2000 SG344: asteroid or Saturn rocket?

From: Matson, Robert (ROBERT.D.MATSON@saic.com)
Date: Mon Nov 13 2000 - 20:23:44 PST

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    Hi All,
    Ralph McConahy provided me a table of astrometric information for
    NEO (asteroid) 2000 SG344 so that I could determine if a Saturn IV-B
    rocket body could be excluded as a possible candidate for this
    unusual object.
    From the table, the coordinates on 2000-Nov-9 00:00 were
    RA 171.94066, Dec 2.74031, Range .098678 A.U., ApMag 24.25.
    The solar location at this date/time was roughly RA 14.9616h,
    Dec -16.883d.  This is 55.38 degrees away from the asteroid
    as viewed from earth.  The equation to be solved is:
    Mag = StdMag - 15 + 2.5*LOG10(Range^2/PhaseFactor)
    where Range is in km (14,762,019 km), Mag is +24.25, and PhaseFactor
    is given by:
    PhaseFactor = SIN(55.38) - 55.38*(Pi/180)*COS(55.38) = .2738
    24.25 = StdMag - 15 + 2.5*14.901
    StdMag = 2.00
    Now the Saturn IV-B (the Apollo 12 3rd stage was proposed as a
    candidate for 2000 SG344) is basically a cylinder 6.6 meters in
    diameter and 17.8 meters long.  Even under the most favorable
    geometry (cylinder axis perpendicular to line-of-sight), I don't
    believe it can achieve a standard magnitude of +2.0.  Magnitude
    +2.7 is about the most I'd expect, which is a factor of 1.9
    too dim.
    If I use the predicted coordinates and brightness for 11/24/2000
    from the table, the standard magnitude comes out to about +1.8 --
    i.e. brighter still.  So I'd say that despite the suspicious
    ecliptic orbit with nearly the same orbital period as the earth,
    we're probably not talking about a manmade object.
    Some factors which would keep the possibility alive:
    1.  uncertainty in the measured brightness of 2000 SG344
    2.  Saturn IV-B reflectivity higher than today's rocket bodies
    3.  significant error in the assumption that a 2.4-meter diameter,
        7.4-meter long Cosmos booster has a full-phase visual
        magnitude of no brighter than ~4.75 at a range of 1000 km.
    This last point is a sticky issue with me.  The typical Molczan
    standard magnitude for a 7.4 x 2.4 meter cylinder is listed as
    +5.5, where standard magnitude is defined as 50% illumination at
    a range of 1000 km.  The "50% illumination" part is the key.  Can
    someone on the list (Mike McCants or Ted Molczan, preferably)
    walk through how they convert between physical dimensions and
    this standard magnitude?
    My hope is that the magnitude is actually first computed for
    100% illumination, and then 1.24 magnitudes is added (a factor
    of 1/pi in brightness) to convert it to the 50% value.  Running
    with this assumption, a 17.8-meter x 6.60-meter rocket has 6.61
    times the projected area of the 7.4 x 2.4 meter rocket, which
    means it should be 2.05 magnitudes brighter, assuming the same
    range, phase and reflectivity.  +4.75 - 2.05 = magnitude +2.7,
    the figure used above.
    Now if instead the standard magnitude was computed by taking
    the 100% illumination magnitude and only adding +0.75 mags
    (a factor of 1/2 in brightness) to get the 50% illumination
    value, then the true standard magnitude of the 7.4m x 2.4m
    rocket should be +5.99 (5.5 - 0.75 + 1.24).  This in turn
    would mean that the Saturn rocket standard magnitude would
    dim to 3.94.  This is almost a factor of 6 dimmer than the
    derived standard magnitude of 2000 SG344.
    I look forward to comments from Mike, Ted or anyone else that
    feels they have a handle on these standard magnitudes.
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