Path:news.helsinki.fi!news.funet.fi!newsfeed.sunet.se!news00.sunet.se!sunic!news.spri ntlink.net!newsfeed.internetmci.com!newsrelay.netins.net!news.netins.net!wmcclain From: wmcclain@worf.netins.net (Bill McClain) Newsgroups: sci.astro.amateur Subject: (FAQ) Astronomical Calculations for the Amateur Date: Tue, 02 Jan 1996 16:16:30 -0600 Organization: INS Info Services, Des Moines, Iowa, USA Lines: 332 Message-ID: <4ccaso$rpb@insosf1.netins.net> NNTP-Posting-Host: worf.netins.net X-Newsreader: MacSOUP 1.0d5 FAQ - Astronomical Calculations for the Amateur =============================================== Revised January 2, 1996. [This FAQ is limited to questions about calculating planetary positions and related problems of spherical astronomy. Other areas of interest, such a calculations of telescope optics, are beyond the bounds of this document]. Calculation of astronomical events is a vast field with literature stretching back centuries, even to ancient times. This "frequently asked questions" list is directed toward the amateur astronomer who is looking for starting points. If you become familiar with the first two books recommended below, you will be well on your way. You will, in fact, have surpassed the author of the FAQ! Of course, I invite your suggestions. ====================================================================== 1. What is a good source of books and software? 2. What is the best beginner's book? 3. How much computer power does it take to perform these calculations? 4. What is a more advanced reference work? 5. Are there any relevant periodicals for amateurs? 6. Where are online sources of algorithms? 7. Where are online sources of data? 8. What commercial and shareware programs are available? 9a. How do I convert right ascension and declination to altitude and azimuth? 9b. What's the hour angle? 9c. What's the sidereal time? 10. How do I predict the ocean tides? 11. How do I calculate the date of Easter? ====================================================================== 1. What is a good source of books and software? The Willmann-Bell catalog has a large section on "Computational "Astronomy", as well as many other astronomy books, atlases and telescope-making supplies: Willmann-Bell Inc PO Box 35025 Richmond VA 23235 Monday-Friday, 9AM-5PM Eastern time Orders: 800-825-STAR Info: 804-320-7016 24 hour fax: 804-272-5920 [After a delay of several months, I finally received catalog #20 in December]. If you have access to a good library, books under the subject headings "Spherical Astronomy" and "Celestial Mechanics" would be the places to start. 2. What is the best beginner's book? _Astronomical Algorithms_ by Jean Meeus, Willmann-Bell 1991, $24.95. Software supplements in Basic, Pascal and C are available to purchasers of the book for $24.95 each. Although it requires some study, this is the closest thing to a "cookbook" approach I have seen. Better than that, it explains and makes comprehensible many difficult concepts, and has many worked examples and illustrations. It is not restricted to elementary problems, but treats many advanced topics. No calculus is required. Beginners face two obstacles before they can calculate anything useful: (1) they must learn to convert between civil and astronomical dates and times (a task made more difficult by the fact that the Earth's rate of rotation is variable), and (2) they must learn a number of translations between coordinate systems (Sun-centered to Earth-centered to location-centered, as well as ecliptic to equatorial to horizon) and the application of corrections for precession and nutation and parallax. This is why questions such as "How do I predict the location of the moon?" do not have simple answers. You must know how to do (1) and (2) before you can start on the moon. The proper order of corrections and coordinate conversions had previously been very confusing for me, but Meeus gave me everything I needed to overcome these obstacles. He covers the basics of time and coordinate transformations, corrections for precession and nutation, and for the observer's true "topocentric" location as offset from the center of the Earth. For any given time, you can predict the positions of the Sun, Moon and planets and derive all the normal phenomena of the almanac. You can derive physical ephemerides (that is, the orientation of the objects as seen through a telescope) for the Sun, Moon, Jupiter, Mars and Saturn's rings. He provides both low-precision and high-precision techniques for charting Jupter's four largest moons. The Keplerian techniques of dealing with the orbits of new bodies such as comets and asteroids are also given. IMPORTANT NOTE #1: Ask for the errata sheet when you place your order from the publisher. There are typos in the text, and some errors in the software supplements. IMPORTANT NOTE #2: I *strongly* recommend that you get one of the software supplements. Not only is the source code very illuminating, but Meeus relies on some modern table-driven models which would be unfeasible to type in yourself. Pay the $24.95 and get a diskette. The software is for DOS machines, but I had no trouble translating the C-language version to Macintosh. (I did have to write a small DOS program to unpack the large data tables). 3. How much computer power does it take to perform these calculations? Modern personal computers, especially those with floating point hardware, are very capable machines. Calculating the position of all the planets several different ways, using Meeus' techniques, takes my 68040 a small fraction of a second. Performance on a PowerPC or Pentium would be stunning. 