Glossary

updated 2026-09-16

The terms below are the ones marked with an explainer panel across the site. Where two topics define the same term, the first definition in folder order stands.

aberration: The displacement of an apparent direction caused by the observer's velocity, up to 20.5 arcsec for the Earth's orbital motion. It shifts the Sun and Moon by the same vector to first order and so cancels in the Sun-Moon relative geometry, but both bodies must be reduced the same way.
antialiasing: Assigning intermediate values to raster pixels that straddle a boundary, so that the edge is represented at sub-pixel precision rather than as a jagged step. In the SVS method the value comes from the sum of limb-test failures against a threshold set by the pixel area.
antumbra: The extension of the Moon's shadow cone beyond its vertex, within which the Moon appears smaller than the Sun. Where the antumbra reaches the ground the eclipse is annular.
apparent place: A body's direction as seen from the Earth's centre at an instant, including light-time, aberration, precession and nutation, referred to the true equator and equinox of date.
apparent semidiameter: Half the angular diameter of a body as seen by the observer, arcsin(R / distance), where R is the adopted physical radius. Contacts occur when the separation of the centres equals the sum or difference of the two semidiameters.
argument of latitude: The angle $F$ of the Moon along its orbit measured from the ascending node. A solar eclipse requires the new moon to occur with $F$ near 0 or 180 degrees, which Meeus tests with $|\sin F| < 0.36$ .
astrometric place: A position corrected for light-time only, referred to the ICRS axes. Astropy's get_body and SPICE's LT option return this level of reduction.
atmospheric refraction: The bending of light in the atmosphere that lifts the apparent altitude of a body, by about 34 arcminutes on the horizon, 10 arcminutes at 5 degrees and 1 arcminute at 45 degrees.
auxiliary angle ψ: The angle with $\sin\psi = \Delta/L$ , where $\Delta$ is the perpendicular distance from the observer to the relative path of the shadow axis. The semi-duration of a phase is $L\cos\psi/n$ .
auxiliary elements: Derived rates $a'$ , $b'$ , $c'$ built from the Besselian elements and their time derivatives that make the condition for the northern and southern limits a single equation in the position angle $Q$ .
Baily's beads: Points of photospheric light shining through valleys on the lunar limb in the seconds around second and third contact. Their times at a site follow from the limb profile evaluated at each position angle.
bead residual: For a single Baily's bead event, the difference between the observed time and the time predicted for a given solar radius and limb profile, usually converted into an equivalent correction to the solar radius in arcseconds.
Besselian elements: The time-dependent quantities $x$ , $y$ , $d$ , $\mu$ , $l_1$ , $l_2$ and the constants $\tan f_1$ , $\tan f_2$ that describe the Moon's shadow relative to the fundamental plane, from which any eclipse circumstance can be computed.
broken annular: A central eclipse phase, occurring in the gap between the umbra and the antumbra of a hybrid eclipse, in which the Moon is too large to fit inside the Sun and too small to cover it, so a thin ring of sunlight is interrupted by lunar peaks. Wright and Young map it where the range of limb radii exceeds the Sun to Moon separation.
canon of eclipses: A publication listing every eclipse over a long span with elements or maps for each, such as Oppolzer 1887, Mucke and Meeus 1983 and the NASA Five Millennium Canon of 2006.
canonical solar radius: The angular semidiameter of the Sun at 1 au adopted as a standard from 1895 to 2015, 959.63 arcseconds, derived by Auwers in 1891 and still used in almanac eclipse predictions. About 695,990 km with the modern astronomical unit.
central eclipse: An annular, total or hybrid eclipse in which the axis of the Moon's shadow crosses the Earth's surface, producing a central line. Most have two path limits, a few grazing cases have only one.
central line: The locus of points where the shadow axis meets the Earth's surface. It is found at each instant from $\xi = x$ , $\eta_1 = y/\rho_1$ and $\zeta_1 = \sqrt{1 - \xi^2 - \eta_1^2}$ , and exists only while the axis intersects the Earth.
centre of figure: The centre of the Moon's mean limb figure. The ephemeris tabulates the centre of mass, which lies about 1.9 km away, mostly along the Earth-Moon line, so the sky-plane part is about 0.5 arcseconds, historically applied as +0.50 arcseconds in longitude and −0.25 arcseconds in latitude. A limb profile referenced to the centre of mass, as the LOLA and Kaguya grids are, supersedes the correction.
centre of mass: The point whose motion the lunar ephemeris describes. Modern DEMs express heights relative to a sphere centred here, which is why they need no centre-of-figure correction.
