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    Re: Computer space required to get 1" accuracy
    From: Antoine Couëtte
    Date: 2010 Apr 8, 01:48 -0700

    Dear Frank, and Dear Peter

    After a long and busy night and before I can get some rest ... I have had many hours to think over our Friendly Challenge and Exercise while watching our Magnificent and Superb Night Skies.

    Did you see for example how delta2 of the Scorpion (I just "think" it is delta2 but I am not sure) is so bright now ??? Second to none now, but only to Antares, ... amazing!

    *******

    Yes, Frank, we fully have the choice for any form of the data we are to put in our daily array, with linear interpolation to be used for the times between tabular values.

    Accordingly Ecliptic (R,L,B) coordinates are fully "legal" for this exercise, as they might be preferable to (X,Y,Z) if they enable us deriving shorter daily data.

    It looks like there are at least 2 different initial choices for our exercise : should we use geocentric data or heliocentric ones ? There is a trade-off to be studied here.

    For a number of reasons (no time to fully explain them in great detail now) I would think that we should probably use the "most smoothly changing coordinates" because we are to LINEARLY interpolate (probably a quite significant constraint in our exercise) to the accuracy of 1".

    As a result, for all Planets, we should probably use Heliocentric Elements and Geocentric Elements for the Moon.

    On top of that, this should be the best way to tackle the sometimes very "acute" geocentric apparent orbit of Mars when at/or close from Opposition or the "fast" changing coordinates of Venus when at closest from the Earth. In counterpart we will need better accuracy criteria - translating into just some additionnal significant digit(s) - on the heliocentric elements of Mars, Earth and Venus since any heliocentric position error for any of these planets is subject to be amplified in a very significant manner (up to almost 4 times for Venus) when seen from the Earth.

    BTW, with a 1" accuracy I mean "Published True Value minus Published Computed Value obtained from 'our' array" not to exceed one arcsecond anytime. Does this make sufficient sense ?


    And concerning the Moon, if we go with Geocentric Coordinates (seems a reasonable starting option), we would (just?) need to determine the maximum time interval/duration during which Linear Interpolation generates no errror exceeding one arc-second. I will have to dig this from the books ...


    At the end of the day, probably the best and most reliable answer would be to try various methods (geocentric vs. heliocentric coordinates as an example), to fully validate some points in our upcoming conclusions, but our current exercise still remains a quite interesting drill. An alternate "overkill" solution is : let's tabulate the geocentric coordinates of all bodies with 15 significant figures for every single minute and perform linear interpolation from that point on ... But I am not convinced that you might agree here !!! :-)


    Frank, if you have some additional early comments, please let me know them, just in case you might prevent me from taking a too long cut instead of a short one. I would not like to re-invent the wheel here since I actually have NO personnal experience in using arrays.

    Any Help/Contribution from anybody most warmly encouraged !!!

    Best Regards


    Kermit

    NOTE 1 : If you also allow me Frank, I would like to also perform the very same exercise for CelNav Accuracy, i.e. 6" second accuracy obtained through daily arrays, simply because I have an independent bench here.

    NOTE 2 : If we want to minimize DATA SIZE, a VERY PERFORMING OPTION for the Navigation Planets is just to use their (R,L,B) elements developped under Chebisheiev series ... which by ALL MEANS are EXTREMELY CONDENSED.

    See for example the yearly values published in Connaissance des Temps : just a few kb at the most ... for one full year here. I still need to check whether they can guarantee a 1" accuracy.

    Enjoy !!!


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