Estimating standard visual magnitude from RCS

From: Matson, Robert (
Date: Mon May 21 2001 - 14:44:25 PDT

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    Hi Jonathan and list,
    Jonathan was inquiring about how to approximate a satellite's
    visual magnitude when only its RCS is given.  As others have
    eluded, you can't really.  RCS is very sensitive to the
    geometry of the object in question.  For example, if a tiny
    portion of the satellite has three mutually perpendicular
    surfaces forming a concave cavity (i.e. a corner reflector),
    you will have a deceptively huge RCS.
    Fortunately, most orbiting objects behave better than this,
    such that increasing RCS tracks fairly well with increasing
    satellite projected area.  Around a decade ago, I wrote a
    program to compare the correlation between RCS and standard
    magnitude for several thousand objects for which both values
    were known.  I basically made a scatter plot of RCS vs.
    standard magnitude in order to find the slope of the best
    fit line.  (I think I also eliminated the largest RCS and
    brightest satellites from the analysis, reasoning that my
    goal was to estimate visual magnitudes for the thousands
    of objects that have reported RCS values, but unknown
    standard magnitude.)
    Turned out an object with an RCS of 1 m^2 had an average
    standard magnitude of about +8.  I've long since lost
    track of the data, so don't know what the 1-sigma error
    bars were on that value.  In any case, I modeled SkyMap
    on this 1 m^2 = +8 mag assumption.  So the conversion
    would be:
    Std. mag = 8 - 2.5*LOG(RCS)
    where RCS is in square meters.
    I've just downloaded Mike McCants' latest RCS.ZIP file, so
    at some point I'll try the analysis again to see what
    answer I get.
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