# Glossary

The definitions on this page are consistent with those in the 2023 edition of
*The Astronomical Almanac*.

**ΔT**: the difference between Terrestrial Time (TT) and Universal Time (UT): \(\Delta {\rm T} = {\rm TT} - {\rm UT}1\).

**ΔUT1 (or ΔUT)**: the value of the difference between Universal Time (UT) and Coordinated Universal Time (UTC): \(\Delta {\rm UT1} = {\rm UT1} - {\rm UTC}\).

**aberration (of light)**: the relativistic apparent angular displacement of the observed position of a celestial object from its geometric position, caused by the motion of the observer in the reference system in which the trajectories of the observed object and the observer are described. (See aberration, planetary.)

aberration, annual: the component of stellar aberration resulting from the motion of the Earth about the Sun. (See aberration, stellar.)

aberration, diurnal: the component of stellar aberration resulting from the observer's diurnal motion about the center of the Earth due to Earth's rotation. (See aberration, stellar.)

aberration, E-terms of (obsolete): the terms of annual aberration which depend on the eccentricity and longitude of perihelion of the Earth. (See aberration, annual; perihelion.)

aberration, elliptic (obsolete): see aberration, E-terms of.

aberration, galactic: the apparent angular displacement of the observed position of an extra-galactic celestial object from its geometric position, arising from the motion of the solar system about the galactic center.

aberration, planetary: the apparent angular displacement of the observed position of a solar system body from its instantaneous geometric direction as would be seen by an observer at the geocenter. This displacement is produced by the combination of aberration of light and light-time displacement.

aberration, secular: the component of stellar aberration resulting from the essentially uniform and almost rectilinear motion of the entire solar system in space. Secular aberration is usually disregarded. (See aberration, stellar.)

aberration, stellar: the apparent angular displacement of the observed position of a celestial body resulting from the motion of the observer. Stellar aberration is divided into diurnal, annual, and secular components. (See aberration, annual; aberration, diurnal; aberration, secular.)

**altitude**: the angular distance of a celestial body above or below the horizon, measured along the great circle passing through the body and the zenith. Altitude is 90° minus the zenith distance.

**annual parallax**: see parallax, heliocentric.

**anomaly**: the angular separation of a body in its orbit from its pericenter.

anomaly, eccentric: in undisturbed elliptic motion, the angle measured at the center of the orbit ellipse from pericenter to the point on the circumscribing auxiliary circle from which a perpendicular to the major axis would intersect the orbiting body. (See anomaly, mean; anomaly, true.)

anomaly, mean: the product of the mean motion of an orbiting body and the interval of time since the body passed the pericenter. Thus, the mean anomaly is the angle from the pericenter of a hypothetical body moving with a constant angular speed that is equal to the mean motion. In realistic computations, with disturbances taken into account, the mean anomaly is equal to its initial value at an epoch plus an integral of the mean motion over the time elapsed since the epoch. (See anomaly, eccentric; anomaly, mean at epoch; anomaly, true.)

anomaly, mean at epoch: the value of the mean anomaly at a specific epoch, i.e., at some fiducial moment of time. It is one of the six Keplerian elements that specify an orbit. (See Keplerian elements; orbital elements.)

anomaly, true: the angle, measured at the focus nearest the pericenter of an elliptical orbit, between the pericenter and the radius vector from the focus to the orbiting body; one of the standard orbital elements. (See anomaly, eccentric; anomaly, mean; orbital elements.)

**aphelion**: the point in an orbit that is the most distant from the Sun.

**apocenter**: the point in an orbit that is farthest from the origin of the reference system. (See aphelion; apogee.)

**apogee**: the point in an orbit that is the most distant from the Earth. Apogee is sometimes used with reference to the apparent orbit of the Sun around the Earth.

**apparent place (or position)**: the proper place of an object expressed with respect to the true (intermediate) equator and equinox of date.

**apparent solar time**: see solar time, apparent.

**appulse**: the least apparent distance between two celestial objects from the observer's point of view. The time of appulse is close to that of conjunction in ecliptic longitude for objects moving on or near the ecliptic.

**Aries, First point of**: another name for the vernal equinox.

**aspect**: the position of any of the planets or the Moon relative to the Sun, as seen from the Earth.

**asteroid**: a small solar system body orbiting the Sun that is not massive enough to be a dwarf planet. Unlike a comet, asteroids rarely exhibit the ejection of volatile material. The term ''asteroid'' is sometimes restricted to bodies with orbital semi-major axes less than or approximately equal to that of Jupiter, and is often used interchangeably with the term ''minor planet''.

**astrometric ephemeris**: an ephemeris of a solar system body in which the tabulated positions are astrometric places. Values in an astrometric ephemeris are essentially comparable to catalog mean places of stars after the star positions have been updated for proper motion and parallax.

**astrometric place (or position)**: the position of a solar system body formed by applying corrections for light-time displacement to the geometric position. This position is directly comparable with the catalog positions of nearby background stars after those positions have been updated for proper motion and parallax. There is no correction for aberration or deflection of light. It is assumed that these correction are nearly identical for both the solar system body and background stars.

**astronomical coordinates**: the longitude and latitude of the point on Earth relative to the geoid. These coordinates are influenced by local gravity anomalies. (See latitude, terrestrial; longitude, terrestrial; zenith.)

**astronomical refraction**: see refraction, astronomical.

**astronomical unit (au)**: a conventional unit of length equal to 149 597 870 700 m exactly. Prior to 2012, it was defined as the radius of a circular orbit in which a body of negligible mass, and free of perturbations, would revolve around the Sun in \(2 \pi /k\) days, \(k\) being the Gaussian gravitational constant. This is slightly less than the orbital semi-major axis of the Earth's orbit.

**astronomical zenith**: see zenith, astronomical.

**atomic second**: see second, Système International (SI).

**augmentation**: the increase in the topocentric apparent semidiameter of a celestial body compared to its apparent semidiameter when viewed from the geocenter.

**autumnal equinox**: see equinox, autumnal.

**azimuth**: the angular distance measured eastward along the horizon from a specified reference point (usually north). Azimuth is measured to the point where the great circle determining the altitude of an object meets the horizon.

**barycenter**: the center of mass of a system of bodies; e.g., the center of mass of the solar system or the Earth-Moon system.

**barycentric**: with reference to, or pertaining to, the barycenter (usually of the solar system).

**Barycentric Celestial Reference System (BCRS)**: a system of barycentric space-time coordinates for the solar system within the framework of General Relativity. The metric tensor to be used in the system is specified by the IAU 2000 resolution B1.3. For all practical applications, unless otherwise stated, the BCRS is assumed to be oriented according to the ICRS axes. (See Barycentric Coordinate Time (TCB).)

**Barycentric Coordinate Time (TCB)**: the coordinate time of the Barycentric Celestial Reference System (BCRS), which advances by SI seconds within that system. TCB is related to Geocentric Coordinate Time (TCG) and Terrestrial Time (TT) by relativistic transformations that include a secular term. (See second, Système International (SI).)

**Barycentric Dynamical Time (TDB)**: a time scale defined by the IAU in 1976, named in 1979, and revised in 2006 for use as an independent argument of barycentric ephemerides and equations of motion. TDB is a linear function of Barycentric Coordinate Time (TCB) that on average tracks TT for an extended time period around the current standard epoch, JD 245 1545.0. The difference between TT and TDB remains less than 2 ms for several thousand years around the this epoch. (See second, Système International (SI).)

**Besselian elements**: quantities tabulated for the calculation of accurate predictions of an eclipse or occultation for any point on or above the surface of the Earth.

