# How accurate should sunmoon ephemeris be for calculating eclipses?

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I am writing a program to simulate eclipses for about -2000 to 6000. My question is, how accurate does my ephemeris for the sun and moon have to be to get a decent accuracy for eclipses? I currently have an accuracy of about 1"for the Sun and an accuracy of about 12"for the moon. Is this good enough, or should I find a more accurate system?

Edit: I'm still rather new to calculating eclipses, though I have some experience with calculating ephemerises. I'd like to calculate several things: when they occur, the duration, the path of the shadow on the earth for a solar eclipse, and perhaps the percent covered. I suppose I'd like the accuracy on these to be about $$pm 0.005$$ or better. I have access to several resources that should help me do this, but I need to know how accurate to get the ephemeris.

I suspect this is fundamentally a question of error propagation. My personal favorite reference is "Data Reduction and Error Analysis" by Philip Bevington. Basically, once you have the formulas in place, such as

eclipse_time = f(sun_ephem, moon_ephem)

You take all the partial derivatives and "stuff" them into the error propagator formulas along with the known or estimated standard deviations (error/uncertainty) of your input variables. The uncertainty in the output just pops right out.

There is always something interesting happening in the sky. The Moon cycles through its phases and occasionally passes near a bright planet. Sometimes the Moon eclipses the Sun. And sometimes the Moon itself is eclipsed as it passes through Earth's shadow. The planets move against the stars and are most prominent at opposition (Mars, Jupiter and Saturn) or at greatest elongation (Mercury and Venus). Earth makes its annual orbit around the Sun and passes through its four seasons.

SKYCAL (Sky Events Calendar) will help you keep track of the sky by calculating the local date and time of all these celestial happenings. It displays them on a convenient calendar that you can print and hang on the wall. You can generate a calendar for a single month or for an entire year. Just choose your Time Zone.

To use SKYCAL, make your selections in three simple steps:

• Section 1: Select a Time Zone for the calendar you wish to generate.
• Section 2: Select the sky events to include in the calendar (moon phases, eclipses, planet positions, meteor showers, etc).
• Section 3: Select the year or year and month of the calendar.

For time zones in North America and Europe, a Daylight Saving Time (DST) control appears that can be toggled on or off. In most of North America, DST is observed from the second Sunday of March through the first Sunday of November. In Europe, DST is called Summer Time (ST). ST is observed from the last Sunday of March through the last Sunday of October. The initial settings of SKYCAL (Time Zone & DST) are based on the time zone setting in your computer's internal clock.

All sky events in section 2 are selected by default. Change them as needed. In Section 3, enter the year or year and month of your calendar. At present, SKYCAL works for all years from 1801 through 2100. This range will increase soon. You can select calendars other than the western Gregorian Calendar by clicking the Other Calendars button and choosing a calendar from the drop-down menu.

Besides the traditional 7-day per week calendar format, you can also display the sky events in a table (opened in a new window). This format shows additional information about many events because it has more room to display the extra data. The table can be printed and saved.

To learn more about SKYCAL, see About the Sky Events Calendar. Related links include:

## How accurate should sunmoon ephemeris be for calculating eclipses? - Astronomy

Most people use computer software to find positions for planets and rising and setting times. The resources on this page are mostly computer programs designed to calculate positions, but I also include some online calculators and some books. Many 'star chart' programs will also display the positions of the planets and other orbiting objects. I list 'freeware' software where possible. I have tried to give some indication of the kind of output the software generates, the system it works under (usually DOS), and the level of accuracy claimed.

The URL for each resource leads to a page about the resource, usually provided by the authors or sponsoring institution. The URL itself is shown in the text to make this page useful when printed out on paper, or when being sent as an e-mail in ascii code.

This page provides some basic definitions of the orbital elements. The page has a bias towards low Earth orbits for satellites, but the information is still relevant to planetary orbits.