4. What is a more advanced reference work? _Explanatory Supplement to the Astronomical Almanac_, edited by P.K. Seidelmann, University Science Books 1992, 752 pages, $65 (available from Willmann-Bell). "Completely Revised and Rewritten", so make you sure you get the 1992 edition. This explains how the data in the annual "Astronomical Almanac" is produced. It is also a high-quality spherical astronomy text with many references to the current research literature. If you've read Meeus and want "more", this is the logical next step. Note that it contains very few worked examples and the math is much more advanced than in Meeus. Some of the chapters deal with issues of the professional astronomer that will not usually concern the amateur. Examples: plate tectonic motion can cause an observing site to shift its position several centimeters per year. Ocean tidal pressure on the continental shelves, and atmospheric pressure above the continents, can cause elevation to vary by similar amounts. Note also that they use a different method of calculating planetary positions than does Meeus. 5. Are there any relevant periodicals for amateurs? _Sky & Telescope_ magazine has an astronomical computing column. _Astronomy_ publishes programs from time to time. Willmann-Bell sells back issues of _Celestial Computing_, "A Journal for Personal Computers and Celestial Mechanics", dated from 1988 through 1992, edited by David Eagle. This seems to be no longer published. 6. Where are online sources of algorithms? _Sky & Telescope_ maintains an archive of program sources which have appeared in the magazine: http://www.skypub.com/software/software.html Unfortunately, these consist of uncommented BASIC listings. Pseudo-code articles would be of greater use to those trying to understand the calculations. _Astronomy_ magazine provides a small set of BASIC programs: http://www.kalmbach.com/astro/Bytes/Bytes.html Sites listed in the next topic also have software. 7. Where are online sources of data? There are astronomical amounts of data online. Try these web sites are starting points: Astronomical Data Center home page http://adc.gsfc.nasa.gov/ The WWW Virtual Library: Astronomy and Astrophysics http://www.w3.org/hypertext/DataSources/bySubject/astro/astro.html The Space FAQ http://www.cis.ohio-state.edu/hypertext/faq/usenet/space/top.html 8. What commercial and shareware programs are available? [Readers: I have not been paying attention to announcements of these programs in s.a.a. Anyone who has such or knows of same, please e-mail me the info and I will include descriptions here. The emphasis is not on "planetarium" or charting programs, but on ephemeris-generating software. Obviously, these categories overlap...]. * * * * * The freeware ephemeris program "ephem" (version 4.27, sic!) for PC by Elwood Charles Downey (and VGA `Watch' plots by J.D. McDonald) is available by anonymous ftp at ftp.funet.fi directory /pub/astro/pc/solar, filename ephem423.exe (self extracting archive.) The same site carries many other ephemeris programs also for other platforms. [Harald Lang Dec 3 1995] [There is a Web page for the Motif version at: http://iraf.noao.edu:80/~ecdowney/xephem.html Jan 2 1996] * * * * * I have recently completed a freeware program which might interest you. It's called the "Windows Ephemeris Tool" and it calculates tables of positions (and other data) for comets and asteroids. It's available at http://fox.nstn.ca/~ecu/ecu.html or ftp://hercules.stmarys.ca/pub/ecu/wetinst.exe Regards, Dave Lane Nova Astronomics [, Dec 7 1995] * * * * * Willmann-Bell sells several software supplemnts which have ephemeris capabilities. See their catalog ([1] above) for details. * * * * * 9a. How do I convert right ascension and declination to altitude and azimuth? Given the hour angle H of the object with right ascension RA and declination DEC, and the observer's latitude LAT: azimuth = atan2(sin(H), cos(H) * sin(LAT) - tan(DEC) * cos(LAT)) altitude = asin(sin(LAT) * sin(DEC) + cos(LAT)* cos(DEC) * cos(H)) where "atan2(x,y)" is C-library function equivalent to "atan(x/y)". 9b. What's the hour angle? Given an object with right ascension RA and the observer's longitude LONG, and the sidereal time at Greenwich ST: H = ST - LONG - RA where LONG is positive to the west and ST is represented as an angle. 9c. What's the sidereal time? Everything seems to depend on something else, doesn't it? Better get the Meeus book described in [2] above. 10. How do I predict the ocean tides? I have never heard of an amateur doing this. The _Explantory Supplement_ has a small section on the subject and the method seems quite complex. 11. How do I calculate the date of Easter? Many people know the formula: Easter is the first Sunday after the first full Moon following the vernal equinox. Caution! This is "astronomical Easter", and it is usually but not always the same day as "ecclesiastical Easter", which is the date used by the churches and printed on calendars. "Ecclesiastical Easter" is determined by a formula codified many years ago. Here is the method published in the _Explantory Supplement_. Perform integer math and drop all remainders. It is valid for any Gregorian year "Y": C = Y / 100 N = Y - 19 * (Y / 19) K = (C - 17) / 25 I = C - C / 4 - (C - K) / 3 + 19 * N + 15 I = I - 30 * (I / 30) I = I - (I / 28) * (1 - (I / 28) * (29 / (I + 1)) * ((21 - N) / 11)) J = Y + Y / 4 + I + 2 - C + C / 4 J = J - 7 * (J / 7) L = I - J M = 3 + (L + 40) / 44 D = L + 28 - 31 * (M / 4) "M" is the month number (3 -> March, 4 -> April) and "D" is the day of the month. There is a short BASIC program at http://www.skypub.com/software/software.html See also the very informative Royal Greenwich Observatory leaflet on Easter at: http://www.ast.cam.ac.uk/RGO/leaflets/easter/easter.html There is an HTML Ecclesiatical Calendar generator at: http://cssa.stanford.edu/~marcos/ec-cal.html Tidbits: the pattern of Gregorian Easter days, one year to the next, repeats in a cycle 5,700,000 years long. March 22 is the earliest date of Easter, April 25 is the latest, and April 19 is the most frequent. ====================================================================== [This document is archived at file://www.salamander.com/~wmcclain/astro_calc.txt]. Bill McClain or http://www.salamander.com/~wmcclain/