**calendar**: a system of reckoning time in units of solar days. The days are enumerated according to their position in cyclic patterns usually involving the motions of the Sun and/or the Moon.

calendar, Gregorian: The calendar introduced by Pope Gregory XIII in 1582 to replace the Julian calendar. This calendar is now used as the civil calendar in most countries. In the Gregorian calendar, every year that is exactly divisible by four is a leap year, except for centurial years, which must be exactly divisible by 400 to be leap years. Thus 2000 was a leap year, but 1900 and 2100 are not leap years.

calendar, Julian: the calendar introduced by Julius Caesar in 46 B.C. to replace the Roman calendar. In the Julian calendar a common year is defined to comprise 365 days, and every fourth year is a leap year comprising 366 days. The Julian calendar was superseded by the Gregorian calendar.

calendar, proleptic: the extrapolation of a calendar prior to its date of introduction.

**catalog equinox**: see equinox, catalog.

**Celestial Ephemeris Origin (CEO)**: the original name for the Celestial Intermediate Origin (CIO) given in the IAU 2000 resolutions. Obsolete.

**celestial equator**: the plane perpendicular to the Celestial Intermediate Pole (CIP). Colloquially, the projection onto the celestial sphere of the Earth's equator. (See mean equator and equinox; true equator and equinox.)

**Celestial Intermediate Origin (CIO)**: the non-rotating origin of the Celestial Intermediate Reference System. Formerly referred to as the Celestial Ephemeris Origin (CEO).

**Celestial Intermediate Origin Locator (CIO Locator)**: denoted by \(s\), is the difference between the Geocentric Celestial Reference System (GCRS) right ascension and the intermediate right ascension of the intersection of the GCRS and intermediate equators.

**Celestial Intermediate Pole (CIP)**: the reference pole of the P03 precession and IAU 2000A nutation models. The motions of the CIP are those of the Tisserand mean axis of the Earth with periods longer than two days. (See nutation; precession.)

**Celestial Intermediate Reference System**: a geocentric reference system related to the Geocentric Celestial Reference System (GCRS) by time-dependent rotations for precession and nutation. It is defined by the intermediate equator of the Celestial Intermediate Pole (CIP) and the Celestial Intermediate Origin (CIO) at a specific epoch.

**celestial pole**: see pole, celestial.

**celestial sphere**: an imaginary sphere of arbitrary radius upon which celestial bodies may be considered to be located. As circumstances require, the celestial sphere may be centered at the observer, at the Earth's center, or at any other location.

**Centaur**: a small solar system body orbiting the Sun that is not massive enough to be a dwarf planet with a perihelion greater than Jupiter's orbital semi-major axis and an orbital semi-major axis less than Neptune's.

**center of figure**: that point so situated relative to the apparent figure of a body that any line drawn through it divides the figure into two parts having equal apparent areas. If the body is oddly shaped, the center of figure may lie outside the figure itself.

**center of light**: same as center of figure except referring only to the illuminated portion.

**central meridian**: see meridian central.

**comet**: a small solar system body that normally exhibits the ejection of volatile material for some part of its orbital period.

**conjunction**: the phenomenon in which two bodies have the same apparent ecliptic longitude or right ascension as viewed from a third body. Conjunctions are usually tabulated as geocentric phenomena. For Mercury and Venus, geocentric inferior conjunctions occur when the planet is between the Earth and Sun, and superior conjunctions occur when the Sun is between the planet and Earth. (See longitude, ecliptic.)

**constellation**: 1. A grouping of stars, usually with pictorial or mythical associations, that serves to identify an area of the celestial sphere. 2. One of the precisely defined areas of the celestial sphere, associated with a grouping of stars, that the International Astronomical Union (IAU) has designated as a constellation.

**Coordinated Universal Time (UTC)**: the time scale available from broadcast time signals. UTC differs from International Atomic Time (TAI) by an integral number of seconds; it is maintained within \(\pm\) 0^{s}.9 seconds of UT1 by the introduction of leap seconds. (See International Atomic Time (TAI); leap second; Universal Time (UT).)

**culmination**: the passage of a celestial object across the observer's meridian; also called ''meridian passage''.

culmination, lower: (also called ''culmination below pole'' for circumpolar stars and the Moon) is the crossing farther from the observer's zenith.

culmination, upper: (also called ''culmination above pole'' for circumpolar stars and the Moon) or transit is the crossing closer to the observer's zenith.

**day**: an interval of 86 400 SI seconds, unless otherwise indicated. (See second, Système International (SI).)

**declination**: angular distance on the celestial sphere north or south of the celestial equator. It is measured along the hour circle passing through the celestial object. Declination is usually given in combination with right ascension or hour angle.

**defect of illumination**: (sometimes, greatest defect of illumination): the maximum angular width of the unilluminated portion of the apparent disk of a solar system body measured along a radius.

**deflection of light**: the angle by which the direction of a light ray is altered from a straight line by the gravitational field of the Sun or other massive object. As seen from the Earth, objects appear to be deflected radially away from the Sun by up to 1.″75 at the Sun's limb. Correction for this effect, which is independent of wavelength, is included in the transformation from mean place to apparent place.

**deflection of the vertical**: the angle between the astronomical vertical and the geodetic vertical. (See astronomical coordinates; geodetic coordinates; zenith.)

**delta T**: see \(\bf{\Delta {\rm T}}\).

**delta UT1**: see \(\bf{\Delta {\rm UT1}}\) (or \(\bf{\Delta {\rm UT}}\)).

**direct motion**: for orbital motion in the solar system, motion that is counterclockwise in the orbit as seen from the north pole of the ecliptic; for an object observed on the celestial sphere, motion that is from west to east, resulting from the relative motion of the object and the Earth.

**diurnal motion**: the apparent daily motion, caused by the Earth's rotation, of celestial bodies across the sky from east to west.

**diurnal parallax**: see parallax, geocentric.

**dwarf planet**: a celestial body that is in orbit around the Sun, has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, has not cleared the neighbourhood around its orbit, and is not a satellite. (See planet.)

**dynamical equinox**: the ascending node of the Earth's mean orbit on the Earth's true equator; i.e., the intersection of the ecliptic with the celestial equator at which the Sun's declination changes from south to north. (See catalog equinox; equinox; true equator and equinox.)

**dynamical time**: the family of time scales introduced in 1984 to replace ephemeris time (ET) as the independent argument of dynamical theories and ephemerides. (See Barycentric Dynamical Time (TDB); Terrestrial Time (TT).)

**Earth Rotation Angle (ERA)**: the angle, \(\theta\), measured along the equator of the Celestial Intermediate Pole (CIP) between the direction of the Celestial Intermediate Origin (CIO) and the Terrestrial Intermediate Origin (TIO). It is a linear function of UT1; its time derivative is the Earth's angular velocity.

**eccentricity**: 1. A parameter that specifies the shape of a conic section. 2. One of the standard orbital elements, usually denoted by \(e\), used to describe an elliptical orbit or a hyperbolic orbit. For an elliptical orbit, \(e = \sqrt{1 - (b^2/a^2)}\), where \(a\) and \(b\) are the lengths of the semi-major and semi-minor axes, respectively; for an parabolic orbit \(e = 1\); and for a hyperbolic orbit, the quantity \(e = \sqrt{1 + (b^2/a^2)}\). (See orbital elements.)

**eclipse**: the obscuration of a celestial body caused by its passage through the shadow cast by another body.

eclipse, annular: a solar eclipse in which the solar disk is not completely covered but is seen as an annulus or ring at maximum eclipse. An annular eclipse occurs when the apparent disk of the Moon is smaller than that of the Sun. (See eclipse, solar.)

eclipse, lunar: an eclipse in which the Moon passes through the shadow cast by the Earth. The eclipse may be total (the Moon passing completely through the Earth's umbra), partial (the Moon passing partially through the Earth's umbra at maximum eclipse), or penumbral (the Moon passing only through the Earth's penumbra).

eclipse, solar: actually an occultation of the Sun by the Moon in which the Earth passes through the shadow cast by the Moon. It may be total (observer in the Moon's umbra), partial (observer in the Moon's penumbra), annular, or annular-total. (See eclipse, annular.)