William Press is famous as one of the co-authors of the superb Numerical Recipies in C , but the URL above leads to the contents page of a series of lecture notes for an astronomy course. Chapter 4 of the course deals with orbital motion from an advanced mathematical viewpoint. You go from Newton's equations to Kepler's laws for the two-body problem. The mathematical treatment is pitched at the second year undergraduate level (partial differential equations and vector calculus) and the exposition is clear. Chapter 4 is available online as a Web document, or in Adobe Acrobat format, or PostScript format.

Paul Schlyter has provided a comprehensive page about finding the positions of the Sun, Moon and planets to an accuracy of one or two minutes of arc using mean orbits with basic perturbation corrections. Paul has adapted and simplified methods contained in a paper by T. van Flandern and K. Pulkkinen called "Low precision formulae for planetary positions", originally published in the Astrophysical Journal Supplement Series, 1980.

The page contains no graphics and can be saved to your hard drive very easily. I found the use of rectangular coordinates for the planet positions a great simplification over the spherical trigonometry approach.

The Interactive Computer Ephemeris (ICE) has just become available as freeware for DOS computers. The Ephemeris will give you positions for the planets, Sun and Moon for any year from 1801 to 2047 (if you download all four of the files). As the home page says

'The program covers nearly all that is given in the yearly "Astronomical Almanac" published by USNO. Positions of planets rotational and illum- ination data sun/moon/planet rise, transit, and set times. It does not include the satellite (moon) data for other planets the latter IS included in the book. The output is a simple numerical tabulation, no graphics. Accuracy is equivalent to the book, that is, world-class accuracy. Output may be directed to a file for later use.'

The program comes in four ZIP files, and will occupy 1.2 Mb of space when expanded. You can run the program from a floppy disc. The Moon tabulations are not as full or as accurate as the Astronomical Almanac, but the rest of the tabulations are up to navigational standards.

The program will provide apparent and astrometric positions. The astrometric positions are with respect to the mean equator and equinox of J2000.0 and are in the FK5 coordinate system. The apparent positions are referred to the true equinox and equator of the date - i.e. they allow for nutation and include the current inclination of the Earth's equator and are referred to the current position of the 'first point of aries'.

As the US Naval Observatory says

"This page enables you to obtain many kinds of astronomical data, including celestial coordinates, sidereal time, lunar and planetary configurations and aspects, and rise/set times. Specify the type of calculation you want below, click on the "Continue. " button, and fill in the form that will appear. The computations are performed by MICA, the Multiyear Interactive Computer Almanac. The basis of the calculations is the same as for the Astronomical Almanac."

You can get full Astronomical Almanac accuracy on a variety of data using a simple Web interface.

"The program PLANEPH is an executable DOS program for PC which computes the most usual ephemeris of planets between 1900 and 2100. It has to be regarded as an example for the use of the planetary series built by frequency analysis (Chapront, 1995). The representations of the planetary motions are based on numerical integration DE403 provided by Jet Propulsion Laboratory" -- from the 'readme' file

• Executable program : planeph.exe.
• Planetary tables : planeph.tab.
• Locations coordinates : planeph.loc.
• Manual for the program : planeph.doc.

You can export data from the program in decimal format in hours/degrees or radians, or heliocentric x, y, z coordinates. The coefficients of the series used to compute the longitudes of the planets are available in compressed format from the same page. The file series96.doc contains some information about the series, with references to appropriate journals. The Bureau des Longitudes does it again!

There is a wide choice of coordinate frame and kind of position (true, apparent, astrometric, topocentric and so on) available from a slightly confusing menu system.

This is version 2.2 of a Windows 95 program which provides customisable ephemeris plots for the positions of planets, the Sun and the Moon. The output is available as an Excel version 4 or 5 spreadsheet, or as a TAB separated text file. There is considerable control over format, including the insertion of 'special characters' for degrees and minutes and seconds. Numerical format can be decimal, so you can use your spreadsheets for further calculations.

Manfred has supplied some details of the theory used in the program. You can use the built in Lunar and planetary theories, based on Brown and Newcomb as detailed in the book Astronomie mit dem Personal Computer by Montenbruck and Pfleger, published by Springer Verlag. You can also download a pair of extra DLLs which implement the VSOP87 planetary theory and the ELP2000 lunar theory to full accuracy (not as truncated in the book by Meeus).

