ΔT:
ΔUT1 (or ΔUT):
the value of the difference between Universal Time (UT) and Coordinated Universal Time (UTC): ΔUT1=UT1-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:
the terms of annual aberration which depend on the eccentricity and longitude of perihelion of the Earth. (See aberration, annual; perihelion.)
aberration, elliptic:
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, special relativistic:
In special relativity the velocity of light is constant in all inertial frames, and the Lorentz formula for addition of velocities applies. To first order Newtonian and relativistic aberration agree.
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.)
Absolute time:
conceptually a unique uniform time that can be measured by any ideal clock irrespective of its position and state of motion in the whole universe; used in Newtonian physics and mechanics.
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.
analemma:
a curve showing the angular offset, as a function of time, of a celestial body (usually the Sun) from its mean position on the celestial sphere as viewed from another celestial body (usually the Earth). In the case of the Sun as seen from the Earth this is a curve resembling a figure eight that is commonly printed on globes.
angle of the vertical:
angular momentum:
measure of the extent to which an object will continue to rotate or revolve about a reference point unless acted upon by an external torque.
angular momentum vector:
a vectorial integral of motion of a body. In an inertial frame of reference, the time-derivative of the angular momentum vector is equal to the vectorial sum of the external torques. The angular momentum can be decomposed into a sum of the orbital angular momentum vector (associated with the orbital motion of the body as a whole) and the spin angular momentum vector (associated with the rotation of the body about its center of mass). The orbital angular-momentum vector is equal to the mass of the body multiplied by the cross-product of the position and the velocity of the center of mass. The spin angular-momentum vector is equal to the product of the inertia tensor by the angular velocity vector.
annual parallax:
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 one celestial object and another, as viewed from a third body. For objects moving along the ecliptic and viewed from the Earth, the time of appulse is close to that of conjunction in ecliptic longitude.
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.
astrographic place:
same as astrometric place. Obsolete.
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):
direction of a solar system body formed by applying the correction for light-time displacement to the geometric position. Such a position is directly comparable with the catalog positions of background stars in the same area of the sky, after the star positions have been updated for proper motion and parallax. There is no correction for aberration or deflection of light since it is assumed that these are almost identical for the solar system body and background stars. An astrometric place is expressed in the reference system of a star catalog; in The Astronomical Almanac, the reference system is the International Celestial Reference System (ICRS).
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:
astronomical unit (au):
the radius of a circular orbit in which a body of negligible mass, and free of perturbations, would revolve around the Sun in :math:`2π/k` days, :math:`k` being the Gaussian gravitational constant. This is slightly less than the semimajor axis of the Earth’s orbit.
astronomical zenith:
see zenith, astronomical.
atmospheric loading:
crustal deformation caused by changes in the weight of a column of air.
atomic second:
augmentation:
the amount by which the apparent semidiameter of a celestial body, as observed from the surface of the Earth, is greater than the semidiameter that would be observed from the center of the Earth.
autumnal equinox:
see equinox, autumnal.
axis of inertia:
any the three axes constituting an orthogonal right-handed Cartesian coordinate system wherein the inertia tensor of a body assumes a diagonal form. The three diagonal elements are termed the principal moments of inertia. If both the shape and mass density of a celestial body are symmetrical under rotation about a given axis, this axis (the symmetry axis) is a principal axis. It is also referred to as the axis of figure.
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 spacetime 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 timescale defined by the IAU (originally in 1976; named in 1979; 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 over long periods of time; differences between TDB and TT evaluated at the Earth’s surface remain under 2 ms for several thousand years around the current epoch. TDB is functionally equivalent to Teph, the independent argument of the JPL planetary and lunar ephemerides DE405/LE405. (See second, Système International (SI).)
Barycentric Ephemeris Time (Teph):
the time scale of the Jet Propulsion Laboratory development ephemerides (the DE nnn series for solar system bodies) that has been scaled to Terrestrial Time (TT). It is equivalent to the redefined Barycentric Dynamical Time (TDB) as redefined by the IAU in 2006.
(See Barycentric Coordinate Time (TCB); Barycentric Dynamical Time (TDB); Terrestrial Time (TT).)