Chebyshev polynomials: The piecewise polynomial form in which SPK type 2 ephemerides store positions. Velocity is obtained by differentiating the polynomial, and evaluation needs no interpolation tables.
contact times (C1 to C4): First contact when the Moon's disc first touches the Sun's, second contact when totality or annularity begins, third contact when it ends, and fourth contact when the discs separate.
curve of equal magnitude: The contour of points where the magnitude at maximum eclipse has a fixed value, such as 0.5. Obtained by interpolation across the curves of maximum eclipse or by contouring a raster of maximum magnitude.
curve of maximum eclipse: The locus of points at which the eclipse reaches its maximum at a stated instant. Drawn at half-hour steps on world maps and at minute steps inside the umbral path.
digital elevation model (DEM): A gridded dataset of surface heights: for the Moon (LOLA, SLDEM2015, Kaguya LALT) to build limb profiles, for the Earth (SRTM, Copernicus) to raise observers above the ellipsoid.
DUT1: The value of UT1 − UTC broadcast with time signals, rounded to 0.1 s. It is the correction needed to turn UT1 contact times into UTC.
Earth flattening: The quantity $f = (a - b)/a$ of the reference ellipsoid, 1/298.257 in the 1992 Explanatory Supplement. It converts an observer's geodetic latitude to the geocentric coordinates used with Besselian elements.
Earth orientation parameters (EOP): The measured quantities UT1 − UTC, polar motion (x, y), length of day and celestial pole offsets, published by the IERS, that relate the Earth-fixed frame to the celestial frame. They cannot be known in advance and are the only prediction inputs that must be re-fetched before an eclipse.
eclipse magnitude: The fraction of the solar diameter covered by the Moon at maximum eclipse. In the partial phase it is $(L_1' - m)/(L_1' + L_2')$ . Inside the umbra or antumbra NASA reports instead the ratio of the apparent lunar to solar diameters, $(L_1' - L_2')/(L_1' + L_2')$ .
eclipse season: The roughly 34.5-day interval, twice a year, during which the Sun is within about 17 degrees of a lunar node so that any new moon produces a solar eclipse. Successive seasons are 173.3 days apart.
eclipse solar radius: The solar radius that, used in an accurate eclipse model with a lunar limb profile, reproduces observed second and third contacts. Flash-spectrum and photometer measurements put it at 959.95 to 960.0 arcseconds at 1 au, about 0.3 arcseconds larger than the canonical value.
edge observation: Observing a total or annular eclipse from within a few kilometres of the predicted path limit, where the duration of the central phase is most sensitive to every input of the prediction and Baily's beads last a minute or more.
Elev Fact: A multiplicative factor in NASA bulletins by which an umbral limit shifts perpendicular to the path per metre of observer elevation, equal to $\tan(90^{\circ} - A)\sin D$ with $A$ the Sun's altitude and $D$ the difference between the Sun's azimuth and the path azimuth.
elevation factor: Espenak's multiplier $\tan(90^{\circ} - A)\sin D$ , where $A$ is the Sun's altitude and $D$ the difference between the Sun's azimuth and the path-limit azimuth, giving the perpendicular shift of the path limit per unit of observer elevation.
ellipsoidal height: Height above the reference ellipsoid, which is what GPS receivers measure natively and what the eclipse formulas need when the observer is placed on the ellipsoid plus a height.
ELP-2000/82: An analytic lunar theory giving the Moon's position as trigonometric series, used by NASA's eclipse Canon and by Meeus-based libraries for the Moon.
ephemeris: A table or function giving the position and velocity of a body as a function of time. Modern planetary and lunar ephemerides such as JPL DE440 are numerically integrated orbits fitted to observations and distributed as Chebyshev polynomial coefficients.
ephemeris hour angle: The hour angle of the point Z measured from the ephemeris meridian, which lies $1.002738\,\Delta T$ east of Greenwich. Modern tables measure $\mu$ from Greenwich instead and bake ΔT into it.
ephemeris longitude: An observer's longitude shifted by $1.002738\,\Delta T$ so that it can be combined with the shadow-axis hour angle $\mu$ , which is tabulated against Terrestrial Time rather than Universal Time.
equation of the equinoxes: The difference between apparent and mean sidereal time caused by nutation, at most about 1.1 s of time.
