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    Re: LADEE Moon Probe Puzzle
    From: Robin Stuart
    Date: 2013 Sep 17, 16:17 -0700

    Greg,

    The short answer is that I effectively use the distances from 3 stars to get the position. The long answer follows:

    The end of the trail sits near the centre of a triangle formed by Fomalhaut, gamma Sculptoris (left) and delta Piscis Austrini (right). I assumed that this was a small enough area of sky that a linear relationship would be adequate to transform between the pixel (x, y) coordinates and the R.A. and Declination of the stars concerned. Specifically in matrix form

    [R.A.] = [ a b ] [x] + [e]
    [Dec.] [ c d ] [y] [f]

    With the measured positions of 3 stars there is enough information to solve for the 6 constants a-f which in turn allows the R.A. and Declination of the trail's end to determined from its measured position on the photograph. As a check one can use gamma Piscis Austrini that lies a bit beyond delta on the right.

    I found that Wikipedia has some excellent star maps along with detailed star lists for each constellation courtesy of Sky and Telescope. They give the positions in J2000.0 coordinates as well as other information such as the Hipparcos catalogue number. The J2000.0 coordinates are good enough for a position estimation but since we seem to be pushing the limits of precision in this thread, as noted in my previous post, the Apparent Positions for the Current equinox, incorporating the effects of precession, nutation and aberration, should be used. As an example, the J2000.0 position of Fomalhaut is 22h57m38.8s, -29d37.3' but its apparent position at 0h on 7 September was 22h58m26.2s, -29d32.8'. To do the conversion I found the website http://dc.zah.uni-heidelberg.de/apfs/res/apfs_new/hipquery/form where you can enter the stars Hipparcos number and a date to required positions.

    In the photograph I think that there are enough identifiable stars over a wide enough field to attempt a reasonable non-linear calibration,

    Regards,
    Robin Stuart
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