Lunar eclipses, occultations and transits

workingupdated 2026-10-17

Every event in this corpus is one body hiding another from a third. A source, an occulter and a receiver define a fundamental plane perpendicular to the source direction. The contacts are the roots of one quadratic in time on that plane ¹ ².
The shadow is a cone for an extended source and a cylinder for a star. Solar eclipses, transits and satellite eclipses use cones. Lunar and minor-body occultations of stars use a cylinder whose radius is the occulter's radius ³ ⁴.
Each event has one dominant input that is a convention or a model, not a constant of nature. It is the shadow enlargement rule for lunar eclipses, the lunar limb for grazes, the solar and planetary radii for transits, the satellite ephemeris for Jupiter and Saturn, and the orbit of the body for asteroid occultations ⁵ ⁶ ⁷ ⁸ ⁹.
The published instant means different things. Lunar eclipse contacts are geocentric. Transit contacts are tangencies of two discs. IMCCE's satellite phenomena are mid-events in TT. An occultation of a star is a single disappearance at one site ¹⁰ ¹ ¹¹ ³.
A general pipeline needs four additions to the solar one. These are a star-catalogue stage, a satellite-ephemeris layer, a body model that can be oblate, ringed or partly transparent, and a reduction stage that turns an observed time into a residual.

The question

The solar pipeline in pipeline design computes one event: the Moon hiding the Sun from a place on the Earth. This page asks which parts of that pipeline carry over to the other events of the same family, and what each event adds. The raw research is in six topics: lunar eclipses, lunar occultations, transits of Mercury and Venus, Jupiter's satellites, Saturn and the outer satellites and occultations by planets and minor bodies.

One geometry

Bessel's construction needs three bodies. The source gives light. The occulter casts the shadow. The receiver is where the observer stands. The fundamental plane passes through the receiver's centre perpendicular to the line from the source through the occulter. On that plane the occulter's shadow is a circle of radius $L$ , and the observer is a point $(\xi, \eta)$ . A contact is an instant at which the distance between the two equals $L$ . For a lunar eclipse the roles turn round: the Moon is the moving point and $L$ is a limiting separation between the Moon's centre and the shadow axis ¹. With relative position $(u, v)$ and relative motion $(u', v')$ , the 1961 Explanatory Supplement solves this as

t = \frac{L\cos\psi}{n} - \frac{uu' + vv'}{n^2}, \qquad \sin\psi = \frac{uv' - u'v}{nL},

with $n^2 = u'^2 + v'^2$ and $\cos\psi$ negative at ingress ¹. The Supplement's occultation section solves the same quadratic by iteration, and Chauvenet gives the same geometry ³ ².

The events differ in four places:

What the source is. The Sun is an extended disc, so the shadow is a cone with an umbra and a penumbra. A star is a point at infinity, so the shadow is a cylinder of the occulter's radius. For lunar occultations the cylinder radius is $k$ , the Moon's radius in Earth equatorial radii ³.
What the occulter is. The Moon has a limb profile. Jupiter and Saturn are oblate, and Saturn has rings that pass part of the light. A minor body has an unknown shape that the occultation measures ¹² ¹³ ¹⁴.
Where the receiver is. For a solar eclipse, a transit or an occultation the receiver is an observer on the Earth, so the time depends on the site. For a lunar eclipse the receiver is the Moon, and every observer sees the same instant. For a satellite eclipse the receiver is the satellite, and the Earth sees the result after a light-time ¹⁰ ¹². The receiver can also be a spacecraft or a rover. Its state vector then comes from its own SPICE kernel, and SPICE's occultation search accepts any observer ¹⁵. Transit timings from the SOHO and SDO spacecraft ¹⁶ therefore need predictions for the spacecraft's position, not the Earth's centre.
What the reported instant is. See the event definitions.