**ecliptic**: 1. The mean plane of the orbit of the Earth-Moon barycenter around the solar system barycenter. 2. The apparent path of the Sun around the celestial sphere.

**ecliptic latitude**: see latitude, ecliptic.

**ecliptic longitude**: see longitude, ecliptic.

**elements**:a set of parameters used to describe the position and motion or orientation (attitude) of an astronomical object.

elements, Besselian: see Besselian elements.

elements, Keplerian: see Keplerian elements.

elements, mean: see mean elements.

elements, orbital: see orbital elements.

elements, osculating: see osculating elements.

elements, rotational: see rotational elements.

**ellipsoid**: a quadratic surface defined by three mutually perpendicular semi-axes. If two of the semi-axes are equal then the figure is called a spheroid, and if all three are the same it is called a sphere.

**elliptical orbit**: see orbit, elliptical.

**elongation**: the geocentric angle between two celestial objects.

elongation, greatest: 1. For satellites, the maximum value of a satellite elongation during an orbit about its primary. Often a general direction is given. For example, greatest eastern elongation is the maximum value of a satellite elongation that occurs on the eastern half of the apparent orbit. 2. For bodies that orbit the Sun, the maximum value of elongation during an orbit about the Sun.

elongation, planetary: the usually geocentric angle between a planet and the Sun. Planetary elongations are measured from 0° to 180°, east or west of the Sun.

elongation, satellite: the geocentric angle between a satellite and its primary. The elongation is usually designated as being east or west of the primary, but on rare occasions could be designated north or south.

**epact**: 1. The age of the Moon. 2. The number of days since new moon, diminished by one day, on January 1 in the Gregorian ecclesiastical lunar cycle. (See calendar, Gregorian; lunar phases.)

**ephemeris**: a tabulation of the positions of a celestial object in an orderly sequence for a number of dates.

**ephemeris hour angle**: an hour angle referred to the ephemeris meridian.

**ephemeris longitude**: longitude measured eastward from the ephemeris meridian. (See longitude, terrestrial.)

**ephemeris meridian**: see meridian, ephemeris.

**ephemeris time (ET)**: the time scale used prior to 1984 as the independent variable in gravitational theories of the solar system. In 1984, ET was replaced by dynamical time.

**ephemeris transit**: the passage of a celestial body or point across the ephemeris meridian.

**epoch**: an arbitrary fixed instant of time or date used as a chronological reference datum for calendars, celestial reference systems, star catalogs, or orbital motions. (See calendar; orbit.)

**equation of the equinoxes**: the difference apparent sidereal time minus mean sidereal time, due to the effect of nutation in longitude on the location of the equinox. Equivalently, the difference between the right ascensions of the true and mean equinoxes, expressed in time units. (See sidereal time.)

**equation of the origins**: the arc length, measured positively eastward, from the Celestial Intermediate Origin (CIO) to the equinox along the intermediate equator; alternatively the difference between the Earth Rotation Angle (ERA) and Greenwich Apparent Sidereal Time (GAST), namely, (ERA — GAST).

**equation of time**: the difference apparent solar time minus mean solar time.

**equator**: the great circle on the surface of a body formed by the intersection of its surface with the plane passing through the center of the body perpendicular to the axis of rotation. (See celestial equator.)

**equinox**: 1. Either of the two points on the celestial sphere at which the ecliptic intersects the celestial equator. 2. The time at which the center of the Sun croses the Earth's equator. At these times the apparent ecliptic longitude of the Sun is approximately either 0° or 180°. 3. The vernal equinox. (See mean equator and equinox; true equator and equinox.)

equinox, autumnal: 1. The decending node of the ecliptic on the celestial sphere. 2. The time which the apparent ecliptic longitude of the Sun is 180°.

equinox, catalog: the intersection of the hour angle of zero right ascension of a star catalog with the celestial equator. Obsolete.

equinox, dynamical: the ascending node of the ecliptic on the Earth's true equator.

**era**: a system of chronological notation reckoned from a specific event.

**ERA**: see Earth Rotation Angle (ERA).

**flattening**: a parameter that specifies the degree by which a planet's figure differs from that of a sphere; the ratio \(f = (a-b)/a\), where \(a\) is the equatorial radius and \(b\) is the polar radius.

**frame bias**: the orientation of the mean equator and equinox of J2000.0 with respect to the Geocentric Celestial Reference System (GCRS). It is defined by three small and constant angles, two of which describe the offset of the mean pole at J2000.0 and the other is the GCRS right ascension of the mean inertial equinox of J2000.0.

**frequency**: the number of periods of a regular, cyclic phenomenon in a given measure of time, such as a second or a year. (See period; second, Système International (SI); year.)

**frequency standard**: a generator whose output is used as a precise frequency reference; a primary frequency standard is one whose frequency corresponds to the adopted definition of the second, with its specified accuracy achieved without calibration of the device. (See second, Système International (SI).)

**GAST**: see Greenwich Apparent Sidereal Time (GAST).

**Gaussian gravitational constant (obsolete)**: (\(k\) = 0.017 202 098 95). The constant which by means of Kepler's third law defined the astronomical system of units of length [ astronomical unit (au)], mass (solar mass) and time (day) prior to 2012. The dimensions of \(k^2\) are those of Newton's constant of gravitation: \({\rm L^{3}M^{-1}T^{-2}}\).

**geocentric**: with reference to, or pertaining to, the center of the Earth.

**Geocentric Celestial Reference System (GCRS)**: a system of geocentric space-time coordinates within the framework of General Relativity. The metric tensor used in the system is specified by the IAU 2000 resolutions. The GCRS is defined such that its spatial coordinates are kinematically non-rotating with respect to those of the Barycentric Celestial Reference System (BCRS). (See Geocentric Coordinate Time (TCG).)

**Geocentric Coordinate Time (TCG)**: the coordinate time of the Geocentric Celestial Reference System (GCRS), which advances by SI seconds within that system. TCG is related to Barycentric Coordinate Time (TCB) and Terrestrial Time (TT), by relativistic transformations that include a secular term. (See second, Système International (SI).)

**geocentric coordinates**: 1. The latitude and longitude of a point on the Earth's surface relative to the center of the Earth. 2. Celestial coordinates given with respect to the center of the Earth. (See latitude, terrestrial; longitude, terrestrial; zenith.)

**geocentric zenith**: see zenith, geocentric.

**geodetic coordinates**: the latitude and longitude of a point on the Earth's surface determined from the geodetic vertical (normal to the reference ellipsoid). (See latitude, terrestrial; longitude, terrestrial; zenith.)

**geodetic zenith**: see zenith, geodetic.

**geoid**: an equipotential surface that coincides with mean sea level in the open ocean. On land it is the level surface that would be assumed by water in an imaginary network of frictionless channels connected to the ocean.

**geometric position**: the position of an object defined by a straight line (vector) between the center of the Earth (or the observer) and the object at a given time, without any corrections for light-time, aberration, etc.

**GHA**: see Greenwich Hour Angle (GHA).

**GMST**: see Greenwich Mean Sidereal Time (GMST).

**greatest defect of illumination**: see defect of illumination.

**Greenwich Apparent Sidereal Time (GAST)**: the Greenwich hour angle of the true equinox of date.

**Greenwich Hour Angle (GHA)**: angular distance on the celestial sphere measured westward along the celestial equator from the Greenwich meridian to the hour circle that passes through a celestial object or point.

**Greenwich Mean Sidereal Time (GMST)**: the Greenwich hour angle of the mean equinox of date.

**Greenwich meridian**: see meridian, Greenwich.

**Greenwich sidereal date (GSD)**: the number of sidereal days elapsed at Greenwich since the beginning of the Greenwich sidereal day that was in progress at the Julian date (JD) 0.0.

