

→ luminosity; → distance.

The minimum distance between the paths of two orbiting objects around a → primary. Such distance between an object and Earth is called Earth MOID.

→ minimum; → orbit; → intersection; → distance.

The distance between the → Sun and an → object in orbit around it when they are at their closest approach.

→ perihelion; → distance.