Exeligmos: Three Saros periods, 669 synodic months or about 54 years 33 days, after which an eclipse path returns to roughly the same longitudes because the one-third day remainder of the Saros has accumulated to a whole day.
flash spectrum: The emission-line spectrum of the thin solar atmosphere seen for a few seconds around second and third contact when the photosphere is almost fully covered. Its continuum component marks photospheric light and its lines mark the chromosphere, which lets the two be separated in timing.
fundamental plane: The plane through the Earth's centre perpendicular to the axis of the Moon's shadow. Its x axis lies in the equator pointing east, its y axis points north, and the shadow's cross-section on it is an exact circle.
gamma: The distance of the shadow axis from the Earth's centre in Earth equatorial radii at greatest eclipse, positive when the axis passes north of the centre. Values of $|\gamma|$ below about 0.9972 give a central eclipse.
geocentric latitude: The angle between the equatorial plane and the line from the Earth's centre to the observer. Eclipse formulas use it, through $\rho\sin\phi'$ and $\rho\cos\phi'$ , to place the observer in the fundamental plane.
geodetic latitude: The latitude on maps and from GPS, defined by the normal to the reference ellipsoid. It differs from geocentric latitude by up to 11.5 arcminutes near 45 degrees.
geoid: The equipotential surface of the Earth's gravity field that mean sea level would follow. It lies between 106 m below and 85 m above the WGS 84 ellipsoid.
geometric position: The straight-line direction from the observer to a body at an instant with no correction for light-time or aberration.
graze zone: The narrow band, typically 5 to 10 km wide, along each umbral limit where the irregular lunar limb makes the eclipse neither wholly total nor wholly partial and Baily's beads persist. NASA bulletins tabulate its interior and exterior boundaries.
greatest duration: The point on the central line where totality or annularity lasts longest. It is close to, but not the same as, the point of greatest eclipse, and can be shifted by 10 to 20 km by lunar limb effects.
greatest eclipse: The instant when the shadow axis passes closest to the Earth's centre, at which $\gamma$ is defined and the catalogued circumstances are quoted.
Greenwich apparent sidereal time (GAST): The hour angle of the true equinox of date at Greenwich. The Besselian element μ is GAST minus the right ascension of the shadow axis, evaluated at the UT1 of the instant.
horizontal parallax: The angle subtended by the Earth's equatorial radius at a body's distance. The Moon's horizontal parallax $\pi_m$ gives its distance in Earth radii as $1/\sin\pi_m$ . The Sun's at 1 au is 8.794 arcseconds.
hybrid eclipse: An eclipse whose central path is total along some sections and annular along others because the umbral vertex lies close to the Earth's surface. Also called annular-total. Most begin and end annular with a total middle.
ICRF: The International Celestial Reference Frame, the realisation of the ICRS by extragalactic radio sources, to which DE ephemerides are aligned to 0.0002 arcsec. Its axes differ from the J2000 dynamical axes by a constant bias of about 0.02 arcsec.
Inex: An eclipse cycle of 358 synodic months, about 10,571.95 days or 29 years less 20 days, equal to 388.5 draconic months, so successive Inex eclipses occur at opposite nodes. Inex series last about 225 centuries.
inflection-point radius: The radius at which the limb-darkening intensity profile is steepest, the standard definition of the photospheric limb used by limb-imaging instruments. It lies about 0.33 Mm above the Rosseland optical-depth 2/3 surface and about 0.65 arcseconds inside the last detectable photospheric light.
JPL DE series: The Development Ephemerides produced by JPL (DE200, DE405, DE421, DE430, DE440, DE441, DE442). Each is a single fit of the Sun, planets and Moon to tracking and laser-ranging data, with the lunar orbit accurate to about a metre in the present era.
k (lunar radius ratio): The Moon's radius divided by the Earth's equatorial radius. The IAU 1982 mean is 0.2725076; Espenak uses 0.272281 for umbral contacts because it matches the deepest limb valleys and observed totality durations, and the Five Millennium Canon used 0.2724880 for penumbral contacts.
