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GLOSSARY

During the present visit of the solar system, you may have not understood some words or concepts. This glossary will try to help you. Are given below explanations of technical or scientific terms with references to more detailed explanations of the most fundamental concepts.

This glossary provides definitions and explanations for specific words of astronomy. They are presented in alphabetical order. In the glossary, links in italic send to an other item of the glossary since the other links send to pages of the site. This glossary is partly issued from the Introduction aux ephemerides astronomiques published by IMCCE and from the Astronomical Almanach published by USNO. 

Alphabetical list of the entries of the glossary 

 A   B   C   D   E  F  G   H  I   J   K   L   M   N   O  P   Q   R   S   T   U  V  Y  Z


 

Aberration. In astrometry, 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: stellar, Aberration: planetary). 

Aberration: annual. the component of stellar aberration resulting from the motion of the Earth about the Sun. 

Aberration of fixed. See Aberration: stellar. 

Aberration: diurnal. the component of the stellar aberration resulting from the observer’s diurnal motion about the center of the Earth due to Earth’s rotation. 

Aberration: elliptic. the terms of annual aberration which depend on the eccentricity and longitude of perihelion of the Earth. (see perihelion). In catalogues prior to 1984, the elliptic aberration was included in the positions of stars,calculated et the reference date of the catalogue. 

Aberration: instrumental. In optics, phenomena due to the imperfection of instruments deteriorating the quality of the images provided by the optical system. 

Aberration: planetary. The apparent angular displacement of the observed position of a solar system body from its instantaneous geometrical position 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: stellar (or aberration of fixed). 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.)

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.

Anomaly: eccentric. In the keplerian elliptic motion, the angle (OP, OM') where O is the centre of the ellipse, P the pericenter and where M' is the point of the circle with radius OP projected on OP at the same point than the point M being the position of the body at time t. 

Anomaly: mean. In the keplerian elliptic motionn, the product of the mean motion of the body by the elapsed time since the passage of the body at the pericenter. 

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. 

Anomaly: true. In the keplerian elliptic motion, the angle (FP, FM) where F is the focus of the ellipse where is the central body, P the pericenter and M the position of the body at time t. 

Aphelion. The point in an orbit of a planet that is the most distant from the Sun. See Apocenter. 

Apocenter. The point in an orbit of a body that is the most distant from the central object situated at the focus of the ellipse. See Apocenter. 

Apogee.The point in an orbit of a body around the Earth, that is the most distant from the Earth. See Apocenter.  See Apocenter. 

Astrometric direction of a solar system body. Direction joining the position of the Earth at time t to the position of the solar system body at time t - ΔT, ΔT being the light time. It is of the same kind of the direction of a star provided by the catalogue, once made the corrections for the proper motion and the annual parallax. 

Astronomical unit (au). Prior to 2012: Semi-major axis of the orbit described around the Sun by a planet having a negligeable mass, not perturbated, whose mean motion is equal to k radians per day, k being the constant of Gauss. From 2012, IAU decided that the Astronomical Unit will be defined as follows: 149 597 870 700 meters.

Azimuth the angular distance measured eastward along the horizon from a specified reference point (usually north but often south is used by the astronomers). Azimuth is measured to the point where the great circle determining the altitude of an object meets the horizon. 

Barycentric. Relative to a reference system centered at the barycenter of the solar system. 

Calendar: gregorian. Calendar introduced by the 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 1700, 1800, 1900 and 2100 are not leap years. The mean duration of the gregorian year (365.2425 days) is a good approximation of thetropical year.

Calendar: julian.Calendar introduces by Julius Caesar, in -45 (46 before J.-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 month February will have 29 days). The Julian calendar was superseded by the Gregorian calendar.The mean duration of the Julian year (365.25 days) is a bad approximation of the tropical year. The Julian calendar is used by historians and astronomers for the dates before its creation. Historians note "1 before J.-C." the year just before the year 1 of the Christian era: it is a leap year; astronomers note 0 the year 1 before J.-C. (leap year), -1 the year 2 before J.-C. (common) and so on... 

Calendar: proleptic. Calendar extrapolate prior to its date of introduction.

Celestial pole of the ephemerides (CEP). Pole (north) of reference for the motion of the pole and for the nutation. Its direction, close to the rotation axis of the Earth, is defined so it will be no diurnal or quasi-diurnal motion either in Earth or in space. 

Celestial poles. The two intersection points (celestial North pole and celestial South pole) of the celestial sphere with a diameter the direction of which being close to that of the axis of rotation of the Earth.