The events compared

Event	Source	Occulter	Shadow	Receiver	Dominant input	Achievable accuracy	Topic
Solar eclipse	Sun	Moon	Cone	Observer	Lunar limb and solar radius	About 0.2 s for contacts with a modern limb profile	Lunar limb
Lunar eclipse	Sun	Earth with atmosphere	Cone, enlarged	Moon	Enlargement rule	Umbral contacts to a few seconds against many observers, tens of seconds against one	Lunar eclipses
Lunar occultation of a star	Star	Moon	Cylinder of radius $k$	Observer	Limb and event position angle	Most predictions within 0.3 s of video timings	Lunar occultations
Lunar occultation of a planet	Planet disc	Moon	Cone with a small source	Observer	Planet outline and phase	Not quantified in the sources read	Lunar occultations
Transit of Mercury or Venus	Sun	Planet	Cone	Observer	Solar and planetary radii	Predictors agree to about 2 s	Transits
Galilean satellite phenomena	Sun or Jupiter	Jupiter or a satellite	Cone, oblate occulter	Satellite or observer	Satellite ephemeris	Mutual events give 5 to 50 mas	Jupiter's satellites
Saturnian satellite phenomena	Sun or Saturn	Saturn, rings or a satellite	Cone, oblate and ringed	Satellite or observer	Satellite ephemeris and ring transmission	Mutual events give about 20 mas	Saturn and outer satellites
Occultation of a star by a minor body	Star	Asteroid or TNO	Cylinder of the body's size	Observer	Body orbit and star position	About 10 mas with Gaia EDR3	Planets and minor bodies
Mutual events at Uranus and Pluto	Sun or satellite	Satellite or Pluto	Cone	Satellite or observer	Satellite ephemeris and light-curve model	Formal uncertainties below 0.01 arcseconds at Uranus in 2007	Saturn and outer satellites
Occultation of one planet by another	Farther planet	Nearer planet	Cone	Observer	Planet radii and ephemeris	Published times for 2065 disagree by more than two minutes	Planets and minor bodies

The accuracy column quotes each topic's own figures. For solar eclipses the figure is the limb-corrected contact accuracy ¹⁷. For lunar eclipses it is the scatter of crater timings about a given enlargement rule, which falls with the number of observers ⁵. For lunar occultations it is Herald's comparison with video timings ⁶. For transits it is the agreement between Espenak and the IAA for the 2016 and 2019 Mercury transits ¹⁸ ¹⁹. For the satellites it is the rms O−C of mutual-event astrometry ²⁰ ⁸. For minor bodies it is the astrometric precision of a fitted occultation ⁹. For Uranus it is the mutual-event astrometry of 2007 ²¹. For planet-planet occultations it is the spread between published lists for the 2065 Venus and Jupiter event ²² ²³. These numbers measure different things and cannot be ranked against each other.

What the published instant means

A pipeline that compares its output with a published table must use the same definition of the instant.

Solar eclipse and transit contacts are tangencies of two discs, external or internal ¹.
Lunar eclipse contacts P1, U1, U2, U3, U4 and P4 are tangencies of the Moon's disc with the enlarged penumbra or umbra, computed at the Earth's centre. They are the same instant for every observer ¹⁰.
A lunar occultation of a star is the instant the star's direction meets the limb, at one site. A smooth-limb prediction and a limb-corrected prediction differ by the limb height divided by the limb rate $kn\cos\psi$ ³.
Galilean satellite phenomena in IMCCE's tables are mid-events in TT. An eclipse is timed at half flux. Occultations, transits and shadow transits are timed when the satellite or its shadow is bisected by the limb ¹¹. The first or last visible part of the satellite can be 1 to 15 minutes away, depending on the satellite ²⁴.
Phenomena of Saturn's satellites in the 1996 Bureau des longitudes booklet are timed at the satellite's centre ²⁵. The 2009 tables of eclipses by Saturn give a maximum and a half-duration, and the mutual-event tables give contacts ²⁶.
A stellar occultation by a minor body is a pair of disappearance and reappearance times per chord, with Fresnel diffraction and the star's diameter in the light curve ⁴.

What generalises in the pipeline

The pipeline design has nine stages. All nine carry over in some form, and the other events add a tenth.