LDEM: The LOLA Lunar Digital Elevation Model series in the LRO GDR archive, gridded in equirectangular projection at 4, 16, 64, 128, 256, 512 and 1024 pixels per degree with heights in metres above a 1737.4 km sphere.
leap second: A one-second step inserted into UTC to keep it within 0.9 s of UT1. The accumulated offset between TAI and UTC has been 37 s since 2017.
length of day (lod): The duration of the mean solar day measured in SI seconds, minus 86400 s. Its slow growth, about 1.8 ms per century on average, is what makes ΔT increase roughly parabolically.
libration: The slow apparent rocking of the Moon that changes which part of its surface faces an observer, expressed as a longitude and a latitude of the sub-observer point in selenographic coordinates. It ranges about plus or minus 8 degrees in each coordinate and sets which terrain lies on the limb.
light-curve matching: A solar-radius method in which the observed brightness of the last and first beads is compared with light curves simulated by integrating the limb-darkening function over the exposed photosphere, so that a whole curve rather than two contact instants constrains the fit.
light-time: The travel time of light from a body to the observer, 499 s for the Sun and about 1.3 s for the Moon. An astrometric place is the geometric place at the emission time; forgetting the Sun's light-time misplaces it by about 20 arcsec.
limb correction (LC): The correction, in seconds, applied to a smooth-Moon second or third contact time to account for the actual lunar limb profile at the contact position angle. Jubier's maps show it in an LC column.
limb darkening function inflection point: The conventional definition of the solar limb used in radius measurements: the radius at which the drop-off of photospheric brightness is steepest.
limb test zone: In Wright and Young's raster method, the band of observers near the umbra edge for which totality cannot be decided from the mean lunar radius and every limb element must be tested against the solar disk in units of the apparent solar radius.
limb-darkening function: The run of surface brightness with distance from the solar limb. Its steepness determines when a Baily's bead becomes visible, so bead timings depend on both the function and the detector's sensitivity.
lunar laser ranging (LLR): Ranging to retroreflectors on the Moon from stations such as APOLLO, Grasse and McDonald since 1969. The recent range residuals of about 1 cm are what fix the lunar orbit and physical libration in DE440 and INPOP21a.
lunar libration Euler angles: The three angles $\phi$ , $\theta$ , $\psi$ , integrated with the orbit and stored in the DE files or a binary PCK, that rotate the ICRF into the Moon's principal-axis frame and thus give the Moon's orientation at any time.
lunar limb profile: The height of the Moon's silhouette edge above a reference sphere, tabulated as a function of position angle around the disk for a given libration. It is what turns a smooth-disk eclipse prediction into one that knows where the valleys are.
lunation number: The count of synodic months since the new moon of 2000 January 6, negative before it. The Brown Lunation Number equals it plus 953. It indexes the mean new moon in Meeus's method and feeds the closed-form Saros number.
l₁ and l₂: The radii of the penumbra and umbra on the fundamental plane in Earth equatorial radii. $l_1$ is always positive. $l_2$ is negative for a total eclipse and positive for an annular one.
L₁′ and L₂′: The penumbral and umbral cone radii at the observer's own plane, $L' = L - \zeta\tan f$ , where $\zeta$ is the observer's height above the fundamental plane along the axis. $L_2'$ is negative inside the umbra (total) and positive inside the antumbra (annular).
mean limb: The circle a smooth spherical Moon of radius k would present. Limb heights are quoted as departures from it, and uncorrected contact times are computed for it.
Moon mean-Earth/polar-axis (ME) frame: The lunar body-fixed frame whose z axis is the mean rotation pole and whose x axis points to the mean sub-Earth point, as realised by a JPL ephemeris. LRO LOLA, SLDEM2015 and Kaguya LALT grids use the ME frame of DE421; the SPICE frame MOON_ME_DE440_ME421 reproduces it from DE440.
nominal solar radius: The IAU 2015 conversion constant of exactly 695,700 km (959.22 arcseconds at 1 au), chosen to match the helioseismic photosphere. It is a unit for expressing stellar radii, not a measured limb, and is too small for eclipse geometry.
non-central eclipse: An annular or total eclipse in which the shadow axis misses the Earth while one edge of the umbra or antumbra grazes the polar region, producing a track with one limit and no central line.