I compared a Lunar ephemeris produced by the program with the NASA TYPE geocentric Lunar ephemeris, and they agree to the last digit (0.1 of an arc second) at dates throughout the twelve year period of the TYPE.

Herr Dings has provided some information on how to call the VSOP87 and ELP2000 DLLs from your own code, should you need this kind of accuracy in your own applications.

If you have a Windows 3.1 computer, then the German language program Orion 3.2 uses the same Brown and Newcombe thories as Ephtool 3.2, and can save data as CSV files. The program will run from a floppy disc and does not need to be installed.

"MoonCalc provides information relating to the position, age, phase, orientation and visibility of the moon for any given date, time and location on earth. It also provides the time and direction of moonrise and moonset, date/time of astronomical new moon (conjunction) and full moon and predicts the likelihood of visualising the new moon from a particular location." - From Dr Ahmed's manual for the program.

If you want to know the current phase and orientation of the Moon, then this program can provide the information for any location on the Earth. The program runs under DOS - and needs about 500K of disc space - it will run from a floppy. Mooncalc is freeware. An especially nice feature is the screen which prints an image of the visible aspect of the Moon with crater positions marked on the illuminated part of the disc.

Dr Ahmed cites Duffett-Smith and Jean Meeus as sources for the algorithms used for the Moon's position. The latest release is Version 4.0 (9th June 1997), which I am now evaluating after extensive use of version 0.3 (beta).

If you prefer looking at a table on a Web page to running software, then the TYPE provides a listing of the positions of the Sun, Moon and the planets for the twelve years from 1995 to 2006 inclusive. The positions of each object are calculated at 0h TDT each day for the Sun and the Moon, and every two days for the planets. The TYPE provides geocentric positions of the planets corrected for light travel time, nutation of the Earth's axis and stellar aberration. The positions are thus referred to a true equator rather than a mean one - and may not be compared with star positions in catalogues and star charts.

This CGI program accepts the longitude, latitiude and date and produces a page containing information on the rising and setting times and azimuths of the Sun and Moon.

Ascript is commercial software sold as a book package. The program runs under DOS and comes on a single floppy disc. The bibliographic details are

Easy PC Astronomy
by Peter Duffett-Smith
Cambridge University Press
ISBN 0-521-56052-7
Cost about 22 Pounds Sterling.

Astro script is unusual in that you can write your own scripts - the software provides a series of built in functions and calculation templates which you can assemble in various sequences. There is limited control over output and input, and a very basic loop structure allows you to repeat calculations and search for phenomena such as occultations and eclipses.

If any budding programmer is reading this page, IMHO the world does not need another star chart program - how about an interpreter for an astronomical programming language with full support for loops, functions and procedures?

Paul has provided the C code for a program which works out the times of sunrise and sunset and the various twilights. Paul has recently posted a summary and simplification of a 'low precision' method for finding the positions of the Sun, Moon and planets to the news group sci.astro.amateur , and is planning to put the details on a Web page soon. Paul has chosen the terms in the perturbation series to give an accuracy of better than 1 arcminute.

The method is based on the article by van Flandern & Pulkkinen called "Low precision series for planetary positions", published by Astrophysical Journal Supplement in 1979.

## C# Accurate Earth, Moon Sun visual model to predict eclipses

I am trying to make a VISUAL model (in C#) to predict lunar and earth eclipse periods for a satellite that I have accurate ephemeris for.

I want to calculate everything in ECEF reference frame.

How would a go about modeling this system to the accuracy I'm interested in?

I assume I need the following:

1) A reference epoch that coincides with a particular position of moon and position/orientation of earth.
- how would I arrive at this?

2) A time scale, I assume I can use Terrestrial Time, please correct me if I'm wrong.

3) an ephemeris model.
- I would like to be able to update celestial object positions according to a time-slider and/or stop/start button which proceeds at a specified pace. Would calculating my own ephemeris be necessary, or can I use the JPL Horizons data?

4) An earth rotation model. This one is mainly so that I can report coordinates accurately in ECEF, which is the reference frame that I'm interested in.