Stage 1, ephemeris, orientation and time. The planetary ephemeris and the time scales stay. Compute in TT and convert to UT1 only at output. Two layers join the ephemeris: a star catalogue with epoch propagation of Gaia DR3 positions, and satellite ephemerides delivered as SPICE kernels consistent with DE440, such as JUP365 for Jupiter and SAT441 for Saturn ²⁷ ²⁸ ²⁹. Record the kernel pair with every result. The body model grows as well. The occulter can be an oblate spheroid, a body with rings, or a body whose atmosphere sets the edge. Saturn's ring B is close to opaque and ring C is not ¹³. JPL Horizons models the planet as a sphere of the equatorial radius for these events ³⁰.
Stage 2, enumeration and provisional type. The same search for a syzygy near a node finds lunar eclipses and transits. Lunar eclipses use Meeus's closed form with changed coefficients ³¹. Transits need an inferior conjunction near the planet's node ³². Satellite phenomena need a seasonal gate on the planetocentric latitudes of the Earth and the Sun ²⁶.
Stage 3, Besselian elements. The cone code takes a cylinder as a limit, with $l_1 = l_2 = k$ and both cone angles zero for a star ³. For a lunar eclipse the elements shrink to $x$ , $y$ and three limiting separations $L_1$ , $L_2$ and $L_3$ , which are set by an atmospheric enlargement rule ¹. Chauvenet, Danjon and Herald and Sinnott give different values, and the choice moves umbral contacts by 20 to 30 seconds and penumbral contacts by about 1.5 minutes ⁵ ³³. One contact solver serves every event if $L$ is an input built from explicit radii: $k$ , the solar semidiameter, the planet's semidiameter, the occulter's radius or the lunar-eclipse separation ¹.
Stage 4, global circumstances. Paths and limit lines carry over to occultations of stars, where the limit is a graze line, and to minor-body occultations, where the path width is the body's diameter ² ⁴. A lunar eclipse has no path.
Stage 5, partial-eclipse maps. For a lunar eclipse the map is a horizon map of where the Moon is up at each contact. ΔT moves it by 1 degree of longitude per 240 seconds of ΔT ¹⁰.
Stage 6, local circumstances. Site-dependent for transits and occultations as for solar eclipses. Transit tables also publish a three-constant reduction formula per contact ³⁴.
Stage 7, terrain. Shared with lunar occultations, where the observer's height shifts a graze line by $h\tan z$ toward the Moon's azimuth ³⁵.
Stage 8, lunar limb. Shared unchanged between solar eclipses and lunar occultations. A graze uses the same limb test, and Morrison required the event position angle to 0.01 degrees ³⁶. An error of about 0.2 degrees in Occult's position angle once degraded its graze profiles ⁶.
Stage 9, products and uncertainty. Each product gains the conventions in the next section. Minor-body paths gain a cross-track uncertainty from the orbit covariance ³⁷.
A new stage, reduction. An observed time becomes a residual against the prediction. Occultation residuals measure ΔT, lunar-eclipse crater timings measure the shadow layer, and chord timings measure an asteroid's size and position ³⁸ ⁵ ¹⁴.

Conventions to carry as metadata

Each of these choices changes the output and none of them is fixed by nature. A result without them cannot be compared.

Convention	Events	Values in use	Effect
Shadow enlargement	Lunar eclipses	Chauvenet 1.02, Danjon 1.01 on the lunar parallax, Herald and Sinnott 87 km	0.005 in umbral magnitude, 20 to 90 seconds in contacts ⁵
Lunar radius $k$	Solar eclipses, lunar eclipses, occultations	0.272281 for umbral contacts and 0.2724880 or 0.2725076 for penumbral contacts in NASA's solar tables, 0.2724880 in the lunar Canon, 0.2725 for occultation prediction, 0.2725076 adopted by the IAU in 1982	Smooth-limb times and durations ³⁹ ¹⁰ ³ ⁴⁰
Solar radius $s_0$	Solar eclipses, transits	959.63 and 959.95 arcseconds	3.3 to 6.5 seconds per transit contact for that gap, computed from the Supplement's solution with published elements ³² ⁷ ⁴¹
Venus semidiameter	Venus transits	8.34 and 8.41 arcseconds at 1 au	About 5 seconds per contact ⁷ ³¹
Satellite theory	Planetary satellites	Lieske E5, Lainey L1 and NOE, JPL JUP365 and SAT441, TASS 1.7	Tens of milliarcseconds, and grazing events can appear or vanish between theories ⁸ ⁴² ²⁶
Event definition	Satellite phenomena	Mid-event, satellite centre, first or last light	Minutes ²⁴
Longitude sign	Transits, occultations	West-positive in the 1961 Supplement, east-positive in the IAA and RASC tables	Inverts the local correction if mixed ¹⁹ ⁴³
Uncertainty level	Minor-body paths	JPL Horizons gives 3-sigma	Divide by 3 for 1-sigma path lines ³⁰

What a developer should do

Build the contact solver once, with $L$ and the shadow shape as inputs, and test it on the 1961 Explanatory Supplement's worked examples for eclipses, transits and occultations ¹ ³² ³. Then add the events in the order of how much new machinery each needs:

Transits need only a planet radius and a second semidiameter. Test against the Supplement's 1960 examples and the IAA city tables ³² ³⁴.
Lunar eclipses need an enlargement rule and a horizon map. Test against the NASA catalogue with Danjon's rule, then against crater timings in VizieR VI/140 with Herald and Sinnott's rule ¹⁰ ⁴⁴.
Lunar occultations need a star catalogue and the cylinder mode. Grazes reuse the limb stage. Test against the VI/132C archive ⁴⁵.
Satellite phenomena need satellite kernels, an oblate occulter and separate light-time paths from the Sun and to the Earth ¹². Test against IMCCE's published tables with the same event definition ¹¹.
Minor-body occultations need orbit covariance mapped to a cross-track uncertainty, and a diffraction light-curve model for reduction. SORA is the documented open implementation ⁴⁶.

