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.

1-sigma line: A line drawn parallel to a predicted shadow-path edge, offset outward by the 1-standard-deviation cross-track uncertainty. Between the two 1-sigma lines the true path is expected with about 68 per cent probability if the errors are Gaussian.
a and b coefficients: The rates of change of a predicted occultation time with the observer's longitude and latitude, in minutes of time per degree, published with standard-station predictions so that nearby observers can correct the time.
aberration: The change in observed direction caused by the observer's velocity, up to about 20.5 arcseconds for Earth's orbital motion. It is distinct from target retardation. Reduce both bodies through one documented chain when comparing them.
aerosol optical depth (AOD): A measure of how strongly airborne particles attenuate light along a path, here the global stratospheric value inferred from how much darker an eclipse is than a clear-atmosphere prediction.
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 oblateness: The flattening $\epsilon = 1 - b'/a'$ of the ellipse fitted to occultation chords, where $a'$ and $b'$ are the apparent semi-major and semi-minor axes. It describes the projected outline at the instant of the event, not the body's three-dimensional shape.
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.
area-equivalent radius: The radius of the circle with the same area as the fitted limb ellipse, $R_{eq} = \sqrt{a'b'}$ . It is the size usually quoted for a body observed in one occultation.
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 before observer aberration and gravitational deflection. SPICE's LT option returns this reduction. Astropy's get_body additionally transforms to GCRS, including aberration.
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.
aureole of Venus: The thin bright arc around the part of Venus that lies off the solar disc during ingress and egress. It is sunlight refracted by Venus's mesosphere, tens of kilometres above the cloud tops.
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 $Q$ .
B and B′ (ring opening angles): B is the saturnicentric latitude of the Earth referred to the ring plane and B′ is that of the Sun. They set how open the ring ellipse looks and how far the ring shadow falls on the globe. Both are zero at a ring-plane crossing.
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.
black drop: The apparent dark ligament joining the planet to the solar limb near contacts II and III, which delays or blurs the visual instant of internal tangency by seconds to a minute. It comes from the instrument's and the atmosphere's point-spread function acting on the limb-darkened solar edge.
broken annular: A central eclipse phase in which lunar peaks interrupt a thin ring of sunlight, so the observer sees neither complete totality nor an unbroken annulus. Wright and Young's proposed range-of-radii criterion requires common angular normalisation and is not observationally validated in this corpus.
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.
Centaur: A small body on an unstable orbit between Jupiter and Neptune, thought to come from the trans-Neptunian region. Chariklo and Chiron are examples.
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 flash: A brightening at mid-occultation seen by observers near the centre line of an occultation by a body with an atmosphere, caused by refraction focusing starlight from all around the limb. Its shape probes the lowest atmospheric layers.
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.
chord: The segment of the star's track across the occulting body's projected outline that one observer records, from disappearance to reappearance, mapped onto the fundamental plane. Several chords at different cross-track offsets outline the body.
chord extrapolation: Fitting the measured length of the chord where the planet's disc cuts the solar limb, in images taken before and after the black drop, and extrapolating it to zero to time a contact.
closest approach: The minimum angular or projected distance between the star and the centre of the occulting body as seen from a reference point, usually the geocentre, and the instant at which it occurs. An occultation is possible somewhere on Earth if this distance is smaller than the body's radius plus the Earth's radius on the fundamental plane.
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.
crater timing: A visual timing of the instant the umbra's edge crosses a lunar crater or spot during a lunar eclipse, recorded to about 0.1 minute. Many timings together measure the size and shape of the umbra.
cross-track and along-track: Directions on the fundamental plane perpendicular to and along the shadow's motion. Cross-track error moves the predicted path sideways on the ground. Along-track error changes the predicted time.
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.
cusp angle (CA): The angle around the Moon's limb from the nearer cusp to the point of an event, positive on the dark side and negative on the sunlit side, as used in IOTA and RASC predictions.
Danjon scale (L): Danjon's 1921 five-step scale of the brightness and colour of a totally eclipsed Moon, from L = 0, almost invisible, to L = 4, bright copper-red or orange with a bluish rim.
dark limb and bright limb: The unlit and sunlit parts of the Moon's edge. Events at the dark limb are sharp and easy to time. Events at the bright limb are hidden by glare except for bright stars.