I'm thoroughly bewildered after looking through SOFA documentation. After about an hour of reading I guess I got that I can just use a Terrestrial Time scale, but I'm not real sure how I would use SOFA (certainly I have more to read) to implement my objectives. I've also heard of CSPICE, used by NASA, but haven't looked into it yet because I saw that the toolkit was offered in C, and I don't know if I can use that for a C# program, as I'm not sure how that works.

I'm basically just getting started, but any guidance or tutorials or hints/shortcuts that anyone can provide to me will be very much appreciated, and save me a lot of lurking around in the dark until I realize what it is that I need.

## Demostration program for iOS (IPhone)

Deep Pradhan is also working in a iOS version of his Android app. The most recent and updated code is available from this GitHub repository, where the main code follows the Swift code conventions and a little test program is also provided. This is the recommended source, although here you can still download his first Swift v4 code of the Sun/Moon calculator, in which he preserved the code to be as closely as possible to the Java version.

I'm very grateful to him for providing a code that will be very useful also for the community of iOS developers, and for contributing so much to make this post really successful and interesting for all developers. I would love to port my own Android planetarium ClearSky to iOS, but I think is too much hard work.

## Delta T (ΔT)

The orbital positions of the Sun and Moon required by eclipse predictions, are calculated using Terrestrial Dynamical Time (TD) because it is a uniform time scale. However, world time zones and daily life are based on Universal Time[1] (UT). In order to convert eclipse predictions from TD to UT, the difference between these two time scales must be known. The parameter delta-T (ΔT) is the arithmetic difference, in seconds, between the two as:

Past values of ΔT can be deduced from the historical records. In particular, hundreds of eclipse observations (both solar and lunar) were recorded in early European, Middle Eastern and Chinese annals, manuscripts, and canons. In spite of their relatively low precision, these data represent the only evidence for the value of ΔT prior to 1600 CE. In the centuries following the introduction of the telescope (circa 1609 CE), thousands of high quality observations have been made of lunar occultations of stars. The number and accuracy of these timings increase from the seventeenth through the twentieth century, affording valuable data in the determination of ΔT. A detailed analysis of these measurements fitted with cubic splines for ΔT from -500 to +1950 is presented in Table 1 and includes the standard error for each value (Morrison and Stephenson, 2004).

[1] World time zones are actually based on Coordinated Universal Time (UTC). It is an atomic time synchronized and adjusted to stay within 0.9 seconds of astronomically determined Universal Time (UT). Occasionally, a "leap second" is added to UTC to keep it in sync with UT (which changes due to variations in Earth's rotation rate).

## Solar Eclipse Predictions with VSOP87 and ELP2000/82

The coordinates of the Sun used in these eclipse predictions have been calculated on the basis of the VSOP87 theory constructed by P. Bretagnon and G. Francou [1988] at the Bureau des Longitudes, Paris. This theory gives the ecliptic longitude and latitude of the planets, and their radius vector, as sums of periodic terms. In these calculations, we use the complete set of periodic terms of version D of VSOP87 (this version provides the positions referred to the mean equinox of the date).

For the Moon, use has been made of the theory ELP-2000/82 of M. Chapront-Touze and J. Chapront [1983], again of the Bureau des Longitudes. This theory contains a total of 37862 periodic terms, namely 20560 for the Moon's longitude, 7684 for the latitude, and 9618 for the distance to Earth. But many of these terms are very small: some have an amplitude of only 0.00001 arcsecond for the longitude or the latitude, and of 2 centimeters for the distance. In our computer program, we neglected all periodic terms with coefficients smaller than 0.0005 arcsecond in longitude and latitude, and smaller than 1 meter in distance. Due to neglecting the very small periodic terms, the Moon's positions calculated in our program have a mean error (as compared to the full ELP theory) of about 0.0006 second of time in right ascension, and about 0.006 arcsecond in declination. The corresponding error in the calculated times of the phases of a solar eclipse is of the order of 1/40 second, which is much smaller than the uncertainties in predicted values of ΔT, and also much smaller than the error due to neglecting the irregularities (mountains and valleys) in the lunar limb profile.