Open questions

Occult's help file is the missing source in four topics: its lunar eclipse enlargement rule, its graze binning, its treatment of planet phase in lunar occultations, and its asteroid elements. The program is closed source and its help is distributed only with the installer ⁴⁷.
Meeus's Transits (1989) underlies the NASA transit catalogues and was not read ⁴⁸.
The current Astronomical Almanac sections on lunar eclipses, occultations and satellite phenomena would establish its present enlargement rule and satellite theory.
The altitude in Jupiter's atmosphere at which a satellite eclipse reaches half flux is not stated in any source read ¹¹.
No public tool examined models the transmission of Saturn's rings in satellite eclipses ¹³.

References

1peer-reviewed Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (1961), section 9B Eclipses and Transits Read in full (OCR text). Definitive almanac formulation: fundamental plane, point Z, x y z, mu from ephemeris sidereal time, sin f1 sin f2 with tabulated numerators for k = 0.272274, 0.2724807, 0.272281 and 0.2724880, c1 c2 l1 l2, sign convention, observer coordinates, ephemeris meridian 1.002738 ΔT, worked example 1961 Feb 15.
2primary Chauvenet, W., A Manual of Spherical and Practical Astronomy, Vol. I (1863), chapter on Eclipses, Arts. 288 to 296 Read Arts. 288 to 291 and the cone-angle precepts in OCR text (garbled in places). Original almanac form of Bessel's method: point Z as the Sun seen from the Moon's centre, equations (482) for x y z, principal plane of reference, log k = 9.435000, c = z ± k/sin f, l = c tan f.
3peer-reviewed Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (1961, reprint with 1973 added notes), section 10 Occultations, pp. 277-305 Read in full from the archive.org OCR text. Source of the occultation Besselian elements (T, H, Y, x', y'), the formulas for x and y and their rates, the station reduction with f, g and kn cos psi, the position angle, the a and b coefficients, the limiting parallels, the prediction limits, the k values 0.2725, 0.2724953 and 0.2725026, the reduction to delta-sigma, the limb correction arguments and section F on planetary occultations. Some equations are damaged in the OCR text.
4peer-reviewed Gomes-Júnior, A. R., Morgado, B. E., Benedetti-Rossi, G. et al. (2022). SORA: Stellar Occultation Reduction and Analysis. MNRAS 511, 1167-1181 (arXiv:2201.01799) Read in full from the arXiv LaTeX source. Source of the closest-approach equations (Assafin et al. 2010 geometry), the shadow velocity, the magnitude-drop equation, the Fresnel scale f = sqrt(lambda D / 2), the star radius at the body, the exposure length r_t = V_S t_exp, the timing uncertainty sigma_t = sigma_LC t_exp / Delta f, the tangent-plane equations 6 to 9, the 0.021 s light-time and the chord and ellipse chi-square. Its printed albedo equation omits the factor 0.4 that the code applies.
5peer-reviewed Herald, D. and Sinnott, R. W. (2014). Analysis of lunar crater timings, 1842-2011. J. Br. Astron. Assoc. 124(5), 247-253 Read in full from the ADS scan (text extracted; Greek letters in the Symbol font are lost, so equation [4]'s angle is written theta here). Source of equations [1] to [4], the recommended rule with h = 0.0136, the NEL statistics (mean 86.9 +/- 0.2 km, mode 78, median 85), the per-eclipse heights, the ingress-egress and limb-contact biases, the shape result and the 1963 Dec 30 case.
6company Herald, D. (2016-11-20). Update to Occult and Observations Read (curl). States that a position-angle error of up to 0.2 deg in the traditional method corrupted the limb correction, and that with the LOLA lunar limb (Occult download #26) most occultation predictions are within 0.3 s of observation.
7primary IMCCE for ESO VT-2004, Extended InfoSheet B1: Predictions of the Venus transit of June 8, 2004 Read in full (curl). VSOP87, Lieske precession, Wahr nutation, Aoki sidereal time, IAU 1976 constants (solar semidiameter 15'59.63", Venus radius 6051.8 km, Earth radius 6378.140 km), flattening 1/298.257, TT - UTC 65.184 s, general and geocentric phases, the E, F, G coefficients and the Paris example. Formula (1) is an image; its form is reconstructed in the note from the Paris example.