Delisle's method: Determining the solar parallax by comparing the absolute times of the same contact at sites far apart. It needs only one contact per site but accurate longitudes and clocks.
differential light-time: The correction for a satellite being nearer to or farther from the Earth than Jupiter, so that its light left at a slightly different time. In Meeus's form it shifts X by $|Z|/K$ times a geometric factor, with K close to the speed of light divided by the satellite's orbital speed.
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.
disappearance and reappearance (D, R): The two events of an ordinary occultation: the star vanishes at the Moon's leading limb (D) and returns at the trailing limb (R). Reports add the limb, so DD is a disappearance at the dark limb and RB a reappearance at the bright limb.
diurnal parallax: The difference between the direction of a body seen from the observer and from the Earth's centre. For transits it is the difference between the planet's and the Sun's parallax that shifts the local contact times.
DUT1: The value of UT1 − UTC broadcast with time signals, rounded to 0.1 seconds. Subtract UT1 − UTC to convert a UT1 contact time to UTC. Precise comparisons use the unrounded Earth-orientation value for the event epoch.
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.
Earth's penumbra: The region around the Earth's umbra, bounded by the interior common tangents of the Sun and Earth, inside which the Earth hides part of the Sun. At the Moon's distance its radius is about 74 arcminutes.
Earth's umbra: The cone behind the Earth, bounded by the exterior common tangents of the Sun and Earth, inside which the Earth hides the whole Sun. At the Moon's distance its radius is about 41 to 42 arcminutes, about 1.3 lunar diameters, so the umbra is about 2.7 Moon diameters across.
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 of a satellite: The passage of a satellite through Jupiter's shadow. It depends only on the Sun's direction. Disappearance (EC D) and reappearance (EC R) are timed at half the satellite's normal light.
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: A solar radius fitted to observed eclipse contacts or light curves using a specified lunar limb and detection model. Quaglia's flash-spectrum fit is 959.95 ± 0.05 arcseconds at 1 au; other timing and imaging methods give different estimates.
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 correction (tan Z): The shift of a graze limit line on the ground for an observer above sea level, equal to the height times the tangent of the zenith distance and applied toward the Moon's 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 point Z from the ephemeris meridian, offset east of Greenwich by $(1.002738\times15/3600)\Delta T$ degrees when ΔT is in seconds. NASA's tabulated μ requires this correction once downstream. A μ generated with actual UT1 sidereal time already contains it.
ephemeris longitude: For ephemeris-meridian elements, the observer's west longitude shifted by $(1.002738\times15/3600)\Delta T$ degrees, with ΔT in seconds. This accounts for Earth rotation when combining longitude with the tabulated hour angle μ and must not be applied again to elements already computed with UT1.
ephemeris offset method: A prediction technique that measures the difference between new astrometry of a body and a reference ephemeris a few days before an event and applies that difference as a constant correction. It fails when the offset drifts over a few weeks.
epoch propagation: Moving a star's catalogue position, parallax and proper motion from the catalogue epoch to the date of an event, rigorously under uniform space motion, which needs the radial velocity for nearby fast stars.
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.
flux drop: The fraction of a satellite's light lost at the deepest point of an occultation or eclipse, from 0 for no loss to 1 for total disappearance. IMCCE tables give it beside the equivalent magnitude drop.
Fresnel scale: The length $f = \sqrt{\lambda D/2}$ that sets the width of the diffraction fringes at the shadow edge, with $\lambda$ the wavelength and $D$ the observer-body distance. It is about 0.3 km for a main-belt asteroid and about 1.2 km for a body at 40 au in visible light.
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.
Gaia catalogue releases: The star catalogues from ESA's Gaia astrometric mission: DR1 (2016), DR2 (2018), EDR3 (2020) and DR3 (2022). From DR2 onward they give positions, proper motions and parallaxes at the sub-milliarcsecond level for faint stars, which removed the star position as the main error in occultation predictions.
Galilean satellites: Jupiter's four large moons, Io (I), Europa (II), Ganymede (III) and Callisto (IV), discovered by Galileo in 1610. They orbit close to Jupiter's equatorial plane at about 5.9, 9.4, 15.0 and 26.3 Jupiter radii.
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.
grazing occultation: An occultation seen from close to a limit line, where the star appears to skim the Moon's north or south edge and may disappear and reappear several times behind mountains and valleys.
grazing transit: A transit in which the planet's path only just reaches the solar limb, so some observers see all four contacts, some see only I and IV, and some see no transit. Mercury in 1937 May and 1999 November are the twentieth-century examples.
