Re: Satellite visual magnitude equations

From: Jonathan T Wojack (tlj18@juno.com)
Date: Fri Apr 27 2001 - 18:56:35 PDT

  • Next message: Jonathan T Wojack: "Re: Morning Pass Of ISS"

    > Yes -- the equations are specific to the example you
    > gave:  an object at 90-degree phase.
    > >  
    > > It must be possible for an object to be at 1600km distance in more 
    > than
    > > one spot.  Or perhaps the phase angle is irrelevant?
    > 
    > Of course phase is VERY important.  I deliberately
    > excluded the phase-dependence from the equation
    > because your example did not require it.  
    
    Actually, my question had absolutely nothing to do with the Mars Odyssey
    Rocket.  I am just trying to learn about the math involved in satellites.
     This summer, I hope to become an expert on the material covered in "The
    Fundamentals of Astrodynamics".
    
    >I posted
    > a full equation w/phase-dependence on Seesat many
    > months ago, but I'll include one here:
    > 
    > Mag = Std. Mag - 15 + 5*LOG(Range) -
    >       2.5*LOG(SIN(B) + (pi-B)*COS(B))
    > 
    > where Range is in km, and B is in radians and measures
    > the angle from the sun to the satellite to the observer.
    > At full phase, B is 0; at new phase, B is pi (i.e.
    > satellite transiting the sun).
    
    Don't worry, I know more than enough about radians.
     
    > I want to emphasize that this is the correct equation for
    > a spherical satellite with a perfectly Lambertian surface.
    > Of course, few satellites are spherical, and none have
    > perfectly Lambertian surfaces.  Still, it is a good
    > approximation when you don't know the orientation of
    > a satellite. 
    
    Should it be accurate to within a magnitude?
    
    Will this formula work for basically all satellites, including
    asymmetrical satellites such as the ISS?
    
    > >  
    > Perhaps a better approach would be to assume that all
    > satellites are cylinders (since most of the brightest
    > satellites are rocket bodies) and compute the mean
    > reflected radiance (as a function of B) for all
    > orientations.  
    
    The logical approach would be to throughly observe rocket bodies
    (near-perfect cylindrical objects) and create an equation(s) that would
    precisely mirror observations.  Similar to curve-fitting.
    
    >Question for the list -- what do most
    > rocket bodies look like when viewing their ends?
    
    I am very certain that viewing the ends of rocket bodies results in a
    lower brightness than when viewing the "main body (for lack of a better
    term) ".  I believe some one has said on this list that when a rocket
    body is tumbling, the dimmest part of the light curve happens when
    lookking at the ends of the cylinder.
    
    Thanks again!
    
    ------------------------------
    Jonathan T. Wojack                 tlj18@juno.com
    39.706d N   75.683d W            
    
    4 hours behind UT (-4)
    
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