**Greenwich sidereal day number**: the integral part of the Greenwich sidereal date (GSD).

**Gregorian calendar**: see calendar, Gregorian.

**height**: the distance above or below a reference surface such as mean sea level on the Earth or a planetographic reference surface on another solar system planet.

**heliocentric**: with reference to, or pertaining to, the center of the Sun.

**heliocentric parallax**: see parallax, heliocentric.

**horizon**: 1. A plane perpendicular to the line from an observer through the zenith. 2. The observed border between Earth and the sky.

horizon, astronomical: the plane perpendicular to the line from an observer to the astronomical zenith that passes through the point of observation.

horizon, geocentric: the plane perpendicular to the line from an observer to the geocentric zenith that passes through the center of the Earth.

horizon, natural: the border between the sky and the Earth as seen from an observation point.

**horizontal parallax**: see parallax, horizontal.

**horizontal refraction**: see refraction, horizontal.

**hour angle**: angular distance on the celestial sphere measured westward along the celestial equator from the meridian to the hour circle that passes through a celestial object.

**hour circle**: a great circle on the celestial sphere that passes through the celestial poles and is therefore perpendicular to the celestial equator.

**hyperbolic orbit**: see orbit, hyperbolic.

**IAU**: see International Astronomical Union (IAU).

**illuminated extent**: the illuminated area of an apparent planetary disk, expressed as a solid angle.

**inclination**: 1. The angle between two planes or their poles. 2. Usually, the angle between an orbital plane and a reference plane. 3. One of the standard orbital elements that specifies the orientation of the orbit. (See orbital elements.)

**instantaneous orbit**: see orbit, instantaneous.

**intercalate**: to insert an interval of time (e.g., a day or a month) within a calendar, usually so that it is synchronized with some natural phenomenon such as the seasons or lunar phases.

**intermediate place (or position)**: the proper place of an object expressed with respect to the true (intermediate) equator and CIO of date.

**International Astronomical Union (IAU)**: an international non-governmental organization that promotes the science of astronomy. The IAU is composed of both national and individual members. In the field of positional astronomy, the IAU, among other activities, recommends standards for data analysis and modeling, usually in the form of resolutions passed at General Assemblies held every three years.

**International Atomic Time (TAI)**: the continuous time scale resulting from analysis by the Bureau International des Poids et Mesures of atomic time standards in many countries. The fundamental unit of TAI is the SI second on the geoid, and the epoch is 1958 January 1. (See second, Système International (SI).)

**International Celestial Reference Frame (ICRF)**: 1. A set of extragalactic objects whose adopted positions and uncertainties realize the International Celestial Reference System (ICRS) axes and give the uncertainties of those axes. 2. The name of the radio catalog whose defining sources serve as fiducial points to fix the axes of the ICRS, recommended by the International Astronomical Union (IAU). The first such catalog was adopted for use beginning in 1997. The second catalog, termed ICRF2, was adopted for use beginning in 2010.The third catalog, termed ICRF3, was adopted for use beginning in 2019.

**International Celestial Reference System (ICRS)**: a time-independent, kinematically non-rotating barycentric reference system recommended by the International Astronomical Union (IAU) in 1997. Its axes are those of the International Celestial Reference Frame (ICRF).

**international meridian**: see meridian, Greenwich.

**International Terrestrial Reference Frame (ITRF)**: a set of reference points on the surface of the Earth whose adopted positions and velocities fix the rotating axes of the International Terrestrial Reference System (ITRS).

**International Terrestrial Reference System (ITRS)**: a time-dependent, non-inertial reference system co-moving with the geocenter and rotating with the Earth. The ITRS is the recommended system in which to express positions on the Earth.

**invariable plane**: the plane through the center of mass of the solar system perpendicular to the angular momentum vector of the solar system.

**irradiation**: an optical effect of contrast that makes bright objects viewed against a dark background appear to be larger than they really are.

**Julian calendar**: see calendar, Julian.

**Julian date (JD)**: the interval of time in days and fractions of a day, since 4713 B.C. January 1, Greenwich noon, Julian proleptic calendar. In precise work, the timescale, e.g., Terrestrial Time (TT) or Universal Time (UT), should be specified.

**Julian date, modified (MJD)**: the Julian date (JD) minus 2400000.5.

**Julian day number**: the integral part of the Julian date (JD).

**Julian year**: see year, Julian.

**Keplerian elements**: a certain set of six orbital elements, sometimes referred to as the Keplerian set. Historically, this set included the mean anomaly at the epoch, the orbital semi-major axis, the eccentricity and three Euler angles: the longitude of the ascending node, the inclination, and the argument of pericenter. The time of pericenter passage is often used as part of the Keplerian set instead of the mean anomaly at the epoch. Sometimes the longitude of pericenter (which is the sum of the longitude of the ascending node and the argument of pericenter) is used instead of the argument of pericenter.

**Laplacian plane**: 1. For planets see invariable plane. 2. For a system of satellites, the fixed plane relative to which the vector sum of the disturbing forces has no orthogonal component.

**latitude, celestial**: see latitude, ecliptic.

**latitude, ecliptic**: angular distance on the celestial sphere measured north or south of the ecliptic along the great circle passing through the poles of the ecliptic and the celestial object. Also referred to as celestial latitude.

**latitude, terrestrial**: angular distance on the Earth measured north or south of the equator along the meridian of a geographic location.

**leap second**: a second inserted as the 61^{st} second of a minute at announced times to keep UTC within 0^{s}. of UT1. Generally, leap seconds are added at the end of June or December as necessary, but may be inserted at the end of any month. Although it has never been utilized, it is possible to have a negative leap second in which case the 60^{th} second of a minute would be removed. (See Coordinated Universal Time (UTC); second, Système International (SI); Universal Time (UT).)

**librations**: the real or apparent oscillations of a body around a reference point. When referring to the Moon, librations are variations in the orientation of the Moon's surface with respect to an observer on the Earth. Physical librations are due to variations in the orientation of the Moon's rotational axis in inertial space. The much larger optical librations are due to variations in the rate of the Moon's orbital motion, the obliquity of the Moon's equator to its orbital plane, and the diurnal changes of geometric perspective of an observer on the Earth's surface.

**light, deflection of**: see deflection of light.

**light-time**: the interval of time required for light to travel from a celestial body to the Earth.

**light-time displacement**: the difference between the geometric and astrometric place of a solar system body. It is caused by the motion of the body during the interval it takes light to travel from the body to Earth.

**light-year**: the distance that light traverses in a vacuum during one year. Since there are various ways to define a year, there is an ambiguity in the exact distance; the IAU recommends using the Julian year as the time basis. A light-year is approximately 9.46 × 10^{12} km, 5.88 × 10^{12} statute miles, 6.32 × 10^{4} au, and 3.07 × 10^{-1} parsecs. Often distances beyond the solar system are given in parsecs. (See parsec (pc).)

**limb**: the apparent edge of the Sun, Moon, or a planet or any other celestial body with a detectable disk.

**limb correction**: generally, a small angle (positive or negative) that is added to the tabulated apparent semidiameter of a body to compensate for local topography at a specific point along the limb. Specifically for the Moon, the angle taken from the Watts lunar limb data (Watts, C. B., APAE XVII, 1963) that is used to correct the semidiameter of the Watts mean limb. The correction is a function of position along the limb and the apparent librations. The Watts mean limb is a circle whose center is offset by about 0.″6 from the direction of the Moon's center of mass and whose radius is about 0.″4 greater than the semidiameter of the Moon that is computed based on its IAU adopted radius in kilometers.

**local place**: a topocentric place of an object expressed with respect to the Geocentric Celestial Reference System (GCRS) axes.