8peer-reviewed Arlot, J.-E., Emelyanov, N. V., Lainey, V. et al. (2012). Astrometric results of observations of mutual occultations and eclipses of the Saturnian satellites in 2009. Astronomy and Astrophysics 544, A29 Read in full from the HAL PDF (CC BY 4.0). Source of the observation counts 14, 66 and 33 for 1980, 1995 and 2009, the photometric model E(t) = K S(X, Y), the O-C residuals against TASS 1.7, Lainey and SAT351, and the NOE-6-2011-MAIN accuracy statement.
9peer-reviewed Ferreira, J. F., Tanga, P., Spoto, F., Machado, P. and Herald, D. (2022). Asteroid astrometry by stellar occultations: accuracy of the existing sample from orbital fitting. A&A 658, A73 (arXiv:2201.03892) Read from the arXiv text. Source of the pre-Gaia residual level of 30 to 50 mas, the Gaia EDR3 level near 10 mas, the factor of about 5 reduction, the 10 mas FWHM of the residual core, the 3 to 4 mas along-track error level, the RUWE analysis and the statement that 61 per cent of events are single-chord.
10primary Espenak, F. and Meeus, J. (2009). Five Millennium Canon of Lunar Eclipses: -1999 to +3000, NASA/TP-2009-214172, text sections 1 to 5 Read in full (text PDF, 3.2 MB, extracted with pdftotext). Source of the contact definitions, gamma and magnitude definitions, eclipse statistics (12,064 eclipses), VSOP87 D and truncated ELP-2000/82, k = 0.2724880, secular acceleration -25.858 arcsec/cy^2 and the c correction, the enlargement section 1.5 (Chauvenet and Danjon formulas, Tables 1-3 to 1-6), map accuracy and Delta T uncertainty zones, Danjon scale wording, Saros and Inex behaviour. Some tables are misaligned in extraction and were cross-checked against the web pages.
11primary IMCCE, /pub/ephem/satel/phenjupiter/README (2021 September) Read in full. Event codes, TT time scale, mid-event convention, the theory used for each range of years (G-5 to 2014, L1 2015 to 2022, Lainey 2021 after), and the TT-UT table.
12peer-reviewed Thuillot, W. (1983). Theorie des phenomenes des satellites galileens de Jupiter: une representation par les polynomes de Tchebychev. Astronomy and Astrophysics 127, 63-67 Pages 1 to 3 read from the ADS scan (in French). Source of the cone equations with an ellipsoidal Jupiter, the phase correction of 3 min (Io) and 6 min (Callisto), the light-time rules, the Chebyshev form and its 51 s maximum error.
13primary Williams, D. R., NASA NSSDCA, Saturnian Rings Fact Sheet Read 2026-10-17. Ring edge radii (C inner 74,658 km, B inner 91,975 km, B outer 117,507 km, A inner 122,340 km, A outer 136,780 km), optical depths (C 0.05 to 0.35, B 0.4 to 2.5, Cassini Division 0 to 0.1, A 0.4 to 1.0) and thicknesses.
14peer-reviewed Herald, D., Gault, D., Anderson, R. et al. (2020). Precise astrometry and diameters of asteroids from occultations: a data set of observations and their interpretation. MNRAS 499, 4570-4590 (arXiv:2010.06086) Read sections 1 to 6, 8 and 10 to 11 from the arXiv LaTeX source. Source of the reduction on the fundamental plane with Besselian elements and a cubic shadow motion, the inverse Besselian astrometry steps, the single-chord uncertainty rules, the weights 5, 4, 3 and 1, the ellipse-fit treatment of misses, the 40 mas and 40 km pre-Gaia statement, the 586 events of 2019, the Gaia DR2 bright-star frame rotation and the 10 ms timing goal.
15primary NAIF CSPICE gfoclt_c documentation Official documentation read 2026-09-30. Detailed Input accepts ELLIPSOID+ELLIPSOID, ELLIPSOID+POINT, DSK+POINT. POINT requires ANY; exceptions 9 and 14 reject the proposed DSK+finite-Sun FULL search. Cached HTML SHA256 7aef5446d1b4a396bbed8eaba1201da94a2aa118fcaa757a063b7080abf33d3a.
16peer-reviewed Emilio, M., Kuhn, J. R., Bush, R. I. and Scholl, I. F. (2012) Measuring the solar radius from space during the 2003 and 2006 Mercury transits. ApJ 750, 135 (arXiv:1203.4898) Read in full from the arXiv PDF, with the radius equation checked against the ar5iv HTML rendering because the PDF text layer drops its symbols. SOHO/MDI contact fitting, the Shapiro (1980) duration relation, the adopted 959.645 arcsecond nominal radius, observed contacts offset 8 s (2003) and 5 s (2006) from the NASA ephemeris, and the 960.12 plus or minus 0.09 arcsecond result.
17company Espenak, F. Lunar Limb Profile and Eclipse Predictions. EclipseWise Read. Same text as the NASA page with the added statement that Kaguya and LRO data bring the accuracy to about 0.2 seconds.
