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
Solving,
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.
Cheers,
Rob
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