**local sidereal time**: the hour angle of the vernal equinox with respect to the local meridian.

**longitude of the ascending node**: given an orbit and a reference plane through the primary body (or center of mass): the angle, \(\Omega\), at the primary, between a fiducial direction in the reference plane and the point at which the orbit crosses the reference plane from south to north. Equivalently, \(\Omega\) is one of the angles in the reference plane between the fiducial direction and the line of nodes. It is one of the six Keplerian elements that specify an orbit. For planetary orbits, the primary is the Sun, the reference plane is usually the ecliptic, and the fiducial direction is usually toward the equinox. (See node; orbital elements.)

**longitude, celestial**: see longitude, ecliptic.

**longitude, ecliptic**: angular distance on the celestial sphere measured eastward along the ecliptic from the dynamical equinox to the great circle passing through the poles of the ecliptic and the celestial object. Also referred to as celestial longitude.

**longitude, terrestrial**: angular distance measured along the Earth's equator from the Greenwich meridian to the meridian of a geographic location.

**luminosity class**: distinctions in intrinsic brightness among stars of the same spectral type, typically given as a Roman numeral. It denotes if a star is a supergiant (Ia or Ib), giant (II or III), subgiant (IV), or main sequence --- also called dwarf (V). Sometimes subdwarfs (VI) and white dwarfs (VII) are regarded as luminosity classes. (See spectral types or classes.)

**lunar phases**: cyclically recurring apparent forms of the Moon. The principal phases: new moon, first quarter, full moon and last quarter are defined as the times at which the excess of the apparent ecliptic longitude of the Moon over that of the Sun is 0°, 90°, 180° and 270°, respectively. (See longitude, ecliptic.)

**lunation**: the period of time between two consecutive new moons.

**magnitude of a lunar eclipse**: the fraction of the lunar diameter obscured by the shadow of the Earth at the greatest phase of a lunar eclipse, measured along the common diameter. (See eclipse, lunar.)

**magnitude of a solar eclipse**: the fraction of the solar diameter obscured by the Moon at the greatest phase of a solar eclipse, measured along the common diameter. (See eclipse, solar.)

**magnitude, stellar**: a measure on a logarithmic scale of the brightness of a celestial object. Since brightness varies with wavelength, often a wavelength band is specified. A factor of 100 in brightness is equivalent to a change of 5 in stellar magnitude, and brighter sources have lower magnitudes. For example, the bright star Sirius has a visual-band magnitude of -1.46 whereas the faintest stars detectable with an unaided eye under ideal conditions have visual-band magnitudes of about 6.0.

**mean distance**: an average distance between the primary and the secondary gravitating body. The meaning of the mean distance depends upon the chosen method of averaging (i.e., averaging over the time, or over the true anomaly, or the mean anomaly. It is also important what power of the distance is subject to averaging.) In this volume the mean distance is defined as the inverse of the time-averaged reciprocal distance: \((\int r^{-1}\, \rm{d}t)^{-1}\). In the two body setting, when the disturbances are neglected and the orbit is elliptic, this formula yields the orbital semi-major axis, \(a\), which plays the role of mean distance.

**mean elements**: average values of the orbital elements over some section of the orbit or over some interval of time. They are interpreted as the elements of some reference (mean) orbit that approximates the actual one and, thus, may serve as the basis for calculating orbit perturbations. The values of mean elements depend upon the chosen method of averaging and upon the length of time over which the averaging is made.

**mean equator and equinox**: the celestial coordinate system defined by the orientation of the Earth's equatorial plane on some specified date together with the direction of the dynamical equinox on that date, neglecting nutation. Thus, the mean equator and equinox moves in response only to precession. Positions in a star catalog have traditionally been referred to a catalog equator and equinox that approximate the mean equator and equinox of a standard epoch. (See catalog equinox; true equator and equinox.)

**mean motion**: defined for bound orbits only. 1. The rate of change of the mean anomaly. 2. The value \(\sqrt{Gm/a^3}\), where \(G\) is Newton's gravitational constant, \(m\) is the sum of the masses of the primary and secondary bodies, and \(a\) is the orbital semi-major axis of the relative orbit. For unperturbed elliptic or circular orbits, these definitions are equivalent; the mean motion is related to the period through \(nT=2\pi\) where \(n\) is the mean motion and \(T\) is the period. For perturbed bound orbits, the two definitions yield, in general, different values of \(n\), both of which are time dependent.

**mean place**: coordinates of a star or other celestial object (outside the solar system) at a specific date, in the Barycentric Celestial Reference System (BCRS). Conceptually, the coordinates represent the direction of the object as it would hypothetically be observed from the solar system barycenter at the specified date, with respect to a fixed coordinate system (e.g., the axes of the International Celestial Reference Frame (ICRF)), if the masses of the Sun and other solar system bodies were negligible.

**mean solar time**: see solar time, mean.

**meridian**: a great circle passing through the celestial poles and through the zenith of any location on Earth. For planetary observations a meridian is half the great circle passing through the planet's poles and through any location on the planet.

meridian, central (planetary): half of the great circle passing through the planet's poles and through the sub-earth point). This is the same as the longitude of the sub-earth point. Do not confuse with planetary prime meridian. See diagram on page E4.

meridian, ephemeris: a fictitious meridian that rotates independently of the Earth at the uniform rate implicitly defined by Terrestrial Time (TT). The ephemeris meridian is 1.002 738 \(\Delta {\rm T}\) east of the Greenwich meridian, where \(\Delta {\rm T} = {\rm TT} - {\rm UT1}\).

meridian, Greenwich: (also called international or prime meridian) is a generic reference to one of several origins of the Earth's longitude coordinate (zero-longitude). In The Astronomical Almanac, it is the plane defining the astronomical zero meridian; it contains the geocenter, the Celestial Intermediate Pole and the Terrestrial Intermediate Origin. Other definitions are: the x-z plane of the International Terrestrial Reference System (ITRS); the zero-longitude meridian of the World Geodetic System 1984 (WGS-84); and the meridian that passes through the transit circle at the Royal Observatory, Greenwich. Note that the latter meridian is about 100 m west of the others.

meridian, international: see meridian, Greenwich.

meridian, prime: on Earth, same as Greenwich meridian. On other solar system objects, the zero-longitude meridian, typically defined via international convention by an observable surface feature or rotational elements.

**minor planet**: a loosely defined term generally meaning a small solar system body that is orbiting the Sun, does not show a comet-like appearance, and is not massive enough to be a dwarf planet. The term is often used interchangeably with ''asteroid'', although there is no implicit constraint that a minor planet be interior to Jupiter's orbit.

**month**: a calendrical unit that approximates the period of revolution of the Moon. Also, the period of time between the same dates in successive calendar months.

month, sidereal: the period of revolution of the Moon about the Earth (or Earth-Moon barycenter) in a fixed reference frame. It is the mean period of revolution with respect to the background stars. The mean length of the sidereal month is approximately 27.322 days.

month, synodic: the period between successive new moons (as seen from the geocenter). The mean length of the synodic month is approximately 29.531 days.

**moonrise, moonset**: the times at which the apparent upper limb of the Moon is on the astronomical horizon. In The Astronomical Almanac, they are computed as the times when the true zenith distance, referred to the center of the Earth, of the central point of the Moon's disk is 90° 34′ \(+ s - \pi\), where \(s\) is the Moon's semidiameter, \(\pi\) is the horizontal parallax, and 34′ is the adopted value of horizontal refraction.

**nadir**: the point on the celestial sphere diametrically opposite to the zenith.

**Near Earth Object (NEO)**: any small solar system body, including comets, whose orbit brings it near the Earth. A small solar system body is conventionally considered an NEO if its perihelion is less than 1.3 au.

**node**: either of the points on the celestial sphere at which the plane of an orbit intersects a reference plane. The position of one of the nodes (the longitude of the ascending node) is traditionally used as one of the standard orbital elements.

**nutation**: oscillations in the motion of the rotation pole of a freely rotating body that is undergoing torque from external gravitational forces. Nutation of the Earth's pole is specified in terms of components in obliquity and longitude.