Celestial sphere . Sphere having arbitrary centre and radius on which points show directions in space. For any direction D is associated the intersection point of the sphere and of the half line parallele to D the origin of which being the centre of the sphere. 

Conjunction. Phenomenon when two or more bodies have geocentriccelestial longitudes (see celestial longitude) or right ascensions equal. Conjunction of a outer planet with the Sun : the geocentric celestial longitudes of the planet and the Sun are equal. Conjunction of Mercury or Venus with the Sun : the geocentric celestial longitudes of the planet and the Sun are equal. The conjunction is called superior or inferior if the Sun is between the Earth and the planet (superior) or if the planet is between the Earth and the Sun (inferior). Conjunction in right ascension of two planets together, or of a planet and the Moon or a planet and a star : the right ascensions droites of the two objects are equal. The conjunction may also be in longitudes (in the ecliptic reference frame).

Constant of the precession. Coefficient of time in the mathematical representation of the general precession in longitude. This constant is deduced from the observation. 

Coordinates: apparent of a star at time t. Coordinates providing the direction of the star as seen by an observer situated at the center of the Earth at time t. Apparent coordinates are referred to the equinox and equator true of the date or at true equinox and mean ecliptic of the date. 

Coordinates: astrometric of a solar system body at time t. Right ascension and declination of the astrometric direction of the body at time t referred to mean equinox and equator of a reference date (J2000, for present ephemerides). 

Coordinates: astronomical of a place (astronomical longitude and latitude ). Coordinates : polar of the vertical of the site referred to true equator of the date and to the origin direction , intersection of this plane with the terrestrial origin meridian. 

Coordinates: ecliptic of a direction. Coordinates of the direction referred to the mean ecliptic and to the origin direction of this plane defined by the equinox. These coordinates are "true" when they are referred to the mean ecliptic and to the true equinox of the date; mean of the date if referred to the mean ecliptic and equinox of the date and mean of a date when they are referred to the mean ecliptic and equinox of the date of reference. (see Coordinates: true and mean). One uses two kinds of ecliptic coordinates : the cartesian ecliptic coordinates and the polar ecliptic coordinates, the celestial longitude and latitude. 

Coordinates: equatorial of a direction. Coordinates of the direction referred to the celestial equator and to the origin direction of this plane defined by the equinox. These coordinates are called "true" when referred to the true equator and equinox of the date, mean of the date when referred to the mean equator and equinox of the date and mean of a date of reference when referred to the mean equator and equinox of this date of reference (see Coordinates: true and Coordinates: mean). One use two kinds of equatorial coordinates: the cartesian equatorial coordinates and the polar equatorial coordinates right ascension and declination. 

Coordinates: geometric of a body at time t. Coordinates of the geometric position of this body. 

Coordinates: hour of a direction, in a given site (hour angle and declination). Polar coordinate of the direction referred to the true equator of the date and to the origin direction, intersection of this plane with the celestial meridian of the site. 

Coordinates: horizontal of a direction, in a given site (azimuth and altitude). Polar coordinates of the direction referred to the horizontal plane of the site and to the origin direction, intersection of this plane with the vertical including the direction of the celestial pole south (for the astronomers) or north (for the sailors). 

Coordinates: mean. Coordinates referred to the mean equinox and equator or the mean ecliptic of the date (mean coordinates of the date) or of a date of reference (mean coordinates of a date of reference). (see Coordinates: ecliptic, Coordinates: equatorial). 

Coordinates: planetocentric. Coordinates used to identify a point at the surface of a planet. The planetocentric longitude of a point on the surface is the dihedral angle between the meridian of the considered point and an origin meridian chosen by convention . This longitude is counted, from the origin meridian from 0° to 360° in the direct direction. The planetocentric latitude of a point at the surface is the angle made between the direction "center of planet"-point at the surface with the equatorial plane of the planet . It is counted from the equator of the planet from 0° to +90° towards the North pole and from 0° to -90° towards the South pole. 

Coordinates planetographic. Coordinates used to map the surface of a planet or a satellite. The planetographic longitude of a point at the surface is the dihedral angle between the meridian of the considered point and an origin meridian chosen by convention. It is counted from the origin meridian from 0° to 360° in the opposite direction to the rotation of the body. The planetographic latitude of a point at the surface is the angle made by the normal to the surface at this point with the equatorial plane of the body. It is counted from the equator of the body from 0° to +90° towards the North pole and from 0° to -90° towards the South pole. 