nutation: The short-period wobble of the Earth's axis superposed on precession, modelled by the IAU 1980 or IAU 2000A series. It moves the equinox by up to about 17 arcseconds.
obscuration: The fraction of the Sun's apparent disc area covered by the Moon, computed from the overlap of two discs and always 1 during totality.
one-limit eclipse: A central eclipse whose umbral or antumbral shadow partly misses the Earth throughout, so the path has only a northern or only a southern limit. Catalog codes n and s mark these.
orthometric height: Height above the geoid, which is what "elevation above sea level" and most digital elevation models give.
outline curve: The curve of all points at which the eclipse (partial for the penumbra, central for the umbra) is beginning or ending at a stated instant; the shadow's footprint on the ground at that time.
parallactic angle C: The angle at the Sun between the direction to the celestial pole and the direction to the zenith, $\tan C = \xi/\eta$ in fundamental-plane coordinates. It converts north-referenced to zenith-referenced position angles.
parametric latitude: The latitude $\phi_1$ defined by $\sin\phi_1 = \rho\sin\phi'/\sqrt{1 - e^2}$ and $\cos\phi_1 = \rho\cos\phi'$ , which maps the Earth ellipsoid onto a unit sphere so that eclipse curves can be solved without knowing the observer's distance from the geocentre in advance.
path limit: The northern or southern boundary of the umbral (or antumbral) path on the ground, where the duration of totality (or annularity) falls to zero. Smooth-limb limits assume a spherical Moon and ellipsoidal Earth. True-limb limits include the lunar limb profile and terrain.
path width: The width of the umbral or antumbral track measured on the ground perpendicular to the direction of motion, given by Mikhailov's 1931 formula from the shadow radius, the height above the fundamental plane and the direction of motion.
penumbra: The outer part of the Moon's shadow within which the Sun is only partly hidden. Any place inside the penumbra sees at least a partial eclipse.
penumbral cone: The cone formed by the interior common tangents of the Sun and Moon, with vertex between them. Inside it the Sun is at least partly hidden. Subscript 1 in almanac notation.
photospheric extinction: The interval during which no photospheric continuum reaches the observer, the physical definition of totality used to define the eclipse solar radius. Its start and end are second and third contact.
pixels per degree (ppd): The resolution unit of lunar DEMs. At the Moon's equator one degree is 30.3 km, so 128 ppd is 237 m per cell and 512 ppd is 59 m.
planetocentric latitude: Latitude measured as the angle from the equatorial plane at the body's centre, as used for a spherical datum. Lunar DEMs referenced to the 1737.4 km sphere use it, so no ellipsoidal correction is needed when converting pixels to rectangular coordinates.
point Z: The point on the celestial sphere toward which the shadow axis is directed, equal to the direction of the Sun as seen from the Moon's centre. Its right ascension a and declination d orient the fundamental plane.
polar motion: The wandering of the Earth's rotation axis relative to the crust, a few tenths of an arcsecond, which displaces an observer's position relative to the axis by up to about 10 m.
position angle: An angle measured on the sky at the centre of a disk, from celestial north through east, used to locate a point on the limb of the Sun or Moon. Contact points and limb heights are indexed by it.
position angle of axis: Position angle on the lunar disc measured from the Moon's north pole of rotation eastward, the coordinate against which limb-profile heights are tabulated. It differs from the celestial position angle by the position angle of the lunar axis.
position angle of the lunar axis: The angle, measured eastward from celestial north, of the Moon's rotation axis projected on the sky. Limb profiles are indexed from this axis, so it must be computed for the same time and observer as the libration. Written c in Wright and Young's limb test and stored as MoonC in the SVS umbra shapefiles.
position angle P (Q): The angle of a contact point on the solar limb measured eastward (counter-clockwise) from the north point of the disc. At a contact $\tan Q = u/v$ , with the sign of $\sin Q$ reversed for the interior contacts of a total eclipse.
position angle Q: The angle, measured eastward from north in the fundamental plane, of the shadow axis as seen from the observer's projected point. Limit curves and outline curves are parametrised by Q.
precession: The slow drift of the Earth's rotation axis and equinox, about 50 arcseconds per year, which fixes the equator and equinox of date to which Besselian elements are referred.
