RE: 2000 SG344: asteroid or Saturn rocket?

From: Matson, Robert (
Date: Tue Nov 14 2000 - 14:46:39 PST

  • Next message: Tony Beresford: "Observations November 14"

    Thanks to Mike Waterman for posting his report of the
    observation of the Apollo 12 3rd stage (69099B, #04226)
    back in 1969.  You must keep some excellent records!
    > I observed the Apollo 12 3rd stage (69099B = #04226) and its fuel 
    > dump on 19691114 from 2042 to 2056UT.
    > ... At 2043 the rocket was flashing max mag 8, period 2.5s.
    > The range was 29000 km.  I do not have RA/dec at 2043, but it
    > would only move a few degrees until 2057 when RA=20:09
    > Dec=8.6 (epoch 1950).
    > Site = COSPAR 2428 = 51.3136N -0.7417E.
    (Not that it's important to this analysis, but is that
    .7417 east, or .7417 west?  Negative longitudes usually
    imply western longitudes.)
    > The sun would then be about RA=1522 Dec=-19, about 76 degrees away.
    > Using Robert Matson's formula, Phase factor = 0.65
    Yes -- I concur.
    > Standard mag = 8 + 15 - 2.5*log10(29000^2/0.65) = 8+15-22.8 = 0.2 .
    Also correct.  Mike McCants has informed me that the
    7.4 x 2.4m Cosmos boosters are in fact quite dark, so
    it's possible that the Saturn IV-B is many times
    brighter.  One can estimate the theoretical maximum
    brightness for a white lambertian cylinder with the
    dimensions of the Saturn IV-B, in order to put an
    upper limit on the brightness.
    The exoatmospheric solar constant is 1353 W/m^2, though
    this figure varies some with time of year due to the
    earth's elliptical orbit.  Only about 13% of this energy
    is in the spectral range of 5000-6000 angstroms (the peak
    region of the visual response curve).  The inband energy
    percentage increases a bit when you include the full
    4000-7000 angstrom visual band.
    When you convolve the solar spectrum with the photopic
    visual response curve, you get about 384 watts/m^2.  A
    magnitude 0 object corresponds to an illuminance of
    ~2.65 x 10^-6 lumens per meter-squared, and there are
    350 lumens/watt for the solar spectrum across the visual
    band.  So:
    (2.65e-6 lm/m^2) / (350 lm/W) = 7.57e-9 W/m^2
    for a zero magnitude object (e.g. Vega).  Unfortunately,
    I have found conflicting references for the conversion
    factor between watts/meter^2, lumens, and visual magnitude,
    so there is some uncertainty in the above value.  For
    example, I found one reference which gave an exoatmospheric
    illuminance of 2.089 x 10^-6 for a magnitude-0 object, a
    difference of about 0.26 magnitudes from the figure above. 
    But let's turn to the booster.  Viewed broadside, it has
    a projected area of 117.5 square-meters, so at full-phase
    it collects (384 W/m^2)*(117.5 m^2) = 45100 watts.  I won't
    get into the calculus here, but a lambertian reflecting
    cylinder has pi/4 times the brightness of a lambertian
    reflecting plane with the same projected area.  The
    intensity of the booster is:
    (pi/4)*45100 watts / (pi steradians) = 11275 W/sr.  At a
    range of 1000 km, this results in an irradiance of
    1.13e-8 W/m^2, which corresponds to a visual magnitude
    of -0.43 using the above conversion formula.  The
    "standard magnitude" for the booster would be 1.24
    magnitudes dimmer (a factor of pi in brightness) or
    +0.81.  This is ~0.6 magnitudes dimmer than what Mike
    Waterman measured in 1969.  Considering the many possible
    error sources, this is pretty good agreement.
    So, I must agree with Mike McCants' remarks - the Cosmos
    rocket bodies are VERY dark, and thus a poor choice for
    comparison with the Saturn IV-B.  Indeed, even if the
    standard magnitude of these Cosmos rockets is brightened
    from +5.5 to 5.0 (to correct for the factor of pi vs.
    factor of two conversion from 100% phase), their albedo
    works out to about 14%.
    So, allowing for some decrease in albedo after 30 years
    in a space environment, 69099B and 2000 SG344 may indeed
    be one and the same.  To bring a 0.81 standard magnitude
    down to the observed +2 requires a reflectivity of about
    33%; to get it to +1.8 implies a reflectivity of 40%.
    Include some uncertainty in the CCD measurement of the
    magnitude of 2000 SG344, and the derived reflectivity
    could take on a wide range of reasonable values.
    So alas, this analysis shows that the Saturn rocket can
    neither be confirmed or ruled-out as the identity of
    2000 SG344.  I say hit it with radar -- the magnitude
    and variation in signal return over time should be able
    to differentiate a perfect cylinder from a rock.
    Final words from Mike Waterman:
    > Footnote: shiny spheres have no phase factor.
    >   Shiny cylinders will have some phase factor, but I believe
    >   the effect will be less than the formula above.
    Specular spheres indeed have no phase factor.  But shiny
    spheres and shiny cylinders are always dimmer than their
    lambertian counterparts of the same reflectivity.
    Unsubscribe from SeeSat-L by sending a message with 'unsubscribe'
    in the SUBJECT to

    This archive was generated by hypermail 2b29 : Tue Nov 14 2000 - 14:50:18 PST