Coordinates: true. Coordinates referred to the equinox and true equator of the date or to the true equinox and mean ecliptic of the date. (see Coordinates: ecliptic, Coordinates: equatorial). 

Day (d). Time unit of the IAU system of astronomical units. The day is equal to 86 400 seconds SI. 

Declination of a direction. One of the polar equatorial coordinates and one of the hour coordinates . Angle of the direction with thecelestial equator. Declination is counted in degrees, from -90° to +90 °. 

Eclipse. Darkening of a celestial body produced by the arrival of another celestial body between this body and the light source making the first body visible or arrival of a celestial body in the shadow of another body. 

Eclipse of the Moon. Eclipse where the Earth is between the Moon and the Sun. The eclipse of the Moon is named total when the Moon completely disappears in the shadow of the Earth, partial when the Moon does not enter completely in the shadow of the Earth and by the penumbra when the Moon enters only in the penumbra of the Earth without entering in the shadow. 

Eclipse of the Sun. Transit of the Sun behind the Moon for a terrestrial observer. In fact, it is an occultation of the Sun by the Moon. The eclipse of the Sun is named total when the Moon is completely hidden by the Sun (the observer is in the shadow of the Moon), annular when the disc of the Moon is smaller than the disk of the Sun and completely inside it leaving only a ring of light around the disk of the Moon and partial whan the disk of the Moon occults only a part of the disk of the Sun without having a total or an annular eclipse. 

Ecliptic: mean of the date. Plane perpendicular to the cinetic moment of the Earth-Moon barycenter in its heliocentric motion. The ecliptic is named inertial when the velocity is calculated in a non-rotating reference system and rotational when the velocity is calculated in a rotating reference system. The mean cinetic moment is obtained by removing the true component of the cinetic moment issued from a secular theory the terms depending of mean longitudes of planets and of the arguments of the Moon. 

Elements: elliptic. In the keplerian elliptic motion , parameters allowing to define the position of a body on its orbit. Five parameters are sufficient to define an orbit: the semi-major axis, the eccentricity of the ellipse, the inclination of the ellipse on a reference plane, the longitude of the ascending node of the ellipse on a reference plane, the longitude of the pericenter. A sixth parameter is necessary in order to know the position of the body on the orbit, for example the mean anomaly , the true anomaly or the mean longitude. The first five parameters are constants and the sixth is a function of time (linear for the mean anomaly of for the mean longitude). In the perturbated elliptic motion one defines six osculating elliptic elements functions of time (see secular theories, general theories). 

Elements: mean. Secular terms of the mathematical representation of the elliptic elements of a celestial body obtained in a secular theory of the motion of the body. These elements may be referred to the ecliptic and to the mean dynamical equinox to a date of reference (for example J2000) or to the ecliptic and to the mean dynamical equinox of the date. These elements represent the development depending on time of the long periodic terms of the general theories. They are used to obtain the constantes of integration of the secular theories and of the general theories and to à variations seculaires et des theories generales improve the long periodic terms of the general theories. 

Elements: osculating. Elliptic elements taken by a celestial body at time t if, at that time, all the perturbating forces disappeared. The real orbit is tangent to the osculating orbit at time t. 

Elongation (the greatest) of an inferior planet. Instant when the difference between the geocentric celestial longitude of the planet and of the one of the Sun is maximum. 

Epoch (standard). See Origin of time. 

Equator of a body. Great circle on the surface of a body, considered as an ellipsoid of revolution, perpendicular to its rotation axis (see Equateur: celestial). 

Equator: celestial. Great circle of the celestial sphere perpendicular to an axis close to the axis of rotation of the Earth. More generally, plane of thos great circle (see Equator (celestial): true , Equator (celestial): mean). 

Equator (celestial): true (o True equator of the date). Great circle of the celestial sphere perpendicular to the direction of the celestial pole of the ephemerides (CEP). 

Equator: mean of the date. It is deduced from the true equator of the date through a transformation provided by the theory of the nutation. The transformation allowing to go from the mean equator of the date to the mean equator of another is provided by the theory of the precession. See Precession-nutation. 

Equator: true of the date. See True celestial equator. 

Equation of the equinoxes. Difference Truesidereal time minus Mean sidereal time. 

Equation of the centre. Part of the equation of time having a period of one year, due to the eccentricity of the orbit of the Earth. In the elliptic motion of the Earth around the Sun, it represents the difference True anomaly minus Mean anomaly. 

Equation of time. Difference Mean solar time minus True solar time. 

