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This post in reply to [NavList 11184]

Dear Peter,

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DETAILED HISTORY OF ALMANACS

You a raising a very interesting point and the reply is quite complex.

Probably a good first go to get accurate answers would be taking a close look at both :

- The "Explanatory supplement to the Astronomical Ephemeris" from the UK/US Natical Almanac Offices. I hold 2 versions - one is the fourth edition dated 1977 - and the other version is more recent dated 1992 and is labelled as "Completely revised and rewritten", and

- The "Introduction aux Eph�m�rides Astronomiques" published in 1997 by from Bureau des Longitudes, and

- There are also interesting data found on the Web, such as on the Paris Observatory Server which also give interesting data.

All these sources of information are "gold mines" to whoever whishes to get a good starting viewpoint on "detailed history of almanacs".

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FITS TO THE JPL NUMERICAL INTEGRATIONS

You also wrote "I remember someone mentioning that the "Paris predictions" (same as VSOP82, 87?) were constructed as analytic fits to the results of numerical integration of equations of motion done at the JPL for the solar system. Is this correct? "

I did mention this point.

Just an example of a specific reference here. In "Astronomy and Astrophysics" 114, 278-288 (1982) "Th�orie de l'ensemble des plan�tes. Solution VSOP82*" Pierre Bretagnon indicates that "The integration constants are determined by adjustment to the numerical integration DE200" (first page, left column which is the Summary in English).

As a general Practice, many modern analyticla theories have used the JPL DE20x/DE40x data as Integration constants.

Why so ?

In addition to better planetary masses, and better "mathematical models", one of the main back-bones in Planetary Ephemerides is integration constants. In other words, you need to fit any new theory to past observations, which should be as accurate and as remote as possible (both criteria most often being quite contradictory ...).

When starting the then new DE20* theories, the JPL Astronomers were well aware that the weak point of most previous numerical integrations were the quality of their integration constants (i.e. the way ancient observations had been reduced into usable data). As an example, the Jupiter Coordinates based on a then recent numerical integration and published in the Astronomical Almanach just BEFORE 1984 were certainly not better than the Jupiter Coordinates computed then in Connaissance des Temps which came from the Le Verrier Gaillot Theory (1913).

Accordingly the JPL Astronomers performed an extraordinary very high quality reduction of all available historical planetary position. They were also the first ones to include radar ranging data. All this enabled them to produce extremely accurate results.

Rather than duplicating their huge work in terms of planetary positions reduction, it was agreed that the Paris Astronomers would use such results as intergration constants.

What we need to see here is that both theories - JPL numerical integrations and the French Analytical Theories - are complementary. Some data - such as mean elements - can be easily obtained from Analytical Theories while they are more difficult to evidence in Numerical Integrations. On the other hand, it has been customary to consider than in terms of accuracy a leading edge should be put to the credit of the JPL Numerical integrations. This leading edge is to be credited for contemporary results (say +/- 100-150 years around 2000.0). Outside this time frame, and given the uncertainty of our data coming from these periods, both theories are exactly the same in terms of meaningful/realistic accuracies.

This story is a wonderful example of how competition can produce huge benefits for all. Accuracies in Ephemeris has improved about 100 fold in the past 30 years certainly due to intense resarch on both sides.

And the race is not over ... JPL people keep improving their Numerical Integrations while Bureau des Longitudes/IMCCE are also improving their Analytical Theories.

A few examples ?

The new planetary theories VSOP 2000 and followers have virtually reached the exact same accuracy level as the best current JPL theories (DE405/406).

Lately a new Numerical Integration INPOP86 has been produced by IMCCE/Bureau des Longitudes/Observatoire de Paris. It no longer exclusively relies on JPL data. You will find very interesting details here http://syrte.obspm.fr/journees2007/ppt/Laskar.pdf

Let us wait ... and we will see new wonders !

Last point : a very interesting one. More and more JPL publications make a specific refrence to the BDL theories. Very good point which acknowledges that research and results are more and more a Community Work, which obviously does not stop a sometimes quite strong competition.

Best Regards

Antoine

Antoine M. Cou�tte