Welcome to the NavList Message Boards.


A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Add Images & Files
    Re: Celestial data for the planet Mercury
    From: Paul Hirose
    Date: 2016 Feb 24, 23:36 -0800

    On 2016-02-23 23:18, Herbert Prinz wrote:
    > Paul,
    > I agree that any significant discrepancy indicates an error. Now I am 
    curious: How do you arrive at 95 mas difference? I get a little over 101 mas. 
    What is it that one of the two of us is doing wrong (or differently from the 
    other) in a simple subtraction and multiplication?
    The coordinates posted by Dave Walden are:
    2016 Feb 01 11:00:00.0     19 14 15.421     - 20 38 03.89
    2016-Feb-01 11:00     19 14 15.4172 -20 38 03.896
    14 15.42394
    -20 38 3.8918
    The last two differ by 95 mas. To get that figure, the first step is to
    convert from spherical format (assume radius = 1) to rectangular.
    +.297 943 774  -.887 153 335  -.352 403 843  HORIZONS
    +.297 944 211  -.897 153 195  -.352 403 824  IMCCE
    The dot product of those vectors is 1.000 000 000. That's the cosine of
    the separation angle.
    The magnitude of the cross product of the vectors is 4.59e-7. That's the
    sine of the separation angle. In this case we simply take the arc sine
    and obtain 2.63e-5 degrees, or .0947 seconds.
    A more general solution is to treat the cosine and sine as x and y
    respectively, and do a rectangular to polar conversion. That yields a
    precise result whether the angle is tiny or large. In addition, the
    result is correct even if the vectors have different magnitudes.
    In practice, the computation was simpler than what I showed above. My HP
    49G calculator allows vector input in rectangular, spherical, or
    cylindrical format. Also, it has functions to compute dot and cross
    products without any explicit conversion to rectangular format. The
    hardest part is entering the digits without a mistake.
    Regarding the reason for the 95 mas discrepancy, in a private
    communication someone suggested the IMCCE may still be using the IAU
    1976 precession and 1980 nutation models. Let's test that with the DE430
    ephemeris, IAU 1976/80 precession and nutation, with and without frame
    bias. Geocentric apparent place at 2016 Feb 1 11:00:00 UTC:
    19 14 15.42394  -20 38 03.8918  IMCCE
    19 14 15.4244   -20 38 03.892   IAU 76/80 (with bias)
    19 14 15.4239   -20°38'03.893   IAU 76/80 (no bias)
    The first and second lines agree within 6 mas. The first and third are
    only 1 mas different. So my guess is that IMCCE does not apply the frame
    bias correction. That's wrong.
    Frame bias is the difference between the mean equator and equinox
    coordinate system at J2000.0 (= 2000 Jan 1 0 hours Terrestrial time) and
    the ICRS (International Celestial Reference System). When the latter was
    created, it was intended to be as close as practical to the former.
    We now know there's a small offset. It's negligible if you're only
    working to a tenth of an arc second. But at higher accuracy there's a
    disconnect. Modern star catalogs and solar system ephemerides are based
    on the ICRS. On the other hand, the IAU precession models transform
    coordinates from the J2000.0 system to the mean equator and equinox
    system of date. Thus in precise work you're supposed to get the ICRS
    coordinates of the body (including effects such as aberration and light
    time), apply frame bias to obtain its J2000.0 coordinates, then apply
    precession, then nutation.
    It's ironic that the IMCCE coordinates have the most decimal places, but
    throw away much of their precision due to an oversight. When precise
    computations of a body's position differ by nearly a tenth of an arc
    second, it usually indicates a mistake somewhere. With reasonably modern
    tools and data you shouldn't be that far off.

    Browse Files

    Drop Files


    What is NavList?

    Join NavList

    (please, no nicknames or handles)
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.

    Email Settings

    Posting Code:

    Custom Index

    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site