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In reply to [NavList 11340]

Frank,

Thank you for your reply.

You wrote : "Also, the idea that the French BdL analytical theories are somehow different from the JPL integrations is really an illusion."

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As regards the fact that there exists almost NO APPRECIABLE difference between their outputs, I fully agree with your viewpoint : (almost) NO DIFFERENCE between JPL or BDL numerical results, on a COMMERCIAL standpoint.

I still wish to bring another viewpoint on this subject - not a commercial one just covered hereabove - but an important one though, simply because :

- Not only the fact that some data can be much more easily derived from one kind of theory (accurate mean elements for example are best derived from analytical theories), Precession and Nutation quantities of some precision to-day require analytical theories, but also most importantly

- when people attempt computing "pi" or "e" with megazillions decimals, they need using 2 different computers and computer langages and 2 different mathematical algorithms. The mere fact that there now exists TWO different super sophisticated ways of solving the same astronomical positional problems from the same starting point is extremely important for the very same reason as follows :

We have seen that all results yielded by either JPL or BDL theories are essentially the same (i.e. in "essence" since they rely on the same observational data and they are all derived also from the same "basic" equation : F = Mass * Acceleration ) and they are extremely close as regards their numerical values, which generally differ by extremely small amounts, quite often smaller than the accuracy of a number of integration observational data.

What makes both approaches - i.e. Numerical Integrations and Analytical Theories - interesting is that they use different mathematical approaches from the same starting point. In some way, the fact that their results "coincide" extremely well over very extended periods means that the possibility of numerical computation flaw in either Numerical Integrations or Analytical Theories is extremely extremely remote. The Community therefore has extremely good reasons here to think that these results are extremely reliable.

In other words, Numerical Integrations results without Analytical theories to validate their results would be certainly much less reliable, and

Analytical theories results without Numerical Integrations to validate their results would also certainly be less reliable, and

It also has been customary to consider that within close range of the "starting epoch" (+/- 1 or 2 centuries) the best accuracy is achieved with Numerical Integrations, while by essence Numerical Integrations do "numerically and mathematically degrade" for more remote periods, since any result for any epoch has to rely on a chain computation carried out from the starting epoch itself, and

outside this "close period", the accuracies of either methods are absolutely equivalent.

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You also wrote "By the way, are you familiar with Aldo Vitagliano's "Solex" software?
http://chemistry.unina.it/~alvitagl/solex/
The interface is a bit old-fashioned but the output is impressive."

Yeah ! Wahoo !! It certainly is quite amazing ! Thank you for mentioning it !

It just gave me the opportunity of checking that DE406 and VSOP87 agree extremely well on very long time spans (I just reran the example of the Venus Transit occuring at the same time as a Sun Eclipse on April 05, 15232).

Thank you again and

Best Regards

Antoine