The center of figure of the Moon does not coincide exactly with its center of mass. To compensate for this property in their eclipse predictions, many of the national institutes employ an empirical correction to the center of mass position of the Moon. This correction is typically +0.50" in longitude and -0.25" in latitude. Unfortunately, the large variation in lunar libration from one eclipse to the next minimizes the effectiveness of the empirical correction. We choose to ignore this convention and have performed all calculations using the Moon's center of mass position. In any case, it has no practical impact on the present work.

The revised value used for the Moon's secular acceleration (n-dot) is -26 arc-sec/cy*cy, as deduced by Morrison and Ward [1975] from 250 years of Mercury transit observations. The value for delta-T (delta-T = DT - UT) is based on the work of Morrison and Stephenson [2004]

The predictions use a smaller value for the Moon's radius k (=0.272281) than the one adopted by the 1982 IAU General Assembly (k=0.2725076). The smaller k is a better approximation of the Moon's minimum diameter and results in a slightly shorter total or longer annular eclipse when compared with calculations using the IAU value. No correction has been made between the Moon's center of mass and center of figure. The difference is small and of consequence only where careful timings are needed or for observations near the northern or southern path limits. In such cases, a more detailed predictions are required which include the effects of the Moon's limb profile.

The Besselian elements computed for solar eclipses using the VSOP87 and ELP2000/82 ephemerides were originally prepared for the Five Millennium Canon of Solar Eclipses: -1999 to +3000 (2000 BCE to 3000 CE).

### References

Bretagnon, P. and Francou, G., "Planetary Solutions VSOP87", Astronomy and Astrophysics, vol. 202, 309B, 1988.

Chapront-Touze, M. and Chapront, J., "The lunar ephemeris ELP 2000", Astronomy and Astrophysics, vol. 190, no. 1-2, Jan. 1988, p. 342-352.

Chapront-Touze, M. and Chapront, J., "ELP 2000-85 - A semi-analytical lunar ephemeris adequate for historical times", Astronomy and Astrophysics, vol. 190, no. 1-2, Jan. 1988, p. 342-352.

Espenak, F., and J. Meeus., Five Millennium Canon of Solar Eclipses: &ndash1999 to +3000 (2000 BCE to 3000 CE), NASA TP&ndash2006-214141, NASA Goddard Space Flight Center, Greenbelt, Maryland, 648 pp, 2006.

Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, Her Majesty's Nautical Almanac Office, London, 1974.

Meeus, J., Elements of Solar Eclipses: 1951 - 2200, Willmann-Bell, Inc., Richmond, 1989.

Morrison, L. and Stephenson, F. R., "Historical Values of the Earth's Clock Error ΔT and the Calculation of Eclipses", J. Hist. Astron., Vol. 35 Part 3, August 2004, No. 120, pp 327-336 (2004).

Morrison, L.V. and Ward, C. G., "An analysis of the transits of Mercury: 1677-1973", Mon. Not. Roy. Astron. Soc., 173, 183-206, 1975.

Newcomb, S. "Tables of the Motion of the Earth on its Axis Around the Sun",Astron. Papers Amer. Eph., Vol. 6, Part I, 1895.

## Ephemeris

Deep-Sky Planner 8 provides ephemeris calculations (meaning position, magnitude, size, etc.) and 2 styles of ephemeris reporting for the major planets, sun and moon. The detailed ephemeris style is useful for viewing information for an object at a specific time, including physical ephemeris data for sun, moon, Mars, Jupiter and Saturn. The brief ephemeris style is useful for reporting changes to an object over time, such as motion, magnitude or size.

You can calculate an ephemeris for an interval that you define over any range of date and time, but ephemeris calculations lose accuracy in the distant past or future. Motion of each object over time is also calculated and reported.

Similarly, you can calculate and report the date and time of planetary phenomena (events) over a range of date and time. These phenomena include solar and lunar eclipses, lunar phases, greatest elongations (inferior planets), conjunctions/oppositions, aphelions/perihelions, equinoxes/solstices (sun).