Equinox of a catalogue. Origin of the right ascensions provided by the catalogue. This equinox is close to the dynamical mean equinox of the date of reference of the catalogue but not the same. 

Equinox: dynamical of the date. Ascending node of the mean ecliptic of the date on the mean equateur of the date (dynamical mean equinox) or on the true equator of the date (dynamical true equinox). It exists two dynamical equinoxes, one inertial, the other rotational depending on the used mean ecliptic, inertial or rotational (see Mean ecliptic). The transformation to go from the dynamical mean equinox of a date to another date is provided by the theory of the precession. 

Eccentricity. Parameter describing the shape of a conic. For an ellipse, ratio between the distance center-focus to the semi-major axis. The eccentricity is one of the usual elliptical elements. 

Flattening. Parameter showing how a celestial body differs from a sphere: it is the ratio f=(a-b)/a where a is the equatorial radius of the ellipsoid and b the polar radius (b<a). 

Gaussian constant (k = 0.017 202 098 95). Constant defining, in the system of the astronomical units, the unit of length (astronomical unit) from the unit of time (day) and the unit of mass (mass of the Sun) from the third law of Kepler. k2 has dimension L3 M-1 T-2 as the constant of the gravitation. 

General theory. Mathematical representation of the elliptical perturbated motion of a planet where the coordinates are represented under the form of Fourier's series. The arguments of these series are combinations of linear functions of time. These functions of time may be arguments having a period of the order of these of the revolution of planets, as, for example, the mean mean longitudes (arguments of short period, or arguments of period of the order of these of the longitudes of the nodes and of the perihelions (see pericenter) (arguments of long period). These theories have an interval of validity very large (about one million, or a ten million years) but have, in general, a precision not sufficient to build ephemerides. They are used for the study of the evolution of the solar system. 

Geocentric. Referred to a reference system centered at the centre of the Earth. 

Geoid. Surface coinciding with the average equilibrium surface of the seas and extended under the continents everywhere perpendicular to the direction of the gravitational field. 

Height of a direction, for a given place. One of the horizontal coordinates. Angle of the direction with horizontal plane of the place. 

Heliocentric. Referred to a reference system centered at the centre of the Sun. 

Horizontal plane of a place. Plane passing through the centre of the celestial sphere and perpendicular to the vertical of the place. 

Hour angle of a direction, for a given place. One of the hour coordinates . Dihedral angle of the hour circle of the direction and of the meridian of the place taken as origin. The hour angle is taken positively in the retrograde direction. 

Hour circle of a direction. Half great circle of the celestial sphere including the celestial poles and the point of the celestial sphere associated to that direction. The hour circle is then perpendicular to the celestial equator. 

Inclination. Angle between the plane of the orbit of a celestial body and a reference plane. The inclination is one of the elliptical elements. 

Julian Date (JD). Elapsed time from January 1, -4712 at 12h, origin of the Julian period. It is expressed in days and fraction of a day. For rigorous use, one must specify the time scale used (UT, TT, TE, etc.). 

Julian day. Integer part of the Julian date. 

Julian period. Chronology numbering days continuously since January 1, -4712 at 12h.

Keplerian ellipse . Orbit of a body in a keplerian elliptic motion. 

Keplerian elliptic motion. Keplerian motion for which the orbit of the body is an ellipse. It is, for example, the motion described by a planet around the Sun in the case of the planet undergoes only the attraction of the Sun (the Sun and the planet being considered as punctual masses).

Keplerian perturbated elliptic motion. Motion close to the Keplerian elliptic motion in which the body undergoes not only the attraction of the central body but also the attraction of other perturbating bodies having small masses compred to the one of the central body. It is, for example, the motion described by the planets around the Sun (the Sun and the planets being considered as punctual masses). 

Keplerian motion. Relative motion of a punctual body M around a punctual central body O, the mass of M being small compared to the one of O, the only forces being the newtonian attractions between M and O. In a keplerian motion the orbit of M is a conic whose focus is O. 

Lagrange points. Points of equilibrium near the orbit of the Earth. They are five. 

Latitude (astronomical) of a place. One of the astronomical coordinates. Angle of the vertical of the polace with the true equator. The astronomical latitude is counted in degres, from -90° to +90°. 

Latitude (celestial) of a direction. One of the polar ecliptic coordinates . Angle of the direction with the mean ecliptic . The celestial latitude is counted in degrees, from -90° to +90°. 

Latitude: planetocentric. See Planetocentric coordinates. 