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 :smallcaps:`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 :math:`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 IAU 2000A precession nutation model. The motions of the CIP are those of the Tisserand mean axis of the Earth with periods greater than two days. (See nutation; precession.)
Celestial Intermediate Reference System:
a geocentric reference system related to the Geocentric Celestial Reference System (GCRS) by a time-dependent rotation taking into account precession-nutation. It is defined by the intermediate equator of the Celestial Intermediate Pole (CIP) and the Celestial Intermediate Origin (CIO) on a specific date.
celestial pole:
see pole, celestial.
celestial pole offsets:
time-dependent corrections to the precession-nutation model, determined by observations. The IERS provides the celestial pole offsets in the form of the differences, :math:`dX` and :math:`dY`, of the CIP coordinates in the GCRS with respect to the IAU recommended precession-nutation model, IAU 2006/2000A. That is, the CIP is realized by IAU 2006/2000A plus these celestial pole offsets. In parallel, the IERS also provides the offsets, :math:`dψ` and :math:`dε`, in longitude and obliquity with respect to the IAU 1976/1980 precession-nutation model. (See Earth orientation.)
celestial pole offsets at J2000.0:
offsets of the direction of the mean pole at J2000.0, provided by the current IAU precession model, with respect to the GCRS. These offsets are part of what is often called frame bias, which is the matrix that expresses the small difference in orientation between the GCRS and the mean equator and equinox of J2000.0.
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.
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.
cesium fountain:
a precise time and frequency standard that realizes the SI definition of the second by vertically launching supercooled cesium atoms through a microwave cavity and allowing gravity to bring the atoms back down through the cavity. (See second, Système International (SI).)
Chandler wobble:
the approximately 435-day quasi-periodic motion of the CIP in the ITRF corresponding, in the non-rigid Earth, to the free Eulerian motion of a rigid oblate spheroid rotating about its principal axis of symmetry.
coeval stars:
stars that are the same age.
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 timescale available from broadcast time signals. UTC differs from International Atomic Time (TAI) by an integral number of seconds; it is maintained within ±0s.9 seconds of UT1 by the introduction of leap seconds. (See International Atomic Time (TAI); leap second; Universal Time (UT).)
Coriolis effect:
a dynamical effect caused by a fictitious Coriolis force, which appears in the equation of motion of an object in a rotating frame of reference.
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.
datum:
in geodesy, a reference frame in which positional measurements are made or expressed.
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.
deep ocean dissipation:
a process that disperses the ocean tidal energy in the deep oceans. (See tides, ocean.)
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 ΔT.
delta UT1:
see ΔUT1 (or ΔUT).
depression of the horizon:
same as dip of the horizon.
dip of the horizon:
apparent angle between the astrometric horizon and the visible horizon assuming a level region on the Earth’s surface. The effect is largely due to the height of the observer and atmospheric refraction.
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.
Doodson arguments:
a set of six basic angular arguments multiplied by small integers (Doodson numbers) and summed to specify each tidal frequency.
Doppler effect:
the change in frequency of a received signal due to the relative radial motion of an observer with respect to the source of the signal.
Doppler effect, in general relativity:
an extension of the Doppler effect, to the realm of general relativity. While in Newtonian mechanics and special relativity the Doppler effect remains purely kinematic, in general relativity it becomes a dynamical effect, as the gravitational field contributes to the effect.
Doppler effect, in special relativity:
an extension from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity. They describe the total difference in observed frequencies and possess the required Lorentz symmetry.
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 timescales 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 orientation:
information specifying the relationship of terrestrial and celestial reference frames. Typically specified by four small angles and one time difference; two coordinates of the CIP in the ITRS (accounting for polar motion), two celestial pole offsets (corrections to the precessionnutation model), and the quantity UT1UTC (specifying the accumulated difference in length-of-day).
Earth Rotation Angle (ERA):
the angle, :math:`θ`, measured along the equator of the Celestial Intermediate Pole (CIP) between the direction of he 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 secton. 2. One of the standard elements used to describe an elliptic or hyperbolic orbit. For an elliptical orbit, the quantity :math:`e=\sqrt{1—(b2/a2)}`, where :math:`a` and :math:`b` are the lengths of the semimajor and semiminor axes, respectively. (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.
