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    Re: Angular Distance Between Stars By Camera and Sextant
    From: Marcel Tschudin
    Date: 2012 Sep 18, 18:23 +0300
    Hi Brad,

    In case your recalibration requires the observed distance between two stars and that you would verify the accuracy with a noticeably higher accuracy than the 5 sec of arc then I would recommend you (at this moment and after the experiences made with Greg's star distance example) that such almanac data should be accurate to about 1/100th of moa. The USNO almanac data which show the local coordinates in 1/10th of moa appear not to be sufficient because the rounding error of each star may be +/-0.05 moa or 3 sec of arc. However, having said that, by using a lot of measurements you may hope that these rounding errors tend to cancel out. Note that the accuracy of the data does not only depend on the decimals of moa shown in an output, these decimals could actually be wrong. The accuracy of the local coordinates depend on the type of epoch data used (e.g. J2000) and their transformation to date, time and location of observation, i.e. on the program which performs this transformation in time and space. I have not investigated this before. I only notice now that between USNO's, Paul's and Andrés' calculation are differences of 0.3 and 0.4 moa, thus of about 20 seconds of arc which is too much for the purpose of spherical (or positional) astronomy. I hope this discussion leads to a conclusion on the data and program to be used.

    Regards
    Marcel

    P.S: Even though I contribute to NavList I am actually not so familiar with navigation. May be you can explain me off-list what a circle of reflection actually is.


    On Tue, Sep 18, 2012 at 3:39 PM, Brad Morris <bradley.r.morris@gmail.com> wrote:

    Hi Marcel

    Now that I need to recalibrate the arc of my circle of reflection, I want to be very sure I understand your recommendation.

    Firstly, the circle I possess has a published accuracy of 5 seconds of arc.  I wish to confirm to this level. 

    What source of data would be adequate?  Astronomical Almanac?  Nautical Almanac?  Other?

    Best Regards
    Brad Morris

    On Sep 18, 2012 5:03 AM, "Marcel Tschudin" <marcel.e.tschudin@gmail.com> wrote:
    In the mean time I had a look at possible reasons for the 0.3 moa difference between the calculated distance as resulting from Paul's calculation and the one resulting from the USNO data, noticing the following:

    (1) There are some Hc and Zn values which are rounded different to 1/10 of a moa. This means that there are somewhere differences of +/-0.05 moa or +/-3 sec of arc. For navigational purpose this is negligible, but for spherical astronomy calculations it is a lot. Where could this difference have its origin?

    (2) The refraction values provided in the USNO almanac are slightly larger than those Paul used. This seems to confirm that the refraction values in the USNO table relate to observed altitudes; those are the refractions to deduct from the sextant measurement to obtain the Hc value resulting from measurements. The refraction values in the USNO table can therefore not be used for calculating the observed star distance from the Hc values, they have to be calculated separately.

    (3) Calculating the distance D between the local coordinates of e.g. Alioth and Alkaid using Paul's el and az values to 1/10th of moa  results in D=627.6 moa. Using his el and az values to 1/100th of a moa results in D=627.2 moa. With the full accuracy program values Paul obtained D=627.3 moa.

    This example suggests that - independent of the accuracy in measured pixels - the calibration accuracy cannot noticeably be improved by using the distance of two star positions with the local coordinates calculated to 1/10th of a moa (difference in this example is 0.3 moa compared to +/-0.5 moa accuracy from HS observations). Improving the present calibration accuracy would require at least accurate J2000 star positions and a program for converting them to local coordinates to at least 1/100th of a moa (like Paul shows in his output).

    However, for those not fortunate to live close to the sea and looking for a mean to calibrate their camera to somewhere around +/- 0.5 moa, measuring star distances and comparing them with the USNO almanac data, corrected with Saemundsson's refraction, may be an option.

    Marcel

    P.S: Thank you, Paul, for the link.

    On Tue, Sep 18, 2012 at 6:49 AM, Paul Hirose <cfuhb-acdgw@earthlink.net> wrote:
    I'm surprised you could read the message. In the copy of my own message received by email, the link to the file gives a "page not found" error message.

    I did not try to download the attachment. Firefox shows the content of attached text files without downloading them.

       
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