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.
greatest transit: The instant at which the angular separation of the centres of the planet and the Sun is smallest. Catalogues give it for the Earth's centre with the minimum separation in arcseconds.
Greenwich apparent sidereal time (GAST): The hour angle of the true equinox of date at Greenwich, evaluated at the instant's UT1. NASA's ephemeris-meridian μ instead evaluates sidereal time at the numerical TT epoch as if it were UT1, so its consumer must apply ΔT once.
GUST86: The analytical theory of the five main satellites of Uranus by Laskar and Jacobson, fitted to observations from 1911 to 1986. It was the standard Uranian satellite theory for two decades.
Halley's method: Determining the solar parallax from the different durations of a whole transit seen from widely separated latitudes. It needs both ingress and egress at each site but not accurate longitudes.
Hapke model: A physical model of how a rough, porous surface scatters light as a function of incidence, emission and phase angles. Mutual-event fits use it, or the Oren-Nayar model, to set the brightness distribution across a satellite's disc.
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.
immersion and emersion: The instants at which the star disappears behind the occulting body and reappears from behind it. Their times, with the observer's position, fix the two ends of a chord.
impact parameter: The smallest apparent distance during a mutual event between the centres of two satellites in an occultation, or between an eclipsed satellite and the axis of the other's shadow cone in an eclipse. Zero is a central event.
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.
jovicentric declination of the Earth or Sun: The latitude of the Earth (D_E) or the Sun (D_S) above Jupiter's equatorial plane as seen from Jupiter's centre. It stays within about 4 degrees, and it crosses zero at each Jovian equinox.
JPL DE series: JPL's Development Ephemerides integrate and fit the Sun, planets and Moon to tracking and ranging observations. Accuracy statements and inter-release differences have date and component limits. A fitted lunar range residual does not bound every three-dimensional orbit component.
Jupiter's flattening: The fractional difference between Jupiter's equatorial and polar radii, $(71492-66854)/71492 = 0.0649$ with the IAU 2015 radii. It makes the disc and the shadow ellipses about 6.5 per cent shorter north to south.
Jupiter's shadow: The umbral and penumbral cones cast by Jupiter away from the Sun. At the Galilean satellites the umbra is barely narrower than Jupiter and the penumbra is a rim about 750 to 3400 km wide.
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.
kn cos ψ: The quantity in the Explanatory Supplement's prediction method equal to $k$ times the radial rate $n\cos\psi$ at which the observer's projection crosses the Moon's limb along the radius to the star. Timing errors scale as its inverse, so it tends to zero as an occultation becomes a graze.
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: The record of a target's brightness against time. In a mutual event the shape and depth of the light curve encode the relative position of the two satellites.
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 to the observer, about 499 seconds from the Sun and 1.3 seconds from the Moon. A reception correction evaluates the target at emission time and the observer at reception time. Observer aberration is separate.
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.
limiting parallels: The most northerly and most southerly latitudes from which a given occultation can be seen, published with the old prediction elements as a quick visibility test.
lunar eclipse contacts (P1, U1, U2, U3, U4, P4): The instants when the Moon's limb is tangent to a shadow edge: P1 and P4 the first and last exterior contacts with the penumbra, U1 and U4 with the umbra, and U2 and U3 the first and last interior contacts with the umbra, which bound totality.
lunar gamma: The least distance of the Moon's centre from the axis of the Earth's shadow, in Earth equatorial radii, positive when the Moon passes north of the axis. It differs from solar-eclipse gamma, which measures the Moon's shadow axis from the Earth's centre.
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.
lunar occultation: The passage of the Moon in front of a star or planet as seen by an observer. A solar eclipse is the special case in which the occulted body is the Sun.
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).
magnitude drop: The fall in combined brightness when the star is hidden and only the occulting body's light remains, $\Delta M = M_\circ - M_\star + 2.5\log_{10}(1+10^{0.4(M_\star - M_\circ)})$ with $M_\star$ and $M_\circ$ the star and body magnitudes. It decides whether an event can be detected.
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.
mid-event convention: The rule that a published eclipse time is the instant of half flux, and an occultation, transit or shadow transit time the instant the limb or shadow edge bisects the satellite. A visual observer sees the last or first speck instead, a minute or more away.
milliarcsecond: One thousandth of an arcsecond. At a distance of $D$ astronomical units one milliarcsecond spans $0.7253\,D$ km, so about 3 km at Jupiter in opposition and about 6 km at Saturn.