**obliquity**: in general, the angle between the equatorial and orbital planes of a body or, equivalently, between the rotational and orbital poles. For the Earth the obliquity of the ecliptic is the angle between the planes of the equator and the ecliptic; its value is approximately 23°.44.

**occultation**: the obscuration of one celestial body by another of greater apparent diameter; especially the passage of the Moon in front of a star or planet, or the disappearance of a satellite behind the disk of its primary. If the primary source of illumination of a reflecting body is cut off by the occultation, the phenomenon is also called an eclipse. The occultation of the Sun by the Moon is a solar eclipse. (See eclipse, solar.)

**opposition**: the phenomenon whereby two bodies have apparent ecliptic longitudes or right ascensions that differ by 180° as viewed by a third body. Oppositions are usually tabulated as geocentric phenomena.

**orbit**: the path in space followed by a celestial body, as a function of time. (See orbital elements.)

orbit, elliptical: a closed orbit with an eccentricity less than 1.

orbit, hyperbolic: an open orbit with an eccentricity greater than 1.

orbit, instantaneous: the unperturbed two-body orbit that a body would follow if perturbations were to cease instantaneously. Each orbit in the solar system (and, more generally, in any perturbed two-body setting) can be represented as a sequence of instantaneous ellipses or hyperbolae whose parameters are called orbital elements. If these elements are chosen to be osculating, each instantaneous orbit is tangential to the physical orbit. (See orbital elements; osculating elements.)

orbit, parabolic: an open orbit with an eccentricity of 1.

**orbital elements**: a set of six independent parameters that specifies an instantaneous orbit. Every real orbit can be represented as a sequence of instantaneous ellipses or hyperbolae sharing one of their foci. At each instant of time, the position and velocity of the body is characterised by its place on one such instantaneous curve. The evolution of this representation is mathematically described by evolution of the values of orbital elements. Different sets of geometric parameters may be chosen to play the role of orbital elements. The set of Keplerian elements is one of many such sets. When the Lagrange constraint (the requirement that the instantaneous orbit is tangential to the actual orbit) is imposed upon the orbital elements, they are called osculating elements.

**osculating elements**: a set of parameters that specifies the instantaneous position and velocity of a celestial body in its perturbed orbit. Osculating elements describe the unperturbed (two-body) orbit that the body would follow if perturbations were to cease instantaneously. (See orbit, instantaneous; orbital elements.)

**parallax**: the difference in apparent direction of an object as seen from two different locations; conversely, the angle at the object that is subtended by the line joining two designated points.

parallax, annual: see parallax, heliocentric.

parallax, diurnal: see parallax, geocentric.

parallax, geocentric: the angular difference between the topocentric and geocentric directions toward an object. Also called diurnal parallax.

parallax, heliocentric: the angular difference between the geocentric and heliocentric directions toward an object; it is the angle subtended at the observed object. Also called annual parallax.

parallax, horizontal: the angular difference between the topocentric and a geocentric direction toward an object when the object is on the astronomical horizon.

parallax, solar: the angular width subtended by the Earth's equatorial radius when the Earth is at a distance of 1 astronomical unit (au). The value for the solar parallax is 8.794143 arcseconds.

**parallax in altitude**: the angular difference between the topocentric and geocentric direction toward an object when the object is at a given altitude.

**parsec (pc)**: the distance at which one astronomical unit (au) subtends an angle of one arcsecond; equivalently the distance to an object having an annual parallax of one arcsecond. One parsec is 1/sin(1″) = 206264.806 au, or about 3.26 light-years.

**penumbra**: 1. The portion of a shadow in which light from an extended source is partially but not completely cut off by an intervening body. 2. The area of partial shadow surrounding the umbra.

**pericenter**: the point in an orbit that is nearest to the origin of the reference system. (See perigee; perihelion.)

**pericenter, argument of**: one of the Keplerian elements. It is the angle measured in the orbit plane from the ascending node of a reference plane (usually the ecliptic) to the pericenter.

**perigee**: the point in an orbit that is nearest to the Earth. Perigee is sometimes used with reference to the apparent orbit of the Sun around the Earth.

**perihelion**: the point in an orbit that is nearest to the Sun.

**period**: the interval of time required to complete one revolution in an orbit or one cycle of a periodic phenomenon, such as a cycle of phases. (See phase.)

**perturbations**: 1. Deviations between the actual orbit of a celestial body and an assumed reference orbit. 2. The forces that cause deviations between the actual and reference orbits. Perturbations, according to the first meaning, are usually calculated as quantities to be added to the coordinates of the reference orbit to obtain the precise coordinates.

**phase**: 1. The name applied to the apparent degree of illumination of the disk of the Moon or a planet as seen from Earth (crescent, gibbous, full, etc.). 2. The ratio of the illuminated area of the apparent disk of a celestial body to the entire area of the apparent disk; i.e., the fraction illuminated. 3. Used loosely to refer to one aspect of an eclipse (partial phase, annular phase, etc.). (See lunar phases.)

**phase angle**: the angle measured at the center of an illuminated body between the light source and the observer.

**photometry**: a measurement of the intensity of light, usually specified for a specific wavelength range.

**planet**: a celestial body that is in orbit around the Sun, has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and has cleared the neighbourhood around its orbit. (See dwarf planet.)

**planetocentric coordinates**: coordinates for general use, where the \(z\)-axis is the mean axis of rotation, the \(x\)-axis is the intersection of the planetary equator (normal to the \(z\)-axis through the center of mass) and an arbitrary prime meridian, and the \(y\)-axis completes a right-hand coordinate system. Longitude of a point is measured positive to the prime meridian as defined by rotational elements. Latitude of a point is the angle between the planetary equator and a line to the center of mass. The radius is measured from the center of mass to the surface point.

**planetographic coordinates**: coordinates for cartographic purposes dependent on an equipotential surface as a reference surface. Longitude of a point is measured in the direction opposite to the rotation (positive to the west for direct rotation) from the cartographic position of the prime meridian defined by a clearly observable surface feature. Latitude of a point is the angle between the planetary equator (normal to the \(z\)-axis and through the center of mass) and normal to the reference surface at the point. The height of a point is specified as the distance above a point with the same longitude and latitude on the reference surface.

**polar motion**: the quasi-periodic motion of the Earth's pole of rotation with respect to the Earth's solid body. More precisely, the angular excursion of the CIP from the ITRS \(z\)-axis. (See Celestial Intermediate Pole (CIP); International Terrestrial Reference System (ITRS).)

**polar wobble**: see wobble, polar.

**pole, celestial**: either of the two points projected onto the celestial sphere by the Earth's axis. Usually, this is the axis of the Celestial Intermediate Pole (CIP), but it may also refer to the instantaneous axis of rotation, or the angular momentum vector. All of these axes are within 0.″1 of each other. If greater accuracy is desired, the specific axis should be designated.

**pole, Tisserand mean**: the angular momentum pole for the Earth about which the total internal angular momentum of the Earth is zero. The motions of the Celestial Intermediate Pole (CIP) (described by the conventional theories of precession and nutation) are those of the Tisserand mean pole with periods greater than two days in a celestial reference system (specifically, the Geocentric Celestial Reference System (GCRS)).

**precession**: the smoothly changing orientation (secular motion) of an orbital plane or the equator of a rotating body. Applied to rotational dynamics, precession may be excited by a singular event, such as a collision, a progenitor's disruption, or a tidal interaction at a close approach (free precession); or caused by continuous torques from other solar system bodies, or jetting, in the case of comets (forced precession). For the Earth's rotation, the main sources of forced precession are the torques caused by the attraction of the Sun and Moon on the Earth's equatorial bulge, called precession of the equator (formerly known as lunisolar precession). The slow change in the orientation of the Earth's orbital plane is called precession of the ecliptic (formerly known as planetary precession). The combination of both motions --- that is, the motion of the equator with respect to the ecliptic --- is called general precession.