Latitude: planetographic. See Planetographic coordinates. 

Libration of the Moon. Apparent oscillations of the Moon allowing to see more than half of its surface. There are two different librations: first the optical libration due to the variations of the orbital velocity of the Moon (libration in longitude), to the inclination of the equator of the Moon on the plane of its orbit (libration in latitude) and to the motion of the trrestrial observer coming from the rotation of the Earth around its axis (diurnal libration) and, second, the physical libration - much smaller - due to the variations of the rotation of the Moon around its axis. 

Light-time. The interval of time required for light to travel from a celestial body to the Earth. This duration may be considered as constant for a star but not for a solar system body.

Longitude (astronomical) of a place. One of the astronomical coordinates. Dihedral angle of the celestial meridian of the place with the celestial meridian passing through the intersection of the terrestrial origin meridian with the true equator of the date. The astronomical longitude was counted in degrees, i.e. -180° to +180° positively towards West as usual in France, or from 0° to 180° "East" or "West" as recommended by the IAU. 

Longitude (celestial) of a direction for a given date. One of the polar ecliptic coordinates . Dihedral angle of the two half great circles of the celestial sphere passing through the poles of the ecliptic and including, respectively, the point representing the direction and the equinox (half great circle taken as origin). The celestial longitude is counted, in degrees, positively in the direct direction from 0° to 360°. 

Longitude (mean). In the keplerian elliptic motion, the parameter λ defined by M+P where  M represents the mean anomaly and P the longitude of the pericenter 

Mean mean longitude of a planet. Linear function of the time t defined by n t -λ0 where n is the mean motion of the planet and λ0 the constant of integration of the mean longitude of the planet. The mean mean longitudes are the usual arguments of the secular theories and of the general theories. 

Longitude: planetocentric. See Planetocentric coordinates. 

Longitude: planetographic. See Planetographic coordinates. 

Magnitude. Number describing the luminosity of a celestial body, measured on a logarithmic scale. The smallest numbers correspond to the brightest bodies. The apparent magnitude describes the luminosity of a celestial body as seen from the Earth. The absolute magnitude descibes the luminosity of a celestial body as seen from a distance of 10 parsecs of the Earth for the stars and as seen from a distance of one astronomical unit for solar system bodies.

Main problem of the theory of the Moon. Study of the motion of the Moon supposing that the only perturbationg body is the Sun; the Earth-Moon barycenter moving on a Keplerian ellipse. 

Mean solar time. True solar time solaire vrai corrected from the inequalities of the right ascension of the Sun : it is the linear part, function of time, of the true solar time. 

Meridien: celestial (for a given place). Half great circle of the celestial sphere containing the true celestial poles and the zenith of the place (see Vertical of a place). More generally, the half plane containing this half great circle. 

Meridian of Greenwich. Terrestrial meridian passing through the Greenwich observatory. The meridian of Greenwich is now replaced, as origin meridian, by the terrestrial origin meridian. 

Meridian of the ephemerides. Fictitious meridian being at each instant at the position of the terrestrial origin meridian supposing that the Earth was rotating with a constant angular velocity. Its longitude relative to the terrestrial origin meridian is equal to -1.002 7379 ΔT where ΔT= TT - UT1. All the astronomical calculations made using the Terrestrial Time TT and relative to the meridian of the ephemerides are formally identical to those made using UT1 and relative to the terrestrial origin meridian. 

Meridian (of a celestial body). Half great circle of the celestial sphere containing the poles of the body. 

Meridian (terrestrial) of a place. Half great circle of the geocentric celestial sphere containing the terrestrial poles and whose half plane passes through the considered point. 

Meridian: terrestrial origin. Terrestrial meridian, close to the meridian of Greenwich, conventionally defined by the coordinates of points of the earth's surface. 

Meteor. Luminous phenomenon observed in the terrestrial atmosphere, generally due to the crossing of the atmosphere by a meteorite.

Meteorite. Piece of an asteroid or a cometary core orbiting in space named meteorite after falling on Earth or on another planet.

Meteoritic swarm. Ring of particules spread along the orbit of a comet, coming from the dust ejected by its core. 

Mean motion. In the Keplerian elliptic motion, mean angular velocity of a body for a complete revolution on an orbit having a given semi-major axis. The mean motion n is related to the semi-major axis a through the third law of Kepler n2a3 = constant (depending on the central body). 

Nadir. See Vertical of a place. 

Node. One of the two points of the celestial sphere associated to the intersection of the orbital plane with a reference plane. The position of the node is one of the elliptical elements. 