Einstein’s relativity principle, in general relativity:
the outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
Einstein’s relativity principle, in special relativity:
two inertial frames are completely indistinguishable with respect to all non-gravitational interactions. Thus, non-gravitational physical experiments cannot determine in which inertial system an observer is located. More rigorously, in special relativity, all equations of motion stay form-invariant under transformations interconnecting coordinates and time measured in different inertial frames of reference. (When two such frames are parameterized with Cartesian coordinates, the transformations are those of Lorentz.) In general relativity, the relativity principle gives way to a more general statement, called the Equivalence principle.
elements:
a set of parameters used to describe the position and/or motion 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.
ellipsoidal height:
in geodesy, the height above the adopted reference ellipsoid.
elongation:
the geocentric angle between two celestial objects.
elongation, greatest:
the maximum value of a planetary elongation for a solar system body that remains interior to the Earth’s orbit, or the maximum value of a satellite elongation.
elongation, planetary:
the 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. Satellite elongations are measured from 0° east or west of the planet.
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.)
epagomenal days:
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 second:
the second (defined in 1960) as 1/31556925.9747 of the tropical year at 1900 January 0 12 hours Ephemeris Time. It was superseded by the SI second, the length of which was calibrated to the ephemeris second. Obsolete.
ephemeris time (ET):
the timescale used prior to 1984 as the independent variable in gravitational theories of the solar system. In 1984, ET was replaced by dynamical time.
Ephemeris Time Revised (ETR):
timescale used for epochs prior to 1955, whose measurement unit is the SI (atomic) second which had the value of 0h 0m 32.184 s on 1958 January 0, 0h 0m 0s TAI, continuous with Terrestrial Time prior to 1955. Determined prior to 1956 from the comparison of observations and theories of the motions of the Sun, Moon, and planets.
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 (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 the 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 Sun passes through either of these intersection points; i.e., when the apparent ecliptic longitude of the Sun is 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:
equinox, vernal:
1. The ascending node of the ecliptic on the celestial equator. 2. The time at which the apparent ecliptic longitude of the Sun is 0°.
Equivalence principle:
A group of postulates from general relativity (the weak equivalence principle, the strong equivalence principle, and the Einstein equivalence principle) that restrict the information content of physical experiments, that is, the capacity of experiments to distinguish between physical scenarios. For example, these postulates address whether an experiment can distinguish between gravity and acceleration, or between a freely falling frame of reference and one that is unaccelerated but free of any external gravitational field.
era:
a system of chronological notation reckoned from a specific event.
ERA:
Euclidian geometry:
the set of Euclid’s definitions and axioms pertaining to a space and structures therein. This is the study of flat spaces.
FCN:
flattening:
a parameter that specifies the degree by which a planet‘s figure differs from that of a sphere; the ratio :math:`f=(a-b)/a`, where :math:`a` is the equatorial radius and :math:`b` is the polar radius.
foreshortening effect:
(or foreshortening terms) second order changes in the apparent angular motion of a star due to the changing viewing geometry over long periods of time. The effect is important only for nearby stars with high proper motion and high radial velocity. Also called perspective acceleration. (See proper motion.)
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.
free core nutation (FCN):
a free retrograde diurnal mode in the motion of the Earth’s rotation axis with respect to the Earth, due to the non-alignment of the rotation axis of the core and of the mantle; it also appears as a long period (of 432 days) free nutation of the CIP in the GCRS.
free falling frame:
a local frame which falls freely in external gravitational fields and which is sufficiently small that inhomogeneities in external gravitational fields can be ignored.
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).)
Galileo:
a European satellite navigation system. (Formerly a NASA interplanetary spacecraft the orbited Jupiter form 1995 to 2003.)
GAST:
Gaussian gravitational constant:
(:math:`k = 0.017 202 098 95`): the constant defining the astronomical system of units of length (astronomical unit (au)), mass (solar mass) and time (day), by means of Kepler’s third law. The dimensions of :math:`k2` are those of Newton’s constant of gravitation: :math:`L3M-1T-2`.
geocentric:
with reference to, or pertaining to, the center of the Earth.
