# High Precision Ephemerides

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## Overview

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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.

## A few orbit theory links

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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's page: How to compute planetary positions

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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.

## Interactive Computer Ephemeris

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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'.

## Web Multiyear Interactive Computer Ephemeris

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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.

## Planeph 4.1

by G. Francou, J. Chapront

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"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.

## Ephemeris Tool 2.2

by Manfred Dings

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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 4.0

by Dr. Monzur Ahmed

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"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).

## NASA Twelve Year Planetary Ephemeris

provided by Fred Espenak and his team

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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.

## US Naval Observatory Sun and Moon rise calculator

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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.

## Astro Script

by Peter Duffett-Smith

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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

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?

## C source for sunrise calculator

by Paul Schlyter, pausch@saaf.se

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http://www.snippets.org/SUNRISET.C (programs)

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.

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