• compute altitude and azimuth of objects at specified date & time your GO TO telescope to the object (or sync the telescope position with the object) using Argo Navis, Nexus DSC or Sky Commander
• show a star chart centered on the object using TheSky , Redshift , Starry Night, Stellarium or Cartes du Ciel (see version compatibility)
• view a Digitized Sky Survey (DSS) image centered on the reported object
• view a graph of any reported object's altitude over time on the specified date
• view a graph of any reported object's altitude at a time of day over a specified year
• add observations to your log for any reported object
• view logged observations of any reported object
• print or save reports as PDF, formatted text or HTML

Your browser does not support the video tag.
Video snip: Detailed Planet Ephemeris report for Mars on 6 November 2020

### Events

Deep-Sky Planner 8 computes the date and time of various events involving sun, moon and planets. You can compute:

• Greatest Elongation of Mercury & Venus
• Conjunctions & Oppositions of planets
• Aphelion & Perihelion of planets
• Equinoxes & Solstices of the sun
• Lunar and Solar eclipses
• Phases of the Moon

These reports can be exported to several file formats including HTML, delimited text (.csv) and iCalendar (.ics). iCalendar files can be imported into most common calendar programs/ services like Apple Calendar, Google Calendar or Microsoft Outlook.

### Astronomical Darkness Analysis

You can calculate and report the times of astronomical darkness (meaning that the sun is at least 18° below the horizon and the moon is down) over a range of dates. Times of sun rise/set, moon rise/set and moon phase are included. Darkness reports may be presented in either tabular text or graphically. You can also print or save reports as formatted text, HTML or delimited text (CSV.)

 -- Click to enlarge -- Darkness report for November 2020 Graphical darkness report for November 2020

Many astronomical software products incorrectly report that the moon rises or sets on dates when in fact it does not. Deep-Sky Planner accurately reports no moon rise or set for these dates.

### Observe Comets and Asteroids

#### Orbital Elements Manager

Up-to-date orbital elements are required to compute an accurate ephemeris for comets and asteroids but getting correct orbital elements is often tedious or confusing. Deep-Sky Planner addresses this with an innovative data management feature that acquires and maintains orbital elements so that your ephemeris is accurate. You can download updated orbital elements from several sources, and you can do so for groups of objects or enter elements manually for any object, including newly discovered ones. You can also determine when you last updated an object's elements. Read more in a Deep-Sky Planner White Paper.

Click to enlarge

Orbital Elements Manager

#### Reports

Deep-Sky Planner provides 2 ephemeris reporting capabilities for comets and asteroids: ephemeris calculations for selected objects over time, or searching for objects that meet your observing criteria for a specified date and time. The reported data include position, predicted magnitude, solar elongation, phase, rise/set/transit and best time to view.

## Eclipses and Astronomy in Islam

Weather it is to predict the future or looking for the signs of God, studying the skies has always been of particular interest to humans. Seven hundred years after Ptolemy’s Almagest, scholars from the Islamic Golden Age (8th century to the 13th century) delved in to exploring the wonders of the universe with a passion that humanity had forgotten or reduced it to superstition.

### Prophet Muhammad's (s) Eclipse

Prophet Muhammad (s), was born in Mecca in the Year of the Elephant, CE 569-570. His birth year got its name from an invasion by the Abyssinians, who used elephants in the assault. According to some records it is also reported that a solar eclipse occurred during the Year of the Elephant.

In ancient times, births and deaths of leaders were correlated to celestial omens. However, Islamic theology does not accept that the eclipse was sent by God as an omen of the prophet’s birth, a doctrine that is based on another solar eclipse closely tied to Prophet Muhammad when his infant son Ibrahim died sadly on January 22, 632 CE.

Al-Mughira bin Shu'ba a companion of the Prophet narrates: On the day of Ibrahim's death, the sun eclipsed and the people said that the eclipse was due to the death of Ibrahim (the son of the Prophet).

Allah's Apostle said, "The sun and the moon are two signs amongst the signs of Allah. They do not eclipse because of someone's death or life. So when you see them, invoke Allah and pray till the eclipse is clear."