Geocentric Celestial Reference System (GCRS):
a system of geocentric spacetime 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.
geodesic precession and nutation:
an effect from relativistic theory in the transformations of the fixed directions in the BCRS into a dynamically non-rotating geocentric reference system. The largest components of the relativistic rotation of the GCRS with respect to a dynamically non-rotating geocentric reference system in the framework of General Relativity. Geodesic precession is the secular part of the rotation and geodesic nutation is the periodic part. Because the IAU reference systems are defined as kinematically non-rotating, geodesic precession and nutation appear as Coriolis-like motions in the IAU 2000 precession-nutation model, rather than in the BCRS-GCRS transformation.
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.
geop:
a surface of constant geopotential.
GHA:
Global Positioning System (GPS):
a US satellite navigation system. Also known as NAVSTAR or NAVSTAR/GPS.
GLONASS:
a Russian satellite navigation system.
GMST:
GPS:
GPS time:
a timescale based on received time signals from GPS satellites that is maintained within better than 1 microsecond of UTC, or TAI, modulo one second. It is ahead of TAI by 19s and differs from UTC depending on the number of leap seconds, since GPS Time is not adjusted for leap seconds.
greatest defect of illumination:
Greenwich Apparent Sidereal Time (GAST):
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):
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.
grid coordinate systems:
coordinate systems from conformal projection of spherical or ellipsoidal planetary surfaces onto a plane surface.
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:
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:
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.
hydrogen maser:
a precise time and frequency standard that produces coherent electromagnetic waves through stimulated emission of hydrogen atoms.
hyperfine levels:
energy levels in the structure of individual atoms and molecules that originate from the interaction of the spin of the nucleus (or nuclei, in molecules) with internally generated electric and magnetic fields. These levels constitute the hyperfine structure of the atom of a molecule.
IAU:
IAU 2000A nutation model:
the nutation portion of the IAU 2000A precession-nutation model which is still in use in IAU 2006/2000A. This represents the nutation of the CIP in the GCRS for those who need a model at 0.2 mas level of accuracy. An abridged model, designated IAU 2000B, is available for those who require a model at the 1 mas level.
IAU 2000A precession-nutation model:
the IAU recommended precession-nutation model for use between 1 Jan. 2003 and 1 Jan. 2009. When it was adopted, it was intended to replace both the previous precession and nutation. However, the precession portion did not correct for the higher order terms. A new precession theory was adopted by the IAU in 2006. Obsolete. (See IAU 2006/2000A.)
IAU 2006/2000A:
the IAUsanctioned precessionnutation model for use after 1 Jan. 2009. The precession theory is the P03 development from Capitaine, Wallace and Chapront (2003, A&A 412 586) and was officially adopted in 2006 (IAU 2008, resolution B1). The nutation theory is that of Mathews, Herring, and Buffett (2002, JGR, 107, 2068) and was adopted in 2000 (IAU 2001, resolution B1.6). Some implementations of IAU2006/2000A—most notably SOFA—incorporate supplemental adjustments to nutation to make the two theories compatible. These adjustments are from Wallace and Capitaine (2006 A&A, 459 981) and currently total a few 10s of microarcseconds. The precession-nutation model with adjustments is named IAU 2006/2000AR~ within this book when a distinction is needed.
IAU 2006/2000AR:
IAU 2006/2000A precession-nutation model with supplemental adjustments to nutation; the adjustments are from Wallace and Capitaine (2006 A&A, 459 981). Also referred to as IAU 2006/2000AR06 and IAU 2006/2000A(R06).
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.)
inertial coordinate system:
a coordinate system that is capable of parameterising an inertial reference system. While a reference system is a frame constituted by physical bodies, a coordinate system is a chart. Each reference system can be parameterised with a continuous multitude of coordinate systems.
inertial coordinates:
special class of coordinate systems in special relativity or Newtonian physics (i.e. in flat spacetimes) in which the laws of physics are substantially simpler than in non-inertial ones. Inertial coordinates are in constant, uniform motion with respect to each other, while non-inertial coordinates are accelerating with respect to all inertial coordinates.
inertial reference frame:
a frame wherein a body subject to no external influences moves uniformly along a straight line, as postulated by Newton’s First Law. The existence of inertial frames is accepted within the Newtonian physics as well as in special and general relativity. In general relativity, inertial frames are implemented by nonrotating freely falling frames. In these frames, inertial coordinates can be introduced only locally.
inertial reference system:
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 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. (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 212 defining sources serve as fiducial points to fix the axes of the ICRS, recommended by the International Astronomical Union (IAU) in 1997.