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.
mutual event: An occultation of one natural satellite by another as seen from the Earth, or an eclipse of one satellite by another's shadow as seen from the Sun. Such events happen only for months around a planet's equinox, when the Earth or the Sun lies close to the satellites' orbital plane.
mutual planetary occultation: An event in which one planet passes in front of another as seen from Earth. If the nearer planet's disc is smaller than the farther one it is properly a transit. The most recent was Venus and Jupiter on 1818 January 3 and the next is the same pair on 2065 November 22.
negative chord (miss): An observation from a site that saw no occultation. Near the limb it constrains size and shape. It also removes the two-sided ambiguity of a single positive chord.
NIMA: Numerical Integration of the Motion of an Asteroid, the orbit-fitting procedure of Desmars and co-authors used by the Lucky Star project to produce ephemerides of trans-Neptunian objects and Centaurs for occultation prediction, with observations weighted by bias and precision.
node limit: The largest heliocentric distance of the Earth from the planet's node, at the instant the planet crosses the ecliptic, that still allows a transit. It is a few degrees for Mercury and under one degree for Venus, which is why Venus transits are rare.
NOE ephemerides: Numerical Orbit and Ephemerides: the numerically integrated satellite ephemerides of Lainey at IMCCE for the satellites of Mars, Jupiter, Saturn and Uranus, fitted to observations and published as SPICE kernels. A name such as NOE-5-2010-GAL identifies one fitted solution.
nominal solar radius: The IAU 2015 conversion constant of exactly 695,700 km, about 959.22 arcseconds at 1 au. It is a unit for expressing stellar radii rather than a measured eclipse photospheric radius.
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.
normal optical depth: The optical depth $\tau_n$ of a planetary ring measured perpendicular to the ring plane. Light crossing the ring at elevation $B$ above the plane is reduced to the fraction $T = e^{-\tau_n/\sin|B|}$ , and to $e^{-\tau_n}$ at normal incidence.
northern and southern limit lines: The two curves on the Earth's surface along which the star's track is tangent to the Moon's mean limb. Outside them there is no occultation. Near them a graze is seen.
notional eclipse-forming layer (NEL): Herald and Sinnott's name for the height above the oblate Earth at which a straight solar ray must graze to reach the observed umbral edge. It is a fitted quantity, about 87 km on average, not a physical opaque layer.
numerically integrated ephemeris: An ephemeris made by integrating the equations of motion of all the bodies together and fitting the initial conditions and physical parameters to observations. JPL's SAT series and IMCCE's NOE ephemerides are of this kind.
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.
O − C residual: Observed minus computed: the difference between an observed position or time and the value predicted by an ephemeris or theory. Its root mean square over a campaign measures how well the theory fits the data.
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.
occultation by Jupiter: The passage of a satellite behind Jupiter's disc as seen from the Earth. Disappearance (OC D) and reappearance (OC R) are timed when the limb bisects the satellite.
occultation diffraction pattern: The Fresnel fringes in a star's light just before it is cut off by the straight edge of the lunar limb. Their spacing of order 10 m at the Earth sweeps past the telescope in milliseconds, and their smoothing measures the star's angular diameter.
occultation elements: The Besselian elements of a lunar occultation of a star, given once for the instant of conjunction in right ascension: the time $T_0$ , the Greenwich hour angle $H$ of the star, $Y$ , the hourly rates $x'$ and $y'$ , and the star's right ascension and declination.
occultation residual (O−C): The computed angular distance of the star from the lunar limb at the observed time, in arcseconds, written $\Delta\sigma$ and positive outside the limb. It is the observed-minus-computed quantity of an occultation reduction.
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: The angle at the Sun between celestial north and the zenith. Here $q_{\mathrm{par}}=\operatorname{atan2}(\xi,\eta)$ in fundamental-plane coordinates. The Supplement's source-local symbol C differs from this site's C for the offset in Herald's limb construction.
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.
penumbral lunar eclipse: A lunar eclipse in which the Moon enters the Earth's penumbra but not its umbra. Its umbral magnitude is negative in NASA's tables, and it is seldom visible unless the penumbral magnitude exceeds about 0.6.
personal equation: The systematic delay between an event and a visual observer's timing of it, typically several tenths of a second, which reductions subtract.
phase correction: The shift in a predicted contact caused by Jupiter's terminator not coinciding with its limb when the Sun and Earth directions differ. Thuillot gives up to 3 minutes for Io and 6 minutes for Callisto near quadrature.