18company Espenak, F., EclipseWise, 2016 Transit of Mercury (Observer's Handbook article) Read through a fetch summary with quoted table values. Geocentric contacts 11:12:19, 11:15:31, 14:57:26, 18:39:14, 18:42:26 UT1 with position angles 83.2, 83.5, 153.8, 224.1 and 224.4 degrees, minimum separation 318.5 arcseconds, JPL DE406.
19primary Institute of Applied Astronomy RAS, Astronomical Yearbook 2016: Transit of Mercury of 2016 May 9 Read in full (curl). Elements at conjunction in right ascension, geocentric phases with position angles and sub-planet points, the four local-circumstance formulas T = T0 + a r sin f' + b r cos f' cos(c + l), and a table of Russian cities. Ephemeris not stated in the file.
20peer-reviewed Saquet, E., Emelyanov, N., Robert, V., Arlot, J.-E. et al. (2018). The PHEMU15 catalogue and astrometric results of the Jupiter's Galilean satellite mutual occultation and eclipse observations made in 2014-2015. MNRAS 474, 4730-4739 Read in full from the UNESP repository copy. Campaign statistics 1985 to 2015, the photometric model, the Emelyanov reduction equations, NOE-5-2010-GAL and JUP310 residuals.
21peer-reviewed Christou, A. A., Lewis, F., Roche, P. et al. (2009). Observational detection of eight mutual eclipses and occultations between the satellites of Uranus. Astronomy and Astrophysics 497, 589-594 Abstract read in the arXiv version (arXiv:0902.4582); journal DOI 10.1051/0004-6361/200811523 from Crossref. Fifteen light curves with five instruments of 0.4 to 10 m, eight events detected, formal uncertainties below 0.01 arcsecond, and a systematic lag of observed mid-times behind predictions.
22company Gray, B. (Project Pluto). Assorted celestial events: mutual planetary events, -1000 to +6000 Read. The author documents his own search: VSOP theory, times in TD, Gregorian dates, an event listed if at some point on Earth one disc overlaps another, an average rate of about one per 35 years, and the list including 1818 January 3 21:52 and 2065 November 22 12:45 TD.
23unsourced Bogan, L. Mutual Planetary Occultations Past and Future: their observation circumstances (web page) Read. Summarises Albers 1979 and adds events computed with Guide 7.0. Gives the Venus-Jupiter events of 1570, 1818, 2065 and 2123 with times, elongations, diameters and geocentric separations, and the Mercury events to 2133.
24trade Westfall, J. E. (2006). Timing the eclipses of Jupiter's Galilean satellites. ALPO observing instructions Read pages 1 and 2. Table of penumbral widths, ingress and egress durations and eclipse durations; the 1 to 2 minute offset of visual timings from mid-event predictions; comparison standard E-2.
25primary Arlot, J.-E., Derouazi, Th., Ruatti, Ch., Thuillot, W. (1995). Satellites de Saturne I a VIII : phenomenes et configurations pour 1996. Bureau des longitudes Read the bilingual front matter and the phenomena and mutual phenomena explanations. Source of the event codes Pd, Pf, Od, Of, Ed, Ef, Im, Em, the rule that times refer to the satellite centre, the 14 s to 450 s contact-to-contact durations, the use of Dourneau 1993 and VSOP82, and the 10 to 15 arcsecond reading accuracy of the configuration curves.
26peer-reviewed Arlot, J.-E. and Thuillot, W. (2008). Predictions of the events of the satellites of Saturn during the 2009 equinox. Astronomy and Astrophysics 485, 293-298 Read in full from the HAL PDF. Source of the four event types, TASS and Do93 predictions, 441 events from 2008 Sep 9 to 2010 Jun 18 with 123 easily observable, the 10 to 30 s spread in times of maximum, the 0.1 arcsecond to 600 km scale, the column definitions (TT, penumbral and umbral contacts, flux drop, impact parameter), and the Titan shadow transit window 2009 Feb 24 to 2010 Jan 9.
27primary Gaia Collaboration, Gaia DR3 documentation, section 4.1.7 Epoch propagation (chapter CU3 astrometry) Read. Source of equations 4.8 to 4.17 for propagating position, parallax and proper motion under uniform rectilinear motion, the constant A_V = 4.740470464, and the treatment of unknown radial velocity.
28primary NAIF, generic_kernels/spk/satellites/jup365.cmt (BVS/NAIF, 2021-03-14) Read the header. JUP365.26 global fit, DE440 planets, 1600 to 2200, RADIUS 71492 km, Chebyshev interpolation error 16 m, GM values. The .bsp is 1,136,581,632 bytes.