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 realization of ITRS by a set of instantaneous coordinates (and velocities) of reference points distributed on the topographic surface of the Earth (mainly space geodetic observing stations and related markers). Currently the ITRF provides a model for estimating, to high accuracy, the instantaneous positions of these points, which is the sum of conventional corrections provided by the IERS Convention center (solid Earth tides, pole tides ) and of a “regularized” position. At present, the latter is modeled by a piecewise linear function, the linear part accounting for such effects as tectonic plate motion, postglacial rebound, and the piecewise aspect representing discontinuities such as seismic displacements. The initial orientation of the ITRF is that of the BIH Terrestrial System (its predecessor) at epoch 1984.0. (See meridian, Greenwich; Terrestrial Intermediate Origin (TIO).)
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.
International Terrestrial Reference System zero-meridian:
see meridian, Greenwich.
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.
J2000.0:
defined in the framework of general relativity by the IAU as being the event (epoch) at the geocenter and at the date 2000 January 1.5 TT = Julian Date 245 1545.0 TT. Note that this event has different dates in different timescales.
Julian calendar:
see calendar, Julian.
Julian date (JD):
the interval of time in days and fractions of a day, since 4713 :smallcaps:`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 semimajor 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 either the longitude of the ascending node or 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 61st second of a minute at announced times to keep UTC within 0s.9 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 60th second of a minute would be removed. (See Coordinated Universal Time (UTC); second, Système International (SI); Universal Time (UT).)
length of day:
strictly the number of fixed length seconds in the day determined from the rotation of the Earth, but most often used to refer to the excess length of day or the difference between the length of day and 86,400 SI seconds.
Lense-Thirring effect:
also referred to as frame dragging. It originates in the general theory of relativity and is caused by a gravitomagnetic field induced by rotation of a massive body, which drags a local inertial frame in the direction of rotation of the body. As a consequence, the spin of a gyroscope, and/or the orbital plane of a test particle, orbiting the central body, undergo the precession around the angular momentum of the central body. Lense-Thirring precession is a smaller part of geodesic precession and nutation.
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-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 9.46×1012 km, 5.88×1012 statute miles, 6.32×104 au, and 3.07×10-1 parsecs. Often distances beyond the solar system are given in parsecs. (See parsec.)
light, deflection of:
see deflection of light.
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.
Liouville equation:
a generalized Eulerian equation of motion, which allows for internal motions, i.e., mass redistribution inside the rotating system.
local sidereal time:
longitude of the ascending node:
given an orbit and a reference plane through the primary body (or center of mass): the angle, Ω, 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, Ω 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.
Lorentz transformation:
In special and general relativity, a linear, four-dimensional transformation between the time and Cartesian space coordinates parameterizing two inertial frames moving uniformly with constant velocity with respect to each other.
Love numbers:
coefficients relating the observed amplitudes of displacements of the Earth’s surface and variations in the Earth’s gravity field due to the solid Earth tide generating potential.
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. 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.
lunisolar tidal deceleration:
the deceleration of the rotation of the Earth due to tidal interactions, mainly with the Moon and Sun. Conservation of angular momentum is maintained by the acceleration of the Moon’s orbital motion.
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.
mass monopole:
a body whose gravitational field is spherically symmetric in its local frame. In a relativistic framework all higher Blanchet-Damour mass and spin multipole moments (quadrupole and higher mass moments, spin and higher spin moments) of the body vanish in that frame.
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: :math:`(\int r -1 dt)-1`. In the two body setting, when the disturbances are neglected and the orbit is elliptic, this formula yields the semimajor axis, :math:`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:
in undisturbed elliptic motion, the constant angular speed required for a body to complete one revolution in an orbit of a specified semimajor axis.
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, 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 ΔT east of the Greenwich meridian, where ΔT=TT-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, also called the TIO 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.