PHEMU campaign: An international campaign, coordinated by IMCCE, to record light curves of mutual events of the Galilean satellites in one equinox season. Named by year, for example PHEMU15 for 2014 to 2015.
PHESAT: IMCCE's international campaigns to observe phenomena of Saturn's satellites at each Saturnian equinox: PHESAT95, PHESAT09 and the PHEMU-PHESAT campaign of 2024 to 2027. PHEURA07 was the Uranian equivalent.
photocentre: The brightness-weighted centre of a body's image, which astrometry measures. Uneven albedo and phase move it away from the centre of figure.
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.
plane-of-sky error ellipse: The projection of a body's three-dimensional position uncertainty onto the plane perpendicular to the observer's line of sight, given by a semi-major axis, a semi-minor axis and an orientation angle. JPL Horizons quotes it at 3 standard deviations.
planetary equinox: The instant when the Sun crosses a planet's equatorial plane, so that the planetocentric declination of the Sun is zero. For Saturn and Uranus it is the centre of the season of mutual satellite events.
planetary transit: The passage of Mercury or Venus across the Sun's disc as seen from the Earth. It happens only when an inferior conjunction falls close to one of the planet's orbital nodes.
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.
point-spread function (PSF): The image a telescope, camera and atmosphere make of a point source. Its width blurs the planet's edge and the solar limb together and so sets the size of the black drop.
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: The angle of a contact point on the solar limb, measured eastward from celestial north. The local formulas use P. The 1961 Explanatory Supplement calls it Q, distinct from this site's Q for global shadow-edge geometry.
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 and outline curves use Q. It is distinct from the local contact position angle P and from source-specific enumeration auxiliaries.
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.
quincena: NASA's name for the pair formed by a lunar eclipse and the solar eclipse about a fortnight before or after it in the same eclipse season. The QSE code gives the type of that solar eclipse.
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.
reduction formula: An almanac formula that gives a local contact time from the geocentric one as $T = T_0 + a\,\rho\sin\phi' + b\,\rho\cos\phi'\cos(c + \lambda)$ , with constants $a$ , $b$ , $c$ printed for each contact.
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).
refractive tail: The slow final fading of an eclipse light curve caused by sunlight refracted and scattered through Jupiter's atmosphere into the geometric shadow. It lasts minutes at red and near-infrared wavelengths.
relative parallax: The difference between the Moon's and a planet's horizontal parallaxes. Chauvenet uses it in place of the Moon's parallax to treat an occultation of a distant planet by the method for a star.
ring-plane crossing: The passage of the Earth or the Sun through the plane of Saturn's rings, which is Saturn's equatorial plane. An Earth crossing turns the rings edge-on to us. A Sun crossing is Saturn's equinox and puts the satellites' shadows in their common orbital plane.
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.
RUWE: The renormalised unit weight error of a Gaia astrometric solution. Values above about 1.4 indicate that the star's motion does not fit a single-star model, often because of an unresolved companion, and occultation predictions for such stars have been observed to shift.
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.
Sampson-Lieske theory: The analytical theory of the Galilean satellites built by Sampson (1921) and redeveloped by Lieske (1977) with 49 adjustable constants. Its fits E-1 to E5 and Arlot's G-5 underlie most predictions made before about 2014.
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.
satellite X, Y coordinates: The apparent offset of a satellite from Jupiter's centre in the sky plane, in units of Jupiter's equatorial radius, with X along Jupiter's equator and Y towards Jupiter's north pole. The same offsets seen from the Sun decide eclipses and shadow transits.
Saturn equatorial radius: The radius of Saturn's equator at the 1 bar pressure level, 60,268 km in the IAU and NSSDC values. It is not the 60,330 km or 60,000 km reference radii that some gravity models use.
SATxxx ephemeris: A numbered JPL ephemeris of Saturn's satellites, such as SAT415 or SAT441, distributed as SPICE SPK kernels. The number names a fit, not a version order of quality.
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.
semi-analytical theory: A theory of motion that expresses a body's orbital elements as series of periodic terms in time, fitted to observations. TASS and Dourneau's theory are of this kind. Evaluating one needs only the series, not a numerical integration.