Nutation. See Precession-nutation. 

Nutation: luni-solar. See Luni-solar precession-nutation. 

Obliquity of the ecliptic. Inclination of the mean ecliptic on the mean equator for a given date. 

Occultation. Transit of a celestial body behind another body hidding it from an Earth-based observer (or from any observer, for example on a space probe).

Opposition of a superior planet with the Sun. Phenomenon occurring when the geocentric celestial longitudes of the planet and of the Sun differ from 180°. 

Orbit. Path described by a celestial body in space. 

Origin of times (or Standard epoch). In 1984 the origin of times has been fixed on January 1, 2000 at 12 heures in the considered time-scale. It corresponds to the julian date 2 451 545.0 and is designated by J2000.0 or J2000. By definition, the beginning of a Julian year is separated from the Standard epoch by an integer number of Julian years. 

Parallax. Difference between the apparent directions of a celestial body when the observer moves from one place to another. Angle under which is seen, from the body, the distance between the two places of the observer. (see Parallax: annual, Parallax: diurnal). 

Parallax: annual. Difference between the apparent directions of a star as seen by an observer situated at the Sun and an observer on Earth. Angle under is seen from the star the distance Sun-Earth i.e. the astronomical unit or semi-major axis of the orbit of the Earth. 

Parallax: diurnal. Difference between the apparent directions of a celestial body as seen by an observer situated at the center of the Earth and an observer at the surface of the Earth. The diurnal parallax of a star is negligeable. 

Penumbra of the Earth, of a planet or any solar system body: , zone of space where the considered body occults only a part of the Sun.

Pericenter. On an elliptical orbit , the closest point to the central body at focus. The position of the pericenter is one of the usual elliptical elements usuels. The pericenter is called perigee when the central body is the Earth and, perihelion when the central body is the Sun. 

Perigee. Position of a satellite of the Earth during its revolution at the closest distance to the Earth. See Pericenter. 

Perihelion. Position of the Earth during its revolution around the Sun at the closest distance to the Sun. See Pericenter. 

Perturbations (planetary direct) of the theory of the Moon. Perturbations of the motion of the Moon due to the newtonian attractionof the planets on the Earth-Moon vector. 

Perturbations (planetary indirect) of the theory of the Moon. Perturbations of the motion of the Moon due to the deviation coming from the attraction of the planets, between the heliocentric real motion of the Earth-Moon barycenter and a Keplerian elliptic motion. 

Phase Angle. The angle measured at the center of an illuminated body between the light source and the observer.

Phases of the Moon. Configurations of the Moon for values of the geocentric celestial longitudes: equal for the New Moon, differ from 90° for the First Quarter, from 180° for the Full Moon or from 270° for the Last Quarter. 

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.

Poisson's series of order p. Developments in power of time t under the form : S0 + tS1 + t2S2 + ... + tpSp where the functions Si are Fourier's series. 

Poles of a celestial body. The two intersection points of the surface of the body (North pole and South pole) with the axis of rotation of the body.

Position: geometric of a body. Position effectively occupied by the body at time t, without taking into account the speed of light. 

Precession of the equinoxes . See Precession-nutation . 

Precession: general. Sum of the luni-solar precession (see Precession-nutation: luni-solar) and of the planetary precession. 

Precession: general in longitude. Secular shift of the equinox along the mobile ecliptic. This effect is the result of the luni-solar precession (see Precession-nutation: luni-solar) in the retrograde direction along the ecliptic of the reference epoch and of the planetary precession in the direct direction on the mobile equator, due to the shift of the ecliptic. 

Precession: luni-solar. See Luni-solar precession-nutation. 

Precession-nutation. Shift depending on time of the plane of the equator and of the plane of the ecliptic, relative to an inertial system of reference, due to the gravitational actions of the Moon, the Sun and the planets. The mathematical representation of this shift includes secular terms, periodic series and Poisson's series. By convention, we name precession all the secular terms and nutation all the periodic series and the Poisson's series. 

Precession-nutation: luni-solar. Shift of the plane of the equator under the action, essentially, of the Moon and the Sun. The action of the planets is not negligeable and is now taken into account in modern theories. As for the precession-nutation, the luni-solar precession-nutation decomposes conventionally into luni-solar precession and luni-solar nutation. 

Precession: planetary. Slow shift of the plane of the ecliptic due to the gravitational action of planets on Earth.

Proper motion of a star. Motion in right ascension and in declination of a star making its position changing with time. 