Metonic cycle:
metric space:
generally, a region of space wherein the notion of distance between elements is defined. In relativity, a linear space where a dot-product (and, via the dot-product, also a distance) is defined with aid of a metric tensor.
metric tensor:
a mathematical object, expressed by a four-dimensional matrix (symmetrical, in Einstein’s relativity), that is used to calculate distances and angles in spacetime. While in special relativity the metric tensor defines only the geometric properties of the spacetime, in general relativity it also describes the potentials of the gravitational field, which are found by solving the Einstein-Hilbert equations.
moment of inertia:
an integral parameter that measures an object’s resistance to changes in its angular-velocity vector. The moment of inertia is equal to one of the diagonal elements of the inertia tensor in the coordinate system where the inertia tensor is diagonalized.
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 :math:`90° 34′ + s – π`, where :math:`s` is the Moon’s semidiameter, :math:`π` is the horizontal parallax, and :math:`34′` is the adopted value of horizontal refraction.
nadir:
the point on the celestial sphere diametrically opposite to the zenith.
NAVSTAR:
Newcomb’s theory of the Sun:
formally, “Tables of the Motion of the Earth on its Axis and Around the Sun”, developed by Simon Newcomb and published in The Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac, Volume VI, Part I in 1895. It was the basis of the geocentric ephemeris of the Sun, timescales, and astronomical constants for about 80 years.
Newtonian mechanics:
description of motions, based on the laws of Newton acting in a Newtonian spacetime. The latter is a tensor product of a three-dimensional Euclidean space and a one-dimensional time. The time is assumed to be absolute – i.e., to flow uniformly at all points of the Euclidean space, and not to depend upon the motion of the observer.
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.
non-rigid Earth:
a model of the Earth used in geophysical studies that includes the effects of an elastic mantle and liquid outer core. Modern models also often include the effects of oceans on the surface.
non-rotating origin:
in the context of the GCRS or the ITRS, a point on the intermediate (instantaneous) equator that serves as an azimuthal origin. Its instantaneous motion with respect to the system (GCRS or ITRS as appropriate) has no component along the intermediate equator (i.e., its instantaneous motion is perpendicular to it). It is called the Celestial Intermediate Origin (CIO) in the GCRS and the Terrestrial Intermediate Origin (TIO) in the ITRS. The geocentric angle between the CIO and the TIO is the Earth Rotation Angle (ERA).
numerical integration:
the process of calculating the motion of a body by integrating the equations of motion.
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.)
ocean loading:
crustal deformation caused by changes in the weight of a column of water.
of date:
term applied to reference frames or directions to celestial bodies indicating that the effects of precession (mean) and nutation (true) have been applied.
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.
orthometric height:
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:
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:
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 (cresent, 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.
piezoelectric effect:
the ability of some materials (e.g., quartz crystals) to generate an electric potential in response to applied mechanical stress or to deform mechanically when an electric field is applied.
Planck’s constant:
(denoted by :math:`ħ`) a fundamental physical constant equal to the quantum of action in quantum physics. It is the proportionality constant between the energy of a photon and its electromagnetic frequency. It is also the proportionality coefficient between the momentum of a photon and the frequency of its associated electromagnetic wave.
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 :math:`z`-axis is the mean axis of rotation, the :math:`x`-axis is the intersection of the planetary equator (normal to the :math:`z`-axis through the center of mass) and an arbitrary prime meridian, and the :math:`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.
plate motions:
movements of the large-scale portions of the Earth’s crust called tectonic plates. Colloquially, continental drift.
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).)
secular polar motion:
a non periodic motion of the Earth’s pole toward the direction of approximately 75º west longitude.
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)).
post-glacial rebound:
the rise of land masses that were depressed by the weight of ice sheets during the last glacial period. Also called continental rebound, isostatic rebound, post-ice age isostatic recovery.
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.
precession of the ecliptic:
see precession.
precession of the equator (and CIP):
see 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 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.
proper time:
in relativistic theory, time measured by an ideal clock moving together with an observer. Proper time is directly observable and, therefore, independent of any coordinates.
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.
reduction in latitude:
the difference between the geocentric latitude and the geodetic latitude. It is determined by the direction perpendicular to the tangent to the reference ellipsoid at the site. Also called angle of the vertical.
reference ellipsoid:
an oblate spheroid (ellipsoid of revolution) that approximates the geoid over the entire Earth. A reference ellipsoid is specified by its equatorial radius and polar flattening.
reference frame:
realization of a reference system through adopted directions or spatial coordinates.
reference system:
conceptual description of a four dimensional structure required to specify the location of, or directions to, physical objects and their rates of change.