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 $\tan f_2$ .
shadow cylinder: For a star at effectively infinite distance the Moon's shadow is a cylinder of radius $k$ rather than a cone, so on the fundamental plane it is a circle of fixed size whose centre moves with the Moon.
shadow enlargement: The empirical increase of the Earth's computed shadow radii needed to match observed lunar eclipses, caused by the atmosphere. It is applied as Chauvenet's 2 per cent, Danjon's 1/85 of the Earth's radius, or Herald and Sinnott's 87 km layer.
shadow path: The track on the Earth's surface swept by the shadow of an occulting body during a stellar occultation. On the fundamental plane its width equals the body's diameter. On the ground it widens as the star sinks towards the horizon.
shadow transit: The passage of a satellite's shadow across the disc of its planet, seen as a small dark spot on the cloud tops. It is fixed by the Sun's direction, like an eclipse, and its contacts are the shadow's contacts with the planet's limb.
shadow velocity: The speed of the occulting body relative to the star on the fundamental plane, in km per second. It converts a timing error into a distance error and an exposure time into a spatial resolution.
single-chord event: An occultation recorded by one observer or by several observers on effectively the same track. It gives a lower limit on the body's size and an astrometric position whose cross-track uncertainty depends on the body's assumed diameter.
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 parallax: The angle subtended by the Earth's equatorial radius at one astronomical unit, about 8.794 arcseconds. Transit timings measure it, and the astronomical unit follows from it.
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.
stellar occultation: The passage of a solar-system body in front of a star as seen by an observer. Because the star is effectively a point at infinity, the body's shadow is a cylinder of the body's own cross-section, and the event lasts from a fraction of a second to a few minutes.
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.
sublunar point: The place on Earth with the Moon in its zenith at a given instant, at latitude equal to the Moon's declination and longitude given by the Moon's right ascension minus Greenwich apparent sidereal time. The Moon is above the horizon over the hemisphere centred on it.
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.
TASS: Théorie Analytique des Satellites de Saturne, the semi-analytical theory of Mimas to Iapetus by Vienne and Duriez. Version 1.6 was published in 1995 and version 1.7, which adds Hyperion, in 1996.
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.
total penumbral eclipse: A penumbral lunar eclipse in which the whole Moon lies inside the penumbra without touching the umbra. Only 141 of the 4,378 penumbral eclipses from −1999 to +3000 are of this kind.
trans-Neptunian object (TNO): A small body whose orbit lies mostly beyond Neptune, at roughly 30 to 50 au or more. At such distances a body a few hundred kilometres across subtends tens of milliarcseconds.
transit contacts (I to IV): Contact I is the external tangency of the planet's disc with the solar limb at the start, contact II the first internal tangency, contact III the last internal tangency and contact IV the last external tangency. I to II is ingress and III to IV is egress.
transit of a satellite: The passage of a satellite in front of Jupiter's disc as seen from the Earth, from ingress (TR I) to egress (TR E).
transit series: A family of transits separated by a near-commensurability of the planet's and the Earth's orbital periods, 46 years for Mercury and 243 years for Venus, numbered like a Saros series for eclipses.
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 and penumbral magnitude: The fraction of the Moon's diameter inside the umbra or the penumbra at greatest eclipse, $(L_i - m)/(2 s_m)$ with $L_1$ for the penumbra and $L_2$ for the umbra. An umbral magnitude of 1 or more means a total eclipse.
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.
vector separation: The component of a double star's separation along the direction in which the lunar limb moves across it, which is all that one occultation timing measures.
vertex angle V: The contact position angle measured counter-clockwise from the zenith point of the solar disc, $V=P-q_{\mathrm{par}}$ with $q_{\mathrm{par}}$ the parallactic angle. Some calculators report it as a clock-face hour.
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.
XZ catalogue: The zodiacal star catalogue begun at the US Naval Observatory in 1977 for occultation predictions and reductions, covering 6 degrees 40 arcminutes either side of the ecliptic. The current version XZ80Q has 244,437 entries.
Zodiacal Catalogue (ZC): Robertson's 1940 Catalog of 3539 Zodiacal Stars for the Equinox 1950.0, the standard list of brighter stars that the Moon can occult. Its numbers still name the stars in published predictions.
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.
ΔU: The difference between the saturnicentric longitudes of the Sun and the Earth, measured in the ring plane. With B and B′ it fixes on which side of the globe the shadows of the globe and rings appear.
μ (hour angle of the shadow axis): The Besselian element that ties the shadow to the rotating Earth. NASA tabulates ephemeris sidereal time minus the axis right ascension. Convert it to the UT1 hour angle by subtracting $(1.002738\times15/3600)\Delta T$ degrees, with ΔT in seconds, unless the generator already used actual UT1 sidereal time.
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.