Satellite visual magnitude equations

From: Matson, Robert (ROBERT.D.MATSON@saic.com)
Date: Wed Apr 25 2001 - 14:46:18 PDT

  • Next message: Alan Pickup: "Decay watch: 2001 Apr 25"

    Bjoern wrote:
    
    > > If the satellite is spherical, the illuminated fraction of the total 
    > > visible disk is (1 + cos v)/2
    > 
    Jonathan Wojack replied:
    
    > Yes, I was close to deriving that formula...
    > To solve for the angle (if you know the illumination fraction, and want
    > to find the angle), using the formula:
    > Theta = cos ^ -1 ((2 Frac) - 1)
    
    Alas, these formulae have no practical application to
    the computation of satellite brightness.  "Illumination
    fraction" is a term that should never be applied to
    visual satellite observing -- it's irrelevant,
    unobservable, and not directly useful in predicting
    satellite visual magnitude.
    
    > P.S.:  How well do these formulas work for non-spherical objects?
    
    They don't even work for spherical ones -- that's the
    whole point.  Many people have been erroneously applying
    illumination fraction to satellite observing (and the
    prediction of satellite brightness), and it has no
    place there.
    
    Jonathan's other question had to do with how another
    list member computed a predicted magnitude of 6.5
    from a standard magnitude of 5.5 for an object at
    1600-km range and ~90-degree phase.  This case is
    straightforward (due to the 90-degree phase) since
    this is the phase at which standard magnitude is
    defined.  So it's a simple case of adjusting the
    magnitude for the different range.
    
    Standard magnitude is defined for 1000 km range;
    brightness is inversely proportional to range
    squared.  So at 1600 km, the satellite is dimmer
    by a factor of (1600/1000)^2 or 2.56 (which is
    close to one visual magnitude).  The exact value
    would be given by:
    
    Mag = Std. mag + 2.5*LOG((1600/1000)^2)   -or-
    Mag = Std. mag + 5*LOG(1600/1000)
        = 5.5 + 1.02 = 6.52
    
    A simplified general equation for object at 90-degree
    phase angle is:
    
    Mag = Std. mag - 15 + 5*LOG(Range)
    
    where Range is in km.  --Rob
    
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