### Astronomy in the Quran

Muslims recognize that everything in the heavens and on earth is created and sustained by the Lord of the universe, God Almighty. Throughout the Qur'an, people are encouraged to observe and reflect on the beauties and wonders of the natural world - as signs of God's majesty.

"Allah is He, who created the sun, the moon, and the stars -- (all) governed by laws under His commandment." Quran 7:54

"It is He who created the night and the day and the sun and the moon. All (the celestial bodies) swim along, each in its orbit." Quran 21:33

"The sun and the moon follow courses exactly computed." Quran 55:05

### Muslim Scholars on eclipses

Muslim scholars of the past have recorded in detail several eclipses of the Moon and the Sun, in different parts of the Muslim world. These observations are among the most accurate and reliable data from the pre-telescopic period.

Abu al-Rayhan al-Biruni (d. 1048), the famous scientist who excelled in mathematical and applied astronomy, made various observations of eclipses. In his book Kitab Tahdid nihayat al-amakin li-tashih masafat al-masakin (The Determination of the Coordinates of Positions for the Correction of Distances between Cities) he notes:

"The faculty of sight cannot resist it [the Sun's rays], which can inflict a painful injury. If one continues to look at it, one's sight becomes dazzled and dimmed, so it is preferable to look at its image in water and avoid a direct look at it, because the intensity of its rays is thereby reduced… Indeed such observations of solar eclipses in my youth have weakened my eyesight."

In Afghanistan, he observed and described the solar eclipse on April 8, 1019, and the lunar eclipse on September 17, 1019, in detail, and gave the exact latitudes of the stars during the lunar eclipse.

On the solar eclipse which he observed at Lamghan, a valley surrounded by mountains between the towns of Qandahar and Kabul, he wrote:

"At sunrise we saw that approximately one-third of the sun was eclipsed and that the eclipse was waning."

He observed the lunar eclipse at Ghazna and gave precise details of the exact altitude of various well-known stars at the moment of first contact.

Another account of the total solar eclipse of 20 June 1061 CE was recorded by the Baghdad historian Abu-al-Faraj Ibn Al-Jawzi (508-597 H), who wrote approximately a century after the event, in his Al-Muntadham fi tarikh al-muluk wa-'l-umam (in 10 volumes):

"(453 H.) On Wednesday, when two nights remained to the completion of (the month of) Jumada al-Ula, two hours after daybreak, the Sun was eclipsed totally. There was darkness and the birds fell whilst flying. The astrologers claimed that one-sixth of the Sun should have remained [uneclipsed] but nothing of it did so. The Sun reappeared after four hours and a fraction. The eclipse was not in the whole of the Sun in places other than Baghdad and its provinces."

In Western astronomy, most of the accepted star names are Arabic and can be traced back to the star catalog of the astronomer al-Sufi, known in medieval Europe as Azophi. His full name was Abu 'l-Hussain 'Abd al-Rahman ibn Omar al-Sufi, and he is recognized today as one of the most important scientists of his age.

Studying the cosmos is ingrained in the Quran which propelled the early Muslim scientists to chart the horizons and lay the foundations of modern astronomy.

The study of astronomy in Islamic countries is by no means over. In 2016 scientists in Qatar at the Qatar Exoplanet Survey announced their discovery of three new exoplanets orbiting around other stars.

## How accurate should sunmoon ephemeris be for calculating eclipses? - Astronomy

This site contains low precision formulas, algorithms and some code for calculating the equatorial, ecliptic and horizon coordinates and the rise, transit and set times of the Sun, Moon and the planets. You will also find some information on plotting star charts, horizon charts and planispheres all based on the polar and equatorial stereographic projection.

Disclaimer: The methods in this Web site are low precision and are not suitable for celestial navigation, occultation prediction, eclipse prediction or similar circumstances where high accuracy is needed. Thanks to people who have pointed out errors - some are bound to remain so check results against known sources before trusting the methods here.

Latest Addition | VBA module that defines 'user functions' for finding the sunrise/set and times of the three twilights for any latitude. - Added 2nd Jan 2003