Proper time. in relativistic theory, time measured in a laboratory by an ideal clock moving together with an observer. Proper time is directly observable and, therefore, independent of any coordinates. It is different from the time coordinate. 

Quadrature of a superior planet with the Sun. Phenomenon occurring when the geocentric celestial longitudes of the planet and of the Sun differ from 90°. 

Radiant. Point of the celestial sphere from where the meteors of a meteoritic swarm seem to come. 

Reduction to the equator. Part of the equation of time having a six month period, due to the obliquity of the ecliptic. 

Reference inertial system (or galilean). Reference spatial system used in newtonian mechanics, associated to an uniform time scale. Two reference inertial systems are deduced one from the other by a translational motion of constant velocity. It is in these reference systems that the fundamental laws of general mechanics are valid. 

Reference system: spatio-temporal. Reference system used in relativistic mechanics in which there is no more separation between spatial coordinates and time coordinates (see Time-coordinate). In the framework of the general relativity, there is no more universal reference system but only local systems. In the solar system, it is possible to have a hierarchy between the reference systems: barycentric system centered at the barycenter of the solar system, heliocentric centered at the Sun, Earth-Moon local centered at the barycenter of the Earth-Moon system, geocentric centered at the center of mass of the Earth and topocentric the origin of which being a point at the surface of the Earth. 

Refraction (astronomical). Change in the direction of the luminous rays coming from a celestial body due to the crossing of the terrestrial atmosphere (or more generally of a planetary atmosphere). The refraction makes that the observed zenithal distance of the body is smaller than the zenithal distance without atmosphere. Its magnitude depends on the zenithal distance of the body, on the atmospheric conditions and of the wavelength of the light rays. 

Right Ascension of a celestial body. 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 counted from 0h to 24h and is usually given in combination with declination in order to determinate the direction of the object on the celestial sphere.

Rise and set of a celestial body, for a given site. Instants when the zenithal distance of the celestial body z outside the atmosphere is: z = 90° + R(90°) where R(90°) is the value of the refraction for a zenithal distance of 90° (refraction at horizon). The value of the refraction at horizon being not well-known, the instants of rise and set of the celestial bodies may not be determined with an accuracu better than one minute of time. 

Rise and set of the Moon, for a given site. That are referred either to the upper limb of the Moon or to its center and are calculated by takin into account the parallax. The instants of rise and set of the upper limb of the Moon are the instants when the zenithal distance z of the centre of the Moon outside the atmosphere is z = 90° + R(90°) + s - pi where R(90° ) is the refraction at horizon, s the apparent radius of the Moon and pi the parallax. 

Rise and set of the Sun, for a given site. They are referred either to the upper limb of the Sun or to its center. The instants of rise and set of the upper limb of the Sun, are the instants when the zenithal distance z of the centre of the Sun outside the atmosphere is z = 90° + R(90°) + s where R(90°) is the refraction at horizon and where s is the apparent radius of the Sun. One will take most of time 34' as value of the refraction at horizon and 16' as the value of the apparent radius of the Sun. 

Second SI (s). Unit of time of the Système International since 1967. the second SI is the duration of 9 192 631 770 cycles of the radiation corresponding to the transition between two hyperfine levels of the fundamental state of the atom of Cesium 133. 

Secular Terms. Polynomials of time encountered in the mathematical representation of different astronomical phenomena, as, for example the theories of the motion of celestial bodies or the theory of the precession-nutation. 

Semi-major axis. Parameter corresponding to half of the major axix of an ellipse. The semi-major axis is one of the usual elliptic elements . 

Shadow (or Umbra) of the Earth, of a planet or of a natural satellite. Area in space where the Sun is completely hidden by the considered body. 

Sidereal Timefor a given place, at a given instant. Hour angle of the equinox. The Sidereal Time is named true when it is the true equinox and mean for the mean equinox of the date. For a given place, at a given date, the sum of the true right ascension of a celestial body and its hour angle is equal to the true sidereal time. At the time of the superior transit of a celestial body at meridian, its true right ascension is equal to the true sidereal time. 

Sub-solar point. Point of the surface of a celestial body being at the intersection of the half-line joining the center of the body to the center of the Sun.

Sub-terrestrial point. Point of the surface of a celestial body being at the intersection of the half-line joining the center of the body to the center of the Earth. 