**prime meridian**: see meridian, prime.

**proleptic calendar**: see calendar, proleptic.

**proper motion**: the projection onto the celestial sphere of the space motion of a star relative to the solar system; thus the transverse component of the space motion of a star with respect to the solar system. Proper motion is usually tabulated in star catalogs as changes in right ascension and declination per year or century.

**proper place**: direction of an object in the Geocentric Celestial Reference System (GCRS) that takes into account orbital or space motion and light-time (as applicable), light deflection, and annual aberration. Thus, the position (geocentric right ascension and declination) at which the object would actually be seen from the center of the Earth if the Earth were transparent, non-refracting, and massless. Unless otherwise stated, the coordinates are expressed with respect to the GCRS axes, which are derived from those of the ICRS.

**quadrature**: a configuration in which two celestial bodies have apparent longitudes that differ by 90° as viewed from a third body. Quadratures are usually tabulated with respect to the Sun as viewed from the center of the Earth. (See longitude, ecliptic.)

**radial velocity**: the rate of change of the distance to an object, usually corrected for the Earth's motion with respect to the solar system barycenter.

**radius vector**: an imaginary line from the center of one body to another, often from the heliocenter. Sometimes only the length of the vector is given.

**refraction**: the change in direction of travel (bending) of a light ray as it passes obliquely from a medium of lesser/greater density to a medium of greater/lesser density.

refraction, astronomical: the change in direction of travel (bending) of a light ray as it passes obliquely through the atmosphere. As a result of refraction the observed altitude of a celestial object is greater than its geometric altitude. The amount of refraction depends on the altitude of the object and on atmospheric conditions.

refraction, horizontal: the astronomical refraction at the astronomical horizon; often, an adopted value of 34′ is used in computations for sea level observations.

**retrograde motion**: for orbital motion in the solar system, motion that is clockwise in the orbit as seen from the north pole of the ecliptic; for an object observed on the celestial sphere, motion that is from east to west, resulting from the relative motion of the object and the Earth. (See direct motion.)

**right ascension**: angular distance on the celestial sphere measured eastward along the celestial equator from the equinox to the hour circle passing through the celestial object. Right ascension is usually given in combination with declination.

**rotational elements**: typically, a set of six time-dependent parameters used to describe the instantaneous orientation (attitude) and the instantaneous spin (angular velocity) of a celestial body. When the orientation and spin are described in inertial space, the set of rotational elements is often chosen to comprise the two angular coordinates of the direction of the north (or positive) pole and the location of the prime meridian at a standard epoch, and the time derivatives of each of those three angles. Additional parameters may be required when the object is a non-rigid body.

**second, Système International (SI)**: the duration of 9 192 631 770 cycles of radiation corresponding to the transition between two hyperfine levels of the ground state of cesium 133.

**selenocentric**: with reference to, or pertaining to, the center of the Moon.

**semidiameter**: half a diameter, radius. Semidiameter is often used in place of radius when the object is mildly elliptical to refer to a semi-axis of interest (e.g. the vertical semidiameter of the Sun or the semidiameter of the greatest defect of illumination of Saturn).

**semi-major axis**: 1. Half the length of the major axis of an ellipse. 2. A standard orbital element used to describe an elliptical orbit or a hyperbolic orbit. (The orbital semi-major axis is negative for a hyperbolic orbit.)) 3. Half the length of the longest axis of an ellipsoid.

**SI second**: see second, Système International (SI).

**sidereal day**: the period between successive transits of the equinox. The mean sidereal day is approximately 23 hours, 56 minutes, 4 seconds. (See sidereal time.)

**sidereal hour angle**: angular distance on the celestial sphere measured westward along the celestial equator from the equinox to the hour circle passing through the celestial object. It is equal to 360° minus right ascension in degrees.

**sidereal month**: see month, sidereal.

**sidereal time**: the hour angle of the equinox. If the mean equinox is used, the result is mean sidereal time; if the true equinox is used, the result is apparent sidereal time. The hour angle can be measured with respect to the local meridian or the Greenwich meridian, yielding, respectively, local or Greenwich (mean or apparent) sidereal times.

**small solar system body**: a body orbiting the Sun that is not massive enough to be a dwarf planet and is not a comet.

**solar parallax**: see parallax, solar.

**solar time**: the measure of time based on the diurnal motion of the Sun.

solar time, apparent: the measure of time based on the diurnal motion of the true Sun. The rate of diurnal motion undergoes seasonal variation caused by the obliquity of the ecliptic and by the eccentricity of the Earth's orbit. Additional small variations result from irregularities in the rotation of the Earth on its axis.

solar time, mean: a measure of time based conceptually on the diurnal motion of a fiducial point, called the fictitious mean Sun, with uniform motion along the celestial equator.

**solstice**: either of the two points on the ecliptic at which the apparent longitude of the Sun is 90° or 270°; also the time at which the Sun is at either point. (See longitude, ecliptic.)

**spectral types or classes**: categorization of stars according to their spectra, primarily due to differing temperatures of the stellar atmosphere. From hottest to coolest, the commonly used Morgan-Keenan spectral types are O, B, A, F, G, K and M. Some other extended spectral types include W, L, T, S, D and C.

**standard epoch**: a date and time that specifies the reference system to which celestial coordinates are referred. (See mean equator and equinox.)

**stationary point**: the time or position at which the rate of change of the apparent right ascension of a planet is momentarily zero. (See apparent place (or position).)

**sub-earth point**: the point on a body's surface that lies directly beneath the Earth on the line (geodesic) connecting the body's center to the geocenter. For spherical bodies, the Earth would be at the zenith for an observer at the sub-earth point. As viewed from the Earth, a body's sub-earth point appears at the center of the body's disk. In The Astronomical Almanac, the sub-earth point is typically described by a planetographic longitude and latitude. See diagram on page E4.

**sub-solar point**: the point on a body's surface that lies directly beneath the Sun on the line (geodesic) connecting the body's center to the heliocenter. For spherical bodies, the Sun would be at the zenith for an observer at the sub-solar point. In The Astronomical Almanac, the sub-solar point of a planet is typically described by a planetographic longitude and latitude, its distance from the sub-earth point (center of disk), and its position angle (north through east). See diagram on page E4.

**sunrise, sunset**: the times at which the apparent upper limb of the Sun is on the astronomical horizon. In The Astronomical Almanac they are computed as the times when the true zenith distance, referred to the center of the Earth, of the central point of the disk is 90° 50′, based on adopted values of 34′ for horizontal refraction and 16′ for the Sun's semidiameter.

**surface brightness**: the visual magnitude of an average square arcsecond area of the illuminated portion of the apparent disk of the Moon or a planet.

**synodic month**: see month, synodic.

**synodic period**: the mean interval of time between successive conjunctions of a pair of planets, as observed from the Sun; or the mean interval between successive conjunctions of a satellite with the Sun, as observed from the satellite's primary.

**synodic time**: pertaining to successive conjunctions; successive returns of a planet to the same aspect as determined by Earth.

**syzygy**: 1. A configuration where three or more celestial bodies are positioned approximately in a straight line in space. Often the bodies involved are the Earth, Sun and either the Moon or a planet. 2. The times of the new moon and full moon.

**T _{eph}**: the independent argument of the JPL planetary and lunar ephemerides DE405/LE405; in the terminology of General Relativity, a barycentric coordinate time scale. \(T_{\rm eph}\) is a linear function of Barycentric Coordinate Time (TCB) and has the same rate as Terrestrial Time (TT) over the time span of the ephemeris. \(T_{\rm eph}\) is regarded as functionally equivalent to Barycentric Dynamical Time (TDB). (See Barycentric Coordinate Time (TCB); Barycentric Dynamical Time (TDB); Terrestrial Time (TT).)

