Talk:American Ephemeris and Nautical Almanac

Where are the equations?
I'm a good friend of both the USN and HMS, but I'm puzzled why the ephemeris, almanac, and explanation are not fully public. Surely the seasonal antics of the moon are not copryrightable? The online version at the USNO site lacks all equations, which is what I was looking for. Dugong.is.good.tucker (talk) 12:44, 31 August 2008 (UTC)


 * The method of calculation varies depending on the year. Because you consulted the online version I presume you want the modern calculations, that is, those used to calculate the ephemerides in the Astronomical Almanac, not the American Ephemeris and Nautical Almanac. The fullest explanation of the modern method is in the Explanatory Supplement to the Astronomical Almanac, edited by P. Kenneth Seidelmann (Mill Valley, CA: University Science Books, 1992). Seidelmann was with the Nautical Almanac Office of the United States Naval Observatory. Analytical equations per se have not been used since 1983. Instead, an iterative solution from the Jet Propulsion Laboratory is used, where the 'present' positions of the planets/moons/asteroids/comets are measured by space probes, radar, and other modern methods, then their new position one time step (a fraction of a day for moons to a few days for the outer planets) in the future or past is calculated using Newton's universal theory of gravitation with some corrections due to Einstein's general theory of relativity. The new position is then used to calculate their positions one more time step into the future or past. Precalculated positions from −3000 to +3000 can be downloaded from the JPL Horizons system or via CD available from Willmann-Bell math and celestial mechanics books. However, if only moderate precision is needed, then analytical equations developed at the Bureau des Longitudes in Paris during the 1980s are usually used, albeit in a truncated form published by Jean Meeus in Astronomical Algorithms (Richmond, VA: Willmann-Bell, 1999). These have been placed online by Bill McClain as Astrolabe. Recently, much more accurate equations have been developed by Professor Vitagliano of the University of Naples. His SOLEX program has been used extensively by Dr. Irv Bromberg of the University of Toronto for calculating the lengths of the seasons over ±100,000 years and the lunar cycle over ±10,000 years. — Joe Kress (talk) 20:17, 31 August 2008 (UTC)

Thank you Joe, but why are those equations and constants not on the US and UK government sites?Dugong.is.good.tucker (talk) 00:30, 5 November 2008 (UTC)


 * The US and UK governments do not use analytical equations to develop the ephemerides in the Astronomical Almanac, so they have no need to mention any equations developed by others. Furthermore, their online sites do not include everything within their printed publications, only the most popular portions. They do mention that their planetary ephemerides come from the Jet Propulsion Laboratory in their list of Contributors, see JPL Solar System Dynamics. Although they mention the Explanatory Supplement to the Astronomical Almanac, which describes their methods, they do not include any portion of it on their site because they don't publish it—University Science Books, a private publisher, holds its copyright. The description of its orbital ephemerides is in Chapter 5 beginning on page 279 (limited online access). The VSOP equations (truncated by Jean Meeus) developed at the Observatoire de Paris are now used for the French almanac, the Connaissance des temps, which no doubt discusses them. — Joe Kress (talk) 04:01, 5 November 2008 (UTC)

Help me here please - the equations and constants governing the motion of the planets are clearly not copyright-able, they are descriptions of our local part of the cosmos. The authors of the almanac are either government employees or contractors who have sold their work to the government. In either case the results of their computations are owned by the government. The question now is: why is the government asking it's citizens to pay again for something they already own? Dugong.is.good.tucker (talk) 00:54, 6 November 2008 (UTC)


 * Why the government used a private publisher also mystified me. The government publishes thousands of books every year via the Government Printing Office, so why not one more? But most of those books are not free—they can only be obtained from the government for a fee (the Astronomical Almanac costs $40). So paying $80 for the Explanatory Supplement is not unusual (it's twice its size). The principle is that users of government services help to pay the expenses the government incurs on their behalf, limiting what the public at large must contribute through income taxes. A small portion of chapter 5 is copied verbatim from DE 102: A numerically integrated ephemeris of the moon and planets spanning forty-four centuries (the PDF version is 3.07 MB), including the basic equations and constants. Each subsequent version of these ephemerides uses slightly different 'constants'. — Joe Kress (talk) 05:40, 7 November 2008 (UTC)


 * I was worried we disagreed (being a peaceable person), but it appears we agree more than we disagree. I understand the GPO business, but if the document need not be printed, why should it cost anything?  It has been paid for.  There is is similar argument for budget and census data.Dugong.is.good.tucker (talk) 18:32, 8 November 2008 (UTC)


 * I neglected to mention IAU's SOFA (Standards of Fundamental Astronomy) which includes Fortran 77 routines to calculate the ephemerides of the Earth and planets. — Joe Kress (talk) 23:22, 21 November 2008 (UTC)