Terrestrial Time (TT). Scale of time used for the geocentric apparent ephemerides for which the unit of time is the second SI. At January 1, 1977, at 0h TAI, TT has the value January 1, 1977, 0h 0min 32.184s. It is an ideal time scale the practical realisation of which being linked to the International Atomic Time TAI, through TT = TAI + 32.184 s. 

Terminator. The boundary between the illuminated and dark areas of a celestial body. 

Theory with secular variations. Mathematical representation of the elliptical perturbated motion of a planet where the coordinates are represented under the form of secular terms and of Poisson's series. The arguments of these series are combinations of linear functions of time. These functions of time are only arguments of a period of the order of the revolution of planets, as, for example, the mean mean longitudes. These theories have an interval of validity of the order of several thousands years, their precision being sufficiently good to build ephemerides. 

Time: International Atomic Time (TAI). The continuous timescale 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. 

Time-coordinate. In relativistic mechanics, the first coordinate of the space-time divided by the speed of light. In a barycentric spatio-temporal reference system, the time-coordinate may be interpreted as the time indicated by a clock at rest referred to the barycenter of the solar system and at the infinite from the planets. 

Time coordinate barycentric (TCB). Scale of time-coordinate linked to the barycentric spatio-temporal reference system which replaces the Barycentric dynamical time TDB in the system recommended by IAU in 1991. TCB differs from the Terrestrial time TT by periodic terms, secular terms and Poison's terms. 

Time coordinate geocentric (TCG). Scale of time-coordinate linked to the geocentric spatio-temporal regerence system. TCG differs from the Terrestrial Time TT only by a secular term. 

Time: Ephemeris Time (TE ou ET). Time-scale used from 1952 to 1976 for dynamical theories and until 1984 for the ephemerides of solar system bodies. This time-scale is defined from the Newcomb's theoretical model of the motion of the Earth around the Sun. This time-scale is now replaced by several time-scales such as: the Terrestrial Time TT, the Time-coordinate Barycentric TCB, the Time-coordinate Geocentric TCG and the barycentric Dynamical Time TDB. 

Time dynamical barycentric (TDB). Scale of time-coordinate recommended by IAU in 1976 for the ephemerides and for the dynamical theories referred to the barycenter of the solar system. TDB differs from the Terrestrial Time TT by periodic terms and by Poisson's terms. In 1991, the IAU has recommended to remplace TDB by the time coordinate barycentric TCB. 

Topocentric. Referred to a reference system centered on a point at the surface of the Earth. 

True solar time for a given place, at a given instant. Hour angle of the center of the Sun for this place, at this instant. 

Universal Time (UT or TU). Scale of time linked to the diurnal rotation of the Earth which has been for a long time the basis of the Legal Time. UT is defined by a mathematical relationship providing the sidereal time as a function of the Universal Time. It is possible to determminate UT from the observations of stars (transits of stars at the meridian, for example). This Universal Time is referred to a fixed pole on Earth and is noted UT0. The Universal Time referred to the celestial pole of the ephemerides CEP is obtained by freeing the movement of the pole and is noted UT1. Since 1984 the legal time scale is no more based upon the Universal Time but on the Universal Time Coordinated UTC. 

Universal Time Coordinated (UTC). Scale of time broadcast by time signals and used as a basis for the legal time. In fact, it is the Atomic International Time TAI shift by an integer number of seconds. This number is regularly modified such that the difference between UTC and the Universal Time UT1 was never larger then 0.9s in absolute value. 

Vertical: the apparent direction of gravity at the point of observation (normal to the plane of a free level surface). The associated point of the celestial sphere is the zenith and the opposite point is the nadir. 

VLBI. Very long base interferometry, method of the radio astronomy recording a signal from two sites at large distance (even on different continents) with a very precise timing allowing to interfer in a correlator. The position of the source may be measured with an accuarcy a few tens of microseconde of degree. 

Year: julian. Unit of time taken as 365.25 days (basis of the Julian calendar). 

Year: sidereal. Elapsed time for the Earth to make a complete revolution of 360° around the Sun in a fixed reference frame. The duration of the sidereal year is 365 days 6 h 9 min 10 s.

Year: anomalistic. Interval of time between two passages of the earth at the perihelion. The duration of the anomalistic year is 365 days 6h 13m 53s. 

Year: tropical. Interval of time between two passages of the Sun at the mean equinox. The duration of the tropical year is 365.2422 days, i.e. 365 days 5h 48m 45s. 

Zenith. See Vertical of a place. 

Zenith distance of a direction, for a given place. Angle between that direction and the direction of the zenith (see Vertical). The zenith distance is the complement of the height.