29primary NAIF, generic_kernels/spk/satellites/sat441.cmt (SPKMERGE log and SATEPHGEN summary for SAT441.24, created 2022-01-29) Read in full. Bodies 601 to 609, 612 to 614, 632, 634 and 699, span 1749 Dec 29 to 2250 Jan 5, planetary ephemeris DE440, model SATORBINT, Chebyshev interpolation error 7.5 m, RADIUS 60,330 km as the harmonic reference radius, ring mass terms RINGM1 to RINGM4.
30primary JPL Horizons System Manual Read live. Observer table quantities, DE440/DE441, satellite eclipse circumstances; no solar eclipse product.
31trade Meeus J. (1991) Astronomical Algorithms, first edition, Willmann-Bell, Chapter 52 Eclipses Read from the Internet Archive OCR text (chapter 52 in the 1991 edition, chapter 54 in the 1998 edition). Source of the |sin F| > 0.36 rule, the corrections to the time of maximum, P, Q, W, gamma, u, the thresholds 0.9972, 1.0260, 1.5433, 0.0047, 0.00464, the partial-magnitude formula and the stated accuracy of 0.36 min mean and 1.1 min maximum for 1951 to 2050. Graded trade as a recognised practitioner's own algorithm text.
32peer-reviewed Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (1961), section 9F Transits of Mercury, pages 262 to 276 Read in full (OCR text). Node condition and the table of node limits, dates and frequencies (Mercury ascending node about 16 November 238 arcminutes, descending 8 May 108; Venus ascending 9 December 37, descending 7 June 41), Newcomb's heliocentric method and the transit fundamental plane, the light-time rule, the contact solution, least distance, position angles with V, Newcomb's q p w, the B C D reduction and Examples 9.26 to 9.32 for 1960 November 7. The node-limit formula for theta and the cone-angle equation are damaged in the OCR text and are not transcribed.
33primary Espenak, F. NASA GSFC Eclipse Web Site, Enlargement of Earth's Shadows (page dated 2009 Feb 02) Read in full. Web version of Canon section 1.5 with correctly aligned Tables 1-3 to 1-6: Chauvenet formula with 0.998340, Danjon formula with 1.01 = 1 + 1/85 - 1/594, magnitude differences 0.006 and 0.026, type-change lists, and which sources use which rule.
34primary Institute of Applied Astronomy RAS, Astronomical Yearbook 2019: Transit of Mercury of 2019 November 11 Read in full (curl). Same layout as 2016, with TDT - UT1 = 70.0 s stated, geocentric contacts 12:35:26.3, 12:37:07.7, 15:19:47.3, 18:02:32.1, 18:04:13.5 UT and the four reduction formulas.
35trade Nugent, R. (ed.) (2007). Chasing the Shadow: The IOTA Occultation Observer's Manual. International Occultation Timing Association Read chapter 4 (software), chapter 5 (grazes: geometry, elevation correction, limit-line shift, Occult graze profile, station placement, central graze time, double stars). Written by IOTA practitioners about their own methods.
36peer-reviewed Morrison, L. V. (1979). An analysis of lunar occultations in the years 1943-1974 for corrections to the constants in Brown's theory, the right ascension system of the FK4, and Watts' lunar-profile datum. MNRAS 187, 41-82 Read the method sections 2 to 4 in the ADS scan (OCR text). Source of the residual definition, the partial derivatives, the 932.58 arcsecond semidiameter relation, the refraction correction, the Watts-chart position-angle shift, the weights with their error components, the 0.49 arcsecond residual spread, and the corrections to mean longitude and the dynamical time scale before 1955.5.
37peer-reviewed Tanga, P. and Delbo, M. (2007). Asteroid occultations today and tomorrow: toward the GAIA era. A&A 474, 1015-1022 (arXiv:0801.2684) Read the sections on astrometric accuracy from the arXiv LaTeX source. Source of sigma_path = sqrt(sigma_CEU^2 + sigma_star^2), the efficiency factor p = 2 theta / sigma_path, the pre-Gaia catalogue errors (FK6 1 mas, Hipparcos 10 mas, Tycho-2 70 mas, UCAC2 20 mas), the 0.5 arcsec ephemeris and 350 km statement, and the 15 per cent success rate of 2005.
38peer-reviewed Stephenson F. R., Morrison L. V., Hohenkerk C. Y. (2016) Measurement of the Earth's rotation: 720 BC to AD 2015, Proc. R. Soc. A 472, 20160404 Open-access copy read 2026-09-15. Quoted: +1.8 ms/cy lod trend versus +2.3 ms/cy tidal, the parabola Delta T = -320.0 + 32.5 ((year-1825)/100)^2 s, the roughly 1500-year oscillation, DE430 acceleration -25.82 arcsec/cy^2, the untimed-eclipse method and the cubic spline fit.