principal-axis (PA) frame: The Moon-fixed frame aligned with the principal axes of the lunar moment of inertia, in which the DE Euler angles are integrated. It is rotated by a constant of about 875 m on the surface from the mean-Earth frame.
realised ΔT error: The difference between the ΔT value adopted when a prediction was published and the value later measured for the eclipse date. It shifts the whole path east or west by about 15 arcseconds of longitude per second of error.
reference case: A published set of local circumstances (site, contact times, duration) from an authoritative implementation, used to test a new implementation to a stated tolerance.
reference ellipsoid: The oblate spheroid that stands in for the Earth's shape in geodesy and in eclipse computation, defined by an equatorial radius and a flattening (for example WGS 84 or the IAU 1976 figure).
rising and setting curve: The locus of points where the partial eclipse begins or ends exactly at sunrise or sunset: the end points of the outline curves, forming two loops or a distorted figure eight on the map. By almanac convention it is drawn for a geometric horizon, Sun's centre at zero altitude, no refraction.
s0 (solar semidiameter): The Sun's angular semidiameter at 1 au adopted for eclipse work, 959.63 arcseconds (Auwers 1891), equivalent to a radius of 696 000 km.
Saros: An eclipse cycle of 223 synodic months, about 6585.32 days or 18 years 11 days 8 hours, after which the Sun, Moon and node return to nearly the same relative geometry. Eclipses one Saros apart belong to the same Saros series.
Saros-Inex panorama: Van den Bergh's two-dimensional arrangement of all eclipses with Saros series as columns and Inex series as rows, so that any interval between eclipses is an integer combination of Saros and Inex periods.
second contact (C2): The instant totality or annularity begins. For a total eclipse it is when the last photospheric bead disappears; for an annular eclipse it is when the ring first closes.
secular acceleration of the Moon: The tidal acceleration of the Moon's mean motion, about −25.8 arcseconds per century squared. Every lunar ephemeris embeds a value of it, and ΔT values derived from historical eclipses depend on which value was assumed.
seismic radius: The solar radius inferred from the frequencies of surface gravity (f) modes, 695,680 ± 30 km from SOHO/MDI. It refers to a subsurface layer and is about 300 km smaller than limb-based radii.
shadow axis: The line through the centres of the Sun and Moon, common to the umbral and penumbral cones. Its intersection with the fundamental plane has coordinates (x, y).
shadow cone: The umbral or penumbral cone tangent to both Sun and Moon, characterised by its half-angle $f$ whose tangent appears in the Besselian elements as $\tan f_1$ and $\tan f_2$ .
SLDEM2015: A merged DEM of LOLA altimetry co-registered with SELENE Terrain Camera stereo, covering 60 S to 60 N at 512 pixels per degree, about 60 m at the equator, with a typical vertical accuracy of 3 to 4 m.
solar-system barycentre: The centre of mass of the whole solar system and the origin of the ICRS and of the DE integrations. The Sun's centre wanders up to about 1.6 solar radii from it, so eclipse elements must use the Sun (body 10), not the barycentre (body 0).
SPICE binary PCK (bpc) Earth orientation kernel: A NAIF file of Earth orientation (precession, nutation, UT1 and polar motion) used by SVS to orient the Earth. The "predict" kernels extrapolate the IERS series into the future.
SPK kernel: A SPICE binary file (.bsp) holding ephemeris segments, each giving the position of a target relative to a centre over a time span. The Moon is segment 3 to 301 and the Earth 3 to 399, both relative to the Earth-Moon barycentre.
sub-observer point: The point on the Moon directly below the observer, whose selenographic longitude and latitude are the topocentric libration. The limb lies on the great circle 90 degrees from it, shifted slightly by parallax at finite distance.
TAI: International Atomic Time, the continuous atomic time scale from which TT (TAI + 32.184 s) and UTC (TAI minus an integer number of leap seconds) are derived.
tan f₁, tan f₂: The tangents of the half-angles of the penumbral ( $f_1$ ) and umbral ( $f_2$ ) shadow cones, about 0.00467 and 0.00465. They convert an observer's height above the fundamental plane into a change of shadow radius.
TDB: Barycentric Dynamical Time, the independent variable of the JPL, INPOP and EPM ephemerides. It differs from Terrestrial Time by periodic terms of about 1.7 ms amplitude, which are negligible for eclipse geometry.