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.
relativistic light-deflection:
bending of the path of light in a gravitational field of a massive body towards that body.
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.
Saros:
cycle of 233 synodic months (approximately 6585.3213 days, or nearly 18 years 11 ⅓ days) used to predict eclipses of the Sun and Moon.
second, ephemeris:
see ephemeris second.
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:
the angle at the observer subtended by the equatorial radius of the Sun, Moon or a planet.
semimajor axis:
1. Half the length of the major axis of an ellipse. 2. A standard element used to describe an elliptical orbit. (See orbital elements.)
Shida number:
coefficients relating the observed amplitudes of the horizontal displacements of the Earth’s surface and the horizontal component of the corresponding static solid Earth tide.
SI second:
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.
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.)
spacetime metric:
see metric tensor.
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).)
stratosphere:
layer of Earth’s atmosphere above the troposphere between approximately 10 km and 50 km above the surface, where temperatures rise with height in contrast with the troposphere where temperatures decrease with height.
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.
survey foot:
non-SI unit of length used in past land surveys whose length can vary from country to country.
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.
Teph:
TAI:
TCB:
TCG:
TDB:
TDT:
tensor:
see metric tensor.
terminator:
the boundary between the illuminated and dark areas of a celestial body.
Terrestrial Dynamical Time (TDT):
the timescale 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 Origin locator (TIO locator):
(denoted by s′) an arc used in locating the TIO. Considering the node of the ITRS equator on the instantaneous equator (orthogonal to the CIO), s’ is the difference in the longitudes of that node measured from (1) the ITRS origin and (2) the TIO. The TIO was originally set at the ITRF origin of longitude and remains very close to it. As a consequence of polar motion, the TIO moves, and s’ changes, by approximately 50 μas (1.5 mm) per century.
Terrestrial Intermediate Origin meridian (TIO meridian):
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, :math:`θ`, around the Celestial Intermediate Pole.
Terrestrial Time (TT):
an idealized form of International Atomic Time (TAI) with an epoch offset; in practice TT=TAI+32s.184. TT thus advances by SI seconds on the geoid. Used as an independent argument for apparent geocentric ephemerides. (See second, Système International (SI).)
tidal acceleration:
tidal deceleration:
tidal friction:
the frictional force caused by the interaction between the tides and the Earth’s surface. (See lunisolar tidal deceleration.)
tides, ocean:
periodic rise and fall of ocean waters due to the attraction of the Moon and Sun.
tides, solid Earth:
periodic rise and fall of areas of the Earth crust due to the attraction of the Moon and Sun.
time dilation:
observed difference of elapsed time between two observers which are moving relative to each other, or being differently situated with respect to nearby gravitational masses.
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.
troposphere:
the lowest portion of Earth’s atmosphere up to approximately 10 km above the surface. It contains approximately 75% of the atmosphere’s mass and 99% of its water vapor and aerosols. (See stratosphere.)
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:
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.
undulation of the geoid:
for a given location on the surface of the Earth, the difference in height between the geoid and the reference ellipsoid.
Universal Time (UT):
a generic reference to one of several timescales 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 timescale 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 timescale but is maintained within 0s.9 of UT1 by the introduction of 1-second steps when necessary. (See leap second.)
UT1:
see Universal Time (UT).
UT1R:
UT1 corrected for the effects of short period zonal tides (periods less that 15 days) specified by the defining table of coefficients.
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).
virtual place:
see proper place.
week:
an arbitrary period of days, usually seven days; approximately equal to the number of days counted between the four phases of the Moon. (See lunar phases.)
WGS-84:
The World Geodetic System 1984 reference ellipsoid, with an equatorial radius of 6378137 meters and a polar flattening of 1/298.257223563. The WGS-84 ellipsoid is the reference for GPS coordinates. Latitude, longitude, and height measured relative to the WGS-84 ellipsoid, converted to geocentric Cartesian form, are consistent with the ITRS to within a few centimeters.
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.)
wobble, Chandler:
see Chandler wobble.
world lines:
path of an object as it travels through four dimensional spacetime.
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 ecliptic longitude 280°. 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:
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 measure 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.