39primary Espenak, F., NASA GSFC, Mean Lunar Radius (reference page for the eclipse bulletins) Read. History of k: 1968-1980 NAO two values 0.2724880 and 0.272281, IAU 1982 k = 0.2725076, Espenak's use of 0.272281 for umbral contacts, 1986 Oct 03 misclassification.
40peer-reviewed Seidelmann, P. K. (ed.), Explanatory Supplement to the Astronomical Almanac (1992), section 9.4 Occultations (pp. 494-498), section 8.12 on k, and section 4.51 on historical UT1 Read sections 9.41, 9.42, the k paragraph of 8.12 and 4.51 in the archive.org OCR text. Source of equations 9.41-2 to 9.41-9 for the shadow on the Earth and the visibility map, the planetary occultation condition 9.42-1, the statement that ILOC in Tokyo reduced timings, and the 1982 adoption of k = 0.2725076 to conform to occultation work. Equation 9.41-8 is partly illegible in the scan.
41company Espenak, F., EclipseWise, 2019 Transit of Mercury (Observer's Handbook article) Read through a fetch summary with quoted table values. Geocentric contacts 12:35:27, 12:37:08, 15:19:48, 18:02:33, 18:04:14 UT1 with position angles, minimum separation 75.9 arcseconds, JPL DE406, local times differing by up to 2 minutes, and the remark that the thread-breaking time is delayed by some seconds, up to a minute.
42peer-reviewed Arlot, J.-E., Lainey, V., Thuillot, W. (2006). Predictions of the mutual events of the Uranian satellites occurring in 2006-2009. Astronomy and Astrophysics 456, 1173-1179 Read in full from the HAL PDF. Source of the 42-year cycle, GUST86 and LA06, their internal and external errors, the 500 km (0.04 arcsecond) model spread, the 5 to 30 minute spread in mid-times, and the rule that an eclipse is computed as an occultation of the Sun seen from the eclipsed satellite with light-time.
43trade Dunham, D. W. (2026). Lunar Occultations. RASC Observer's Handbook 2026 Read (pdftotext). States that graze observations complement LRO laser ranging and have revealed small residual errors still under investigation, and that graze zones are 2 to 3 km wide.
44primary Herald, D. and Sinnott, R. (2014). VizieR VI/140, Catalogue of Lunar Eclipse Crater Timings, ReadMe Read in full (ReadMe dated 12-Sep-2014). Record layout of crater_t.dat (22,539 records), event codes 0 to 9, computed height, umbral latitude and percentage enlargement, and the Schmidt 1842-1879 manuscript scan. The data file itself was not downloaded.
45primary Herald, D. and Gault, D. et al. (2022). VizieR VI/132C, Archive of lunar occultation observations (1623 to the present), doc.txt and ReadMe Read doc.txt in full and the ReadMe column list. Source of the custody history (HMNAO 1943, ILOC 1981 to 2008, IOTA from 2008), the observation counts and correction statistics, the reduction basis (DE440, Gaia EDR3 for most stars, deltaT splines, WGS84 conversion, polar motion, refraction, LOLA limb in a P,D frame at 0.01 degree spacing), and the default personal equations.
46company riogroup/SORA, Stellar Occultation Reduction and Analysis, version 0.3.3, commit 63a1b2d of 2026-08-03 Code read: sora/prediction/core.py (occ_params and prediction), sora/prediction/occmap.py (xy2latlon and the path and 1-sigma lines), sora/lightcurve/utils.py (calc_fresnel, bar_fresnel, calc_magnitude_drop), sora/lightcurve/core.py (occ_model), sora/occultation/utils.py (calc_geometric_albedo) and sora/occultation/fitting.py (fit_ellipse). The authors document their own library, so the grade is company.
47company Occult v4 (David Herald) home page Fetched with curl 2026-09-15. Feature list, C#/.NET 4.5, 42 data files, installer sizes. Eclipse-specific help is inside the Windows help file and was not read.
48primary Espenak, F., NASA GSFC, Seven Century Catalog of Mercury Transits: 1601 CE to 2300 CE Read in full (curl). 94 transits, 31 in May at the descending node and 63 in November at the ascending node; the 13, 33 and 46 year commensurabilities with their residuals in days; the 46-year series; the full table of contacts, minimum separations and series; the 1937 May 11 row with no interior contacts; and the statement that Besselian elements come from Meeus's Transits (1989).