**TAI**: see International Atomic Time (TAI).

**TCB**: see Barycentric Coordinate Time (TCB).

**TCG**: see Geocentric Coordinate Time (TCG).

**TDB**: see Barycentric Dynamical Time (TDB).

**TDT**: see Terrestrial Dynamical Time (TDT).

**TNO**: see trans-Neptunian Object (TNO).

**terminator**: the boundary between the illuminated and dark areas of a celestial body.

**Terrestrial Dynamical Time (TDT)**: the time scale for apparent geocentric ephemerides defined by a 1979 IAU resolution. In 1991, it was replaced by Terrestrial Time (TT). Obsolete.

**Terrestrial Ephemeris Origin (TEO)**: the original name for the Terrestrial Intermediate Origin (TIO). Obsolete.

**Terrestrial Intermediate Origin (TIO)**: the non-rotating origin of the Terrestrial Intermediate Reference System (TIRS), established by the International Astronomical Union (IAU) in 2000. The TIO was originally set at the International Terrestrial Reference Frame (ITRF) origin of longitude and throughout 1900-2100 stays within 0.1 mas of the ITRF zero- meridian. Formerly referred to as the Terrestrial Ephemeris Origin (TEO).

**Terrestrial Intermediate Reference System (TIRS)**: a geocentric reference system defined by the intermediate equator of the Celestial Intermediate Pole (CIP) and the Terrestrial Intermediate Origin (TIO) on a specific date. It is related to the Celestial Intermediate Reference System by a rotation of the Earth Rotation Angle, \(\theta\), around the Celestial Intermediate Pole.

**Terrestrial Time (TT)**: an idealized form of International Atomic Time (TAI) with an epoch offset; in practice \(TT = TAI + 32^{\rm s}.184\). TT thus advances by SI seconds on the geoid. Used as an independent argument for apparent geocentric ephemerides. (See second, Système International (SI).)

**Tisserand mean axis**: the axis of a rotating deformable body chosen such that the contribution to angular momentum arising from its deformation integrated over its volume is 0.

**topocentric**: with reference to, or pertaining to, a point on the surface of the Earth.

**topocentric place (or position)**: the proper place of an object computed for a specific location on or near the surface of the Earth (ignoring atmospheric refraction) and expressed with respect to either the true (intermediate) equator and equinox of date or the true equator and CIO of date. In other words, it is similar to an apparent or intermediate place, but with corrections for geocentric parallax and diurnal aberration. (See aberration, diurnal; parallax, geocentric.)

**transit**: 1. The passage of the apparent center of the disk of a celestial object across a meridian. 2. The passage of one celestial body in front of another of greater apparent diameter (e.g., the passage of Mercury or Venus across the Sun or Jupiter's satellites across its disk); however, the passage of the Moon in front of the larger apparent Sun is called an annular eclipse. (See eclipse, annular; eclipse, solar.)

transit, shadow: The passage of a body's shadow across another body; however, the passage of the Moon's shadow across the Earth is called a solar eclipse.

**trans-Neptunian Object (TNO)**: a solar system body with a semi-major axis greater than Neptune's.

**true equator and equinox**: the celestial coordinate system defined by the orientation of the Earth's equatorial plane on some specified date together with the direction of the dynamical equinox on that date. The true equator and equinox are affected by both precession and nutation. (See mean equator and equinox; nutation; precession.)

**TT**: see Terrestrial Time (TT).

**twilight**: the interval before sunrise and after sunset during which the scattering of sunlight by the Earth's atmosphere provides significant illumination. The qualitative descriptions of astronomical, civil and nautical twilight will match the computed beginning and ending times for an observer near sea level, with good weather conditions, and a level horizon. (See sunrise, sunset.)

twilight, astronomical: the illumination level at which scattered light from the Sun exceeds that from starlight and other natural sources before sunrise and after sunset. Astronomical twilight is defined to begin or end when the geometric zenith distance of the central point of the Sun, referred to the center of the Earth, is 108°.

twilight, civil: the illumination level sufficient that most ordinary outdoor activities can be done without artificial lighting before sunrise or after sunset. Civil twilight is defined to begin or end when the geometric zenith distance of the central point of the Sun, referred to the center of the Earth, is 96°.

twilight, nautical: the illumination level at which the horizon is still visible even on a moonless night allowing mariners to take reliable star sights for navigational purposes before sunrise or after sunset. Nautical twilight is defined to begin or end when the geometric zenith distance of the central point of the Sun, referred to the center of the Earth, is 102°.

**umbra**: the portion of a shadow cone in which none of the light from an extended light source (ignoring refraction) can be observed.

**Universal Time (UT)**: a generic reference to one of several time scales that approximate the mean diurnal motion of the Sun; loosely, mean solar time on the Greenwich meridian (previously referred to as Greenwich Mean Time). In current usage, UT refers either to a time scale called UT1 or to Coordinated Universal Time (UTC); in this volume, UT always refers to UT1. UT1 is formally defined by a mathematical expression that relates it to sidereal time. Thus, UT1 is observationally determined by the apparent diurnal motions of celestial bodies, and is affected by irregularities in the Earth's rate of rotation. UTC is an atomic time scale but is maintained within 0^{s}.9 of UT1 by the introduction of 1- second steps when necessary. (See leap second.)

**UT0**: a rarely used local approximation to Universal Time; not corrected for polar motion.

**UT1**: see Universal Time (UT).

**UTC**: see Coordinated Universal Time (UTC).

**vernal equinox**: see equinox, vernal.

**vertical**: the apparent direction of gravity at the point of observation (normal to the plane of a free level surface).

**week**: an arbitrary period of days, usually seven days; approximately equal to the number of days counted between the four principal phases of the Moon. (See lunar phases.)

**wobble, polar**: 1. In current practice including the phraseology used in The Astronomical Almanac, it is identical to polar motion. 2. In certain contexts it can refer to specific components of polar motion, e.g. Chandler wobble or annual wobble. (See polar motion.)

**year**: a period of time based on the revolution of the Earth around the Sun, or the period of the Sun's apparent motion around the celestial sphere. The length of a given year depends on the choice of the reference point used to measure this motion.

year, anomalistic: the period between successive passages of the Earth through perihelion. The anomalistic year is approximately 25 minutes longer than the tropical year.

year, Besselian: the period of one complete revolution in right ascension of the fictitious mean Sun, as defined by Newcomb. Its length is shorter than a tropical year by 0.148 × \(T\) seconds, where \(T\) is centuries since 1900.0. The beginning of the Besselian year occurs when the fictitious mean Sun is at mean right ascension 18h 40m. Now obsolete.

year, calendar: the period between two dates with the same name in a calendar, either 365 or 366 days. The Gregorian calendar, now universally used for civil purposes, is based on the tropical year.

year, eclipse: the period between successive passages of the Sun (as seen from the geocenter) through the same lunar node (one of two points where the Moon's orbit intersects the ecliptic). It is approximately 346.62 days.

year, Julian: a period of 365.25 days. It served as the basis for the Julian calendar.

year, sidereal: the period of revolution of the Earth around the Sun in a fixed reference frame. It is the mean period of the Earth's revolution with respect to the background stars. The sidereal year is approximately 20 minutes longer than the tropical year.

year, tropical: the period of time for the ecliptic longitude of the Sun to increase 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds.

**zenith**: in general, the point directly overhead on the celestial sphere.

zenith, astronomical: the extension to infinity of a plumb line from an observer's location.

zenith, geocentric: The point projected onto the celestial sphere by a line that passes through the geocenter and an observer.

zenith, geodetic: the point projected onto the celestial sphere by the line normal to the Earth's geodetic ellipsoid at an observer's location.

**zenith distance**: angular distance on the celestial sphere measured along the great circle from the zenith to the celestial object. Zenith distance is 90° minus altitude.