Terrestrial Time (TT): The uniform time scale of the ephemerides and of the Besselian elements, equal to TAI + 32.184 s. Older eclipse tables call it TDT, TD or Ephemeris Time (ET). Elements are computed in TT and converted to UT1 with ΔT before any Earth rotation is applied.
third contact (C3): The instant totality or annularity ends. For a total eclipse it is when the first bead reappears.
topocentric: Referred to the observer's actual position on the Earth's surface rather than to the Earth's centre. Topocentric positions include diurnal parallax and, for the Moon, differ from geocentric ones by up to about one degree.
topocentric libration: The libration seen from a specific point on Earth rather than from the geocentre. It differs from geocentric libration by up to about one degree because of lunar parallax, so the limb profile is observer-dependent.
u, v, m, n: $u = x - \xi$ and $v = y - \eta$ are the shadow axis position relative to the observer in the observer's plane, $m = \sqrt{u^2 + v^2}$ is their distance and $n$ the relative speed in Earth radii per hour. Contacts occur when $m$ equals $L_1'$ or $|L_2'|$ .
umbra: The cone of the Moon's shadow within which the Sun is completely hidden. Where the umbra reaches the ground the eclipse is total.
umbra polygon: The true outline of the umbra on the ground when the lunar limb is modelled: a many-sided figure whose every edge is an arc of a Sun image projected through one limb valley. The 2017 August 21 umbra at 18:00 UTC had 49 edges.
umbral cone: The cone formed by the exterior common tangents of the Sun and Moon, with vertex beyond the Moon. Inside it the Sun is totally hidden; beyond its vertex the eclipse is annular (antumbra). Subscript 2 in almanac notation.
umbral depth: The perpendicular distance from an observing site to the nearer limit of the umbral path, as reported by Jubier's map. IOTA recommends at least 2 km when the limit was computed with the canonical radius.
UT1: Universal Time proper, a measure of the Earth's rotation angle. Eclipse predictions labelled "UT" are in UT1, obtained from TT by subtracting ΔT.
UTC: Coordinated Universal Time, the atomic civil time scale kept within 0.9 s of UT1 by leap seconds. TAI − UTC has been 37 s since 2017 January 1.
vertex angle V: The position angle of a contact measured counter-clockwise from the zenith point of the solar disc, $V = Q - C$ , where $C$ is the parallactic angle. Some calculators report it as a clock-face hour instead.
VSOP87: An analytic planetary theory from the Bureau des Longitudes giving Sun and planet positions as trigonometric series, used by NASA's eclipse Canon for the Sun.
Watts angle: The position angle around the lunar limb used as the argument of Watts' 1963 charts, measured eastward from the projection of the Moon's north pole as Watts constructed it. It differs from the true axis angle by a small constant offset, quoted as 0.21 to 0.25 degrees by different reducers.
Watts charts: The lunar limb profiles published by Chester Burleigh Watts in 1963 from machine tracings of about 700 photographs covering the range of librations, used for eclipse and occultation timing until laser altimetry replaced them.
Watts datum: The smooth reference surface to which Watts' chart heights refer. Occultation analyses found it slightly elliptical, offset from the centre of mass, and varying with libration, so corrections are needed before comparing Watts heights with a centre-of-mass ephemeris.
ΔT: The difference TT − UT1 between uniform Terrestrial Time, in which the elements are computed, and Universal Time, which follows the Earth's irregular rotation. About 69 s in 2024. It converts the hour angle μ to a geographic longitude, is known only by prediction for future eclipses, and is the largest error source for historical ones.
μ (Greenwich hour angle of the shadow axis): The Besselian element that ties the shadow to the rotating Earth. It is ephemeris sidereal time minus the right ascension of the shadow axis, so it is the element through which ΔT enters.
ρ sin φ′, ρ cos φ′: The observer's geocentric coordinates on the ellipsoid, $\rho\sin\phi' = (1 - e^2)\sin\phi\,(1 - e^2\sin^2\phi)^{-1/2}$ and $\rho\cos\phi' = \cos\phi\,(1 - e^2\sin^2\phi)^{-1/2}$ , with $\phi$ the geodetic latitude and $e